CN116560220B

CN116560220B - Artificial pancreas self-adaptive model prediction control system with variable priority

Info

Publication number: CN116560220B
Application number: CN202211188780.8A
Authority: CN
Inventors: 李鸿儒; 李鹏程; 赵宇航; 于霞; 周健; 陆静毅; 马晓静
Original assignee: Shanghai Sixth Peoples Hospital
Current assignee: Shanghai Sixth Peoples Hospital
Priority date: 2022-09-27
Filing date: 2022-09-27
Publication date: 2024-03-01
Anticipated expiration: 2042-09-27
Also published as: CN116560220A

Abstract

The invention discloses a variable-priority artificial pancreas self-adaptive model prediction control system, which can solve the problem of the change of the priority sequence of a plurality of targets according to different blood sugar change conditions of patients by adopting a variable-priority self-adaptive MPC controller, and the priority sequence is not required to be embodied by designing weights for each objective function. According to the artificial pancreas self-adaptive model prediction control system with the variable priority, target priority rules when blood sugar fluctuation is in different conditions are designed, feasibility and stability of a controller are proved under the environment of target change, meanwhile, the designed controller is simulated by adopting a UVa/Padova simulator, performance comparison is carried out on the controller and a GPC controller, effects of the method in the aspects of controlling target convergence effect and controlling blood sugar fluctuation are greatly improved, and the proposed controller is proved to be very advantageous for blood sugar control.

Description

Artificial pancreas self-adaptive model prediction control system with variable priority

Technical Field

The invention relates to the technical field of artificial pancreas model prediction, in particular to an artificial pancreas self-adaptive model prediction control system with variable priority.

Background

Diabetes is a chronic disease that is manifested by abnormally high blood glucose levels due to impaired insulin action and/or insulin secretion. Diabetes is associated with a variety of complications, and persistent hyperglycemia can damage micro, and macro vessels, leading to an increased risk of micro and macro vessel complications. At the same time, diabetes is also an important risk factor affecting various clinical infections.

Although insulin replacement therapy significantly increases the life span of diabetics, it does not cure diabetes. If insulin replacement is inadequate, or increased insulin demand due to stress and disease is not met, metabolic breakdown may lead to fatal ketoacidosis. Over-treatment with insulin may lead to severe impairment of cognitive function and hypoglycemic episodes, as well as death (bedridden death syndrome). It has long been an attractive goal to calculate the proper insulin injection and achieve automatic infusion of insulin in such a way that it can accommodate different moments and daily insulin requirements while reducing the burden of self-care. And more researches and clinical application show that the artificial pancreas system can calculate the insulin infusion in real time through a reasonably designed control algorithm, so that the refined individual management of blood sugar is realized. This system consists of the following three parts: the continuous glucose monitoring system can evaluate the blood sugar level of interstitial fluid in real time; the self-adaptive control algorithm automatically and continuously adjusts the insulin infusion dose according to the blood sugar condition detected by the sensor; an "insulin pump" delivers insulin to a user through a subcutaneous cannula. The APs overcomes the defect of detecting the blood sugar concentration by traditional fingertip blood sampling, can monitor the blood sugar level in a patient in real time all the day, and automatically infuse the optimal insulin amount and other hormones for stabilizing the blood sugar concentration in time. Therefore, it is currently the most successful and effective means of treating diabetes.

The controller algorithm is the core of the closed-loop control method of the artificial pancreas system. The control algorithm of the existing artificial pancreas system mostly adopts the following modes: proportional Integral Derivative (PID) control method, fuzzy logic control, model Predictive Control (MPC), generalized Predictive Control (GPC), reinforcement learning, etc. Among these strategies, MPC offers great advantages due to several features: the predictive nature of MPC makes it possible to predict the state change of blood glucose fluctuations and thus suitable for calculating insulin infusion; through corresponding mathematical prediction models, the MPC can resist disturbance, including meal digestion, insulin absorption delay, movement and the like; the MPC can solve the dead time compensation problem common in the problem of glucose concentration; the MPC can easily handle constraints on system inputs and outputs, etc. GPC can update the model in real time according to the change of the patient state on the basis of MPC, thus improving the self-adaptive capacity of the controller.

APs are successful in treating diabetes because they can calculate the appropriate insulin infusion in real time based on blood glucose conditions without human intervention. And whether the output insulin value of the controller is appropriate is directly related to the patient's life safety. When the injected insulin dose is too large, or the food intake is reduced, it may cause hypoglycemia in patients with type I diabetes, and even death of the patient. If the injected insulin dose is too small, the insulin level in the patient is insufficient to regulate the blood glucose concentration in the postprandial body, which in turn may lead to hyperglycemia in the patient. For patient safety, the infusion dose of insulin is usually set to a range that is often contradictory, both to avoid overdosing the patient's body, and to ensure that the patient's blood glucose follows the control objective. And in meeting the above requirements, it is also expected that the smaller the dose of insulin injected by the patient, the better.

This is a typical constrained multi-objective optimization problem. A common approach is to design a scalar objective function, i.e. a weighted sum of individual objective functions, whose weights reflect the relative priorities of the multiple objectives during the solution. However, selecting an appropriate set of weights is a difficult task because decreasing the weight on one target and increasing the weight on another target does not necessarily produce a proportional response in the face of constraints, and the significance of the weights is difficult to interpret. For MPC controllers, while weighted multi-objective model predictive control (MoMPC) is a widely used method for handling multiple objective priority control, the control objectives do not truly reflect the performance requirements of a constrained system when they conflict with each other, especially in the case of complex models.

Based on the above problems, kerrigan and Maciejowski have designed a generic framework for MoMPC designs with different priority targets using dictionary optimization methods, where the MoMPC problem is represented by a series of single-target MPC problems in target order of priority. It calculates optimal control measures by using explicit target priorities and predictive models, and takes constraints into account in the controller design process, making dictionary-type moscs one of the most effective techniques for flexibly solving the multi-target control problem of constrained systems. Another advantage of the dictionary moscs is that the priorities of the different optimization objectives can be explicitly considered without the need for design weights and without the need to calculate Pareto optimal sets each time.

For patient glycemic control, control goals are often contradictory and priority may change over time during treatment. If the priorities of multiple targets suddenly change, the weights must be properly selected for the previous controllers to ensure the solving conditions for the optimization problem, and it is not easy, if not impossible, to adjust the weights of the running MoMPC controllers on-line. Therefore, there is a need to further investigate a mosc with variable target priorities that satisfies constraints.

For this reason, the following two problems need to be considered:

1. the recursive feasibility and stability of available moscs with constant priority will be lost due to the changing terminal conditions, and how to guarantee the stability of the system in a real-time environment becomes a critical issue in a variable priority environment;

2. for newly added target priority rules, a new dictionary-type MoMPC controller needs to be reset to optimize a plurality of targets, so that when the priority changes, the controller still has feasibility and can converge to an optimal steady-state value.

Disclosure of Invention

(one) solving the technical problems

Aiming at the defects of the prior art, the invention provides an artificial pancreas self-adaptive model prediction control system with variable priority, and the problem that the priority sequence of a plurality of targets changes according to different blood sugar change conditions of patients can be solved by providing the self-adaptive MPC controller with variable priority, and the priority sequence is embodied without designing weights for each objective function. Meanwhile, a target priority rule when the blood sugar fluctuation is in different conditions is designed, and the feasibility and the stability of the controller under the environment of the target change are proved.

(II) technical scheme

In order to achieve the above purpose, the invention is realized by the following technical scheme: a variable priority artificial pancreas adaptive model predictive control system, which is a variable priority adaptive MPC controller for controlling blood glucose of a patient, the control method of the variable priority adaptive MPC controller specifically comprising the following steps:

s1, inputting initial conditions, setting a target function and priority change logic, and enabling k=0;

s2, calculating a change condition of the priority p according to the value of the observer y (k) at time k, and changing the calculation level of the objective function according to the change condition of the priority when p is changed;

s3, calculating insulin constraint u at k moment _min And u _max ；

S4, measuring a k moment state x (k);

s5, u is _min And u _max As a constraint, calculate u _p(l) (x (k)) optimization problem:

s6, determining the dictionary optimal solution of the whole problem through the last layer of optimization problem, namely

And S7, returning to the step S2 when k=k+1, and recalculating.

Preferably, u is calculated in the step S5 _p(l) (x (k)) comprising the following steps:

T1solving the optimization problem of the first-level p (1) of the calculation priority

T2, willAs an optimization problem of constraint substitution priority level two stage p (2), calculate

T3, willAnd->Calculating +.>

Preferably, in step S1, the modeling of blood glucose is first modeling an amax time-series model using weighted RLS fitting, and the amax model is more effectively converted into a state space form through a stability criterion, and the conversion result from the time-series model to the state space is as follows:

x(k)＝Ax(k-1)+Bu(k-1)+Ke(k)

y(k)＝Cx(k-1)+e(k)

wherein k is equal to or greater than 0 and is control time, x is E R ^N And u.epsilon.R ^N System state and control inputs, respectively, N is the predictive control time domain.

Preferably, in said step S2, the different objective functions are represented by L (x, u), which generally conflict with each other and have different orders of priority, defined as p, according to which the arrangement of L (x, u) is represented as L _p ＝{L _p(1) ，...，L _p(l) The sum of objective functions, i.e., L, is },1 _p(1) Is the most important target in optimizing the calculation of the controller, and L _p(l) Is the least important target of the controller, the jth objective function L _p(j) (x, u) corresponding dictionary MPC level total objective function J _p(j) The definition is as follows:

where u= { u (k|k),..u (k+n-1|k) } is a predictive control sequence on the predictive control time domain N;

then according to J _p The priorities of (x (k), u) propose a new dictionary mosc optimization objective function, and at time k, the finite time domain dictionary optimal control problem is defined under the condition that the priority is p and the state is x (k) =x, and the objective function of each layer is as follows:

wherein,is the i-th layer objective function J _p(i) (x, u) optimal value.

Preferably, in the controlling system for blood sugar in step S3, the system is constrained by the control input at each moment by default, and then the constraint condition of the control input is defined; u default set minimum value u _min And maximum value u _max The method comprises the steps of carrying out a first treatment on the surface of the When the control time k is relatively short, the control does not reach equilibrium stability, and when the control time k is long, the default system is stable, where x (k+n|k) =x (k+n-1|k), and all are at the stable point,

so, according to the above description, when k→k+n, a constraint set U of allowable inputs is defined as follows:

U＝{u∈[u _min ，u _max ]|x(k|k)＝x}

when k→infinity, a constraint set U for allowable inputs is defined as follows:

wherein Ω is the equilibrium set of the controller, at blood glucoseIn control, default balance point d _p Is (r) ₀ ，u ₀ )，r ₀ U is the average standard target blood sugar value for different people ₀ Assuming a number approaching 0 and present, the equilibrium point d _p Is attributed to the omega collection.

Preferably, in the step S6, when the state x (k) is corresponding to the time k, the dictionary optimal solution of the optimization problem, that is, the optimization result of the last layer, is obtained

Setting the output u (k) of the controller as the optimal solution of the last layer according to the scrolling time domain control principle of the MPCIs the first element of (a), i.e

To facilitate later demonstration of feasibility and stability, we next derive a closed-loop system from the controller description above, noting that: for the sake of demonstration here, the disturbance e (k) is not considered by default in deriving the closed-loop system.

Definition of DeltaU _k As a sequence of future control input increments,

preferably, it is assumed that the above-mentioned optimization problem has a solutionThe closed-loop control increment obtained according to the predictive control principle is

Because of the numerical solution optimization problem, the specific analytical expression of Δu (k) cannot be solved to obtain 1, but from the functional dependency of the optimization problem, it is known that:

(1) Δu (k) is a function of x (k), N, k;

(2) This functional relationship is nonlinear due to the presence of time domain constraints;

thereby writing out the model predictive control closed loop system as

Preferably, the primary goal is to bring the observer y of the controller closer to the ideal control target r, while at the same time, as an important factor affecting the physical safety of the patient, the output of the controller, i.e. the amounts u and Δu of injected insulin, should be within a limited range and the two magnitudes should be as small as possible while guaranteeing the risk of blood glucose at the time of solving, so the following three-layer objective function is designed for different patient situations, and the priority of the objective will change, using the dictionary MPC for the layer-by-layer solving, as follows:

(III) beneficial effects

The invention provides an artificial pancreas self-adaptive model predictive control system with variable priority. Compared with the prior art, the method has the following beneficial effects: according to the artificial pancreas adaptive model prediction control system with the variable priority, the problem that the priority sequence of a plurality of targets changes according to different blood sugar change conditions of a patient can be solved by adopting the adaptive MPC controller with the variable priority, and the priority sequence is embodied without designing weights for each objective function. Meanwhile, a target priority rule when blood sugar fluctuation is in different conditions is designed, feasibility and stability of the controller are proved under the environment that the target is changed, meanwhile, the designed controller is simulated by adopting a UVa/Padova simulator, performance is compared with a GPC (program control unit) controller result, the effect of the method in the aspects of controlling target convergence effect and controlling blood sugar fluctuation is greatly improved, and the proposed controller is proved to be extremely advantageous for blood sugar control.

Drawings

FIG. 1 is a flow chart of an adaptive MPC controller based on variable priority in accordance with the present invention;

FIG. 2 is a schematic diagram of the control results of CPMPC and GPC controllers on young adult No. 1 according to the embodiment of the present invention;

FIG. 3 is a schematic diagram of the CPMPC and GPC controllers control result for adult No. 1 according to embodiments of the present invention;

FIG. 4 is a schematic diagram of the control results of CPMPC and GPC controllers on children No. 1 according to embodiments of the present invention.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

Referring to fig. 1-4, the embodiment of the present invention provides a technical solution: a variable priority artificial pancreas adaptive model predictive control system, which is a variable priority adaptive MPC controller for controlling blood glucose of a patient, the control method of the variable priority adaptive MPC controller specifically comprising the following steps:

s3, calculating kCarved insulin constraint u _min And u _max ；

S4, measuring a k moment state x (k);

s5, u is _min And u _max As a constraint, calculate u _p(l) (x (k)) optimization problem, comprising in particular the following steps:

t1, calculating the optimization problem of the priority level p (1), and solving

T3, willAnd->Calculating +.>

And S7, returning to the step S2 when k=k+1, and recalculating.

Although dictionary multi-objective MPC may better display hierarchical relationships of priorities, the priorities of blood glucose optimization objectives may vary in different states of patient blood glucose regardless of APs. To this end, the present invention proposes a variable priority adaptive MPC controller that is safe for patient glycemic control.

The blood glucose is first modeled as an ARMAX time series model using a weighted RLS fit. The ARMAX model can be more efficiently converted into a state space form by stability criteria. Conversion result from time series model to state space

In a control system for blood glucose, the system is constrained by control inputs at each moment by default, and control input constraints are defined next. u default set minimum value u _min And maximum value u _max . When the control time k is relatively short, the control does not reach equilibrium stability, and when the control time k is long, we default the system to be stable, where x (k+n|k) =x (k+n-1|k), and all are at the stable point.

So when k→k+N, a constraint set U is defined that allows for input according to the above explanation

U＝{u∈[u _min ，u _max ]|x(k|k)＝x} (1.2)

When k → infinity, a constraint set U for allowing input is defined

Where Ω is the balanced set of controllers. In glycemic control, default equilibrium point d _p Is (r) ₀ ，u ₀ )，r ₀ U is the average standard target blood sugar value for different people ₀ Assume a number approaching 0 and present. Balance point d _p Is of the omega set.

Then consider the multi-objective problem. Different objective functions we use L (x, u) to represent. These objective functions L (x, u) generally conflict with each other and have different orders of priority, defined as p. According to the priority order p, LThe arrangement of (x, u) is denoted as L _p ＝{L _p(1) ，...，L _p(l) And 1 is the total number of objective functions. That is, L _p(1) Is the most important target in optimizing the calculation of the controller, and L _p(l) Is the least important goal of the controller. Jth objective function L _p(j) (x, u) corresponding dictionary MPC level total objective function J _p(j) The definition is as follows:

where u= { u (k|k),..u (k+n-1|k) } is a predictive control sequence on the predictive control time domain N.

Then, we according to J _p The order of preference of (x (k), u) suggests a new dictionary mosc optimization objective function. At time k, the optimal control problem of the finite time domain dictionary is defined under the condition that the priority is p and the state is x (k) =x, and the objective function of each layer

Wherein,is the i-th layer objective function J _p(i) (x, u) optimal value.

Correspondingly, when the state x (k) is corresponding to the moment of time k, the dictionary optimal solution of the optimization problem (1.1) is obtained, namely the optimal result of the last layer

To facilitate later demonstration of feasibility and stability, we next derive a closed-loop system from the controller description above in this subsection. Note that: for the sake of demonstration here, the disturbance e (k) is not considered by default in deriving the closed-loop system.

Definition of DeltaU _k As a sequence of future control input increments,

assuming that the above-mentioned optimization problem has a solutionThe closed-loop control increment obtained according to the predictive control principle is

Because of the numerical solution optimization problem, the specific analytical expression of Δu (k) cannot be obtained by solving. However, from the functional dependency of the optimization problem, it can be known that:

(1) Δu (k) is a function of x (k), N, k;

(2) This functional relationship is nonlinear due to the presence of time domain constraints.

Thus, the model predictive control closed-loop system can be written as

The primary goal is to bring the observer y of the controller closer to the ideal control target r. At the same time, as an important factor affecting the physical safety of the patient, the output of the controller, i.e. the amounts u and Δu of insulin injected, should be within a limited range and the two magnitudes should be as small as possible while guaranteeing a blood glucose risk at the time of solving. Therefore, aiming at different patient conditions, the following three layers of objective functions are designed, the priority of the objective can be changed, and the dictionary MPC is used for carrying out layer-by-layer solution.

In this study, three different priority changing situations are presented for different situations of glycemic control:

1. when the blood sugar is abnormal, the approach of y to the reference target r is the most preferable, except that insulin injection is not needed and calculation is not needed, so L ₁ ＞L ₂ ＞L ₃ 。

2. When the blood sugar is in a normal condition and the blood sugar fluctuation is in a small state, the arrow diagram of the blood sugar fluctuation is equal to or less than +.or equal to +.about. ∈, and the change of insulin injection is preferential. At this time set L ₁ ＞L ₃ ＞L ₂ 。

3. When the blood sugar is normal but the fluctuation is relatively large, namely the blood sugar fluctuation arrow is shown as > +.or < +. ₂ ＞L ₁ ＞L ₃ 。

Next, a constraint u on the insulin injection amount u is given _min And u _max . Obviously, u is when the patient is euglycemic and stable _min =0. For u _max We calculate using literature methods. To calculate reasonable u _max The value requires information about how much BGC decreases after a particular patient takes a unit of insulin, also known as Insulin Sensitivity Factor (ISF). Insulin Sensitivity (IS) IS directly related to ISF. The more sensitive to insulin, the more glucose one unit of insulin decreases. Without any clinical measurements, 1500 and 1800 rules are typically accepted to calculate ISF. These rules apply to most T1D patients. However, as with many of the characteristics of the glycemic dynamics model, ISF is also subject-specific and time-varying. ISF can be used to calculate u in (1.2) and (1.3) _max . It can be expressed as a function of the Total Daily Dose (TDD)

ISF＝1800/TDD (1.14)

TDD can be approximated by the patient's Body Weight (BW) and Insulin Sensitivity Constant (ISC)

TDD＝ISC(k)×BW (1.15)

Then Insulin Sensitivity (IS) IS subject-specific and time-varying. Therefore, we define ISC parameters as a function of glucose prediction and reference trajectories

Where r (k) is the control target reference trajectory.

The accumulated insulin amount IOB in the human body can be predicted as

Wherein the IOB _crv Is a column vector with each element ranging from 0 to 1]Obtained from one of seven IOB curves, and j=1, 2. Since the control system uses only basal insulin infusion, IOB in (1.17) is in U/h

Where st is the sampling time in minutes, where st=5. The term 60/st will u _max The unit of (2) is kept as U/h. In (1.2) and (1.3), u _max The usage (1.18) is updated with each new measurement. In addition to injecting insulin, future values of insulin (not provided to the system) are also limited. Future IOBs are calculated by assuming future values of insulin are provided to the system. The constraints of the controller objective function are adaptively updated at each sampling.

Simulation experiment and performance analysis

To verify the effectiveness of the variable priority based MPC model predictive control, 30 virtual patients in a UVA/Padova type 1 diabetes metabolic simulator were used for verification. Including 10 adults, 10 teenagers and 10 children, and to set the same diet plan for each patient of the same group to obtain control data of one week of three patients of adults, teenagers and children, including blood glucose data, insulin data and the like. First, a graph of control results for adult No. 1, young and children is given. See fig. 2-4 below. The first part of each graph is a graph comparing blood sugar values controlled by the patient by the two controllers, and the second part is an insulin amount infused by the two controllers to the patient at different moments, so that compared with GPC, the CPMPC controller provided by the invention can effectively control blood sugar data in a normal blood sugar interval (70-180 mg/dL), and has good control effect on patients of different ages.

From fig. 2-4, we analyze that for children like child 1, the blood glucose is the greatest challenge for the controller as the insulin changes drastically. It can also be seen from the specific data in appendix b.1 that cppc controller control for child No. 1 sacrifices part of the volatility, but this allows the controller to better keep the patient's blood glucose in the normal range, keeping the blood glucose in the normal range and allowing the controller to consider the highest priority. So like the patient with the wave sensitivity of the child 1, CPMPC makes the blood sugar better follow r (k), thus making the blood sugar of the patient safer.

For patients with low fluctuation sensitivity like adult 1, CPMPC is more conservative for the calculated insulin amount, not only can blood glucose be quickly reduced to normal blood glucose, but also the patient has small fluctuation of blood glucose, and following r (k), excessive insulin cannot be injected to quickly reduce blood glucose to low blood glucose.

Table 1 shows the control of different age groups using different controllers for one week, including time within normal range (TIR), time to hyperglycemia (TAR), time to hypoglycemia (TBR) index values, and volatility coefficient CV and controller-controlled blood glucose values y (k) for each patient control. As can be seen from Table 1, for young children, the fluctuation CV index was increased by 0.04, and for TIR, the average difference between the controlled blood glucose level y (k) and the control target r (k) was also increased significantly. For pediatric patients, as discussed in fig. 4, the sensitivity to fluctuations is high, and cpmppc can better control blood glucose to normal range values, bringing y (k) closer to the control target r (k). For adult patients, the fluctuation sensitivity is low, and the controller can better maintain the blood sugar within the normal value range under the condition that CV and average errors are basically maintained stable. The average insulin usage was also significantly reduced compared to GPC for all populations. The treatment safety of the patient can be effectively improved by reducing the use of insulin, and the method is greatly beneficial to the patient. Based on the data comparison, and the analysis of fig. 2-4, CPMPC is a great advantage in the treatment of and safety of blood glucose control in patients, regardless of age.

TABLE 1 control of different age groups using different controllers for one week

Considering safety issues in patient control, for time-varying blood glucose models, a variable priority adaptive MPC controller approach applied in AP systems is proposed. By considering safety factors such as real-time blood sugar and control targets and insulin amount, a dictionary type MPC controller method is designed, and priority rules related to blood sugar control are set and given. And demonstrates the feasibility and stability of the controller approach for cases where multiple target priorities change. One advantage of this approach is that multiple targets with different priorities can be automatically processed without the need to calculate the entire Pareto optimal solution and select weight values with different priorities. Finally, we simulated 30 patients of different populations on a UVa/Padova simulation platform, and discussed a comparison of the results with GPC control methods, demonstrating the effectiveness and superiority of the new controller. The limitation of the research of the invention is that only a linear model is used for blood sugar prediction, a nonlinear blood sugar prediction model is further designed in the future, and the controller is further improved and optimized aiming at the nonlinear model; meanwhile, in the later study, the rules are further perfected according to clinical experience and individuation characteristics of patients, so that individuation blood sugar accurate control is realized.

Feasibility and stability of controller

1. Feasibility demonstration

The present invention proposes a variable priority adaptive MPC controller based on a dictionary MOMPC controller. In contrast to conventional MPC controllers, the dictionary MOMPC explicitly considers the priority constraints of the objective function to be minimized. If the first layer sub-problem is initially viable, the feasibility of the entire dictionary problem and the stability of the closed loop system can be ensured.

First, for a single target MPC, optimizing the feasibility of the control problem means that the feasibility of the problem at time k+1 is achieved by its feasibility at time k. In other words, the feasible solution of the controller at k+1 may be constructed by some feasible solution of the problem at k. However, the feasibility of MPC at k+1 cannot be achieved by directly using its feasibility at k, since the original multi-objective optimization control problem is translated into a single objective optimization control problem for the l-hierarchy. To solve this problem, for the feasibility of the solution, it is mainly classified into the feasibility of whether the first layer has a feasible solution that can be deduced to the l+1 layer for the same time k and the feasibility of whether the same priority and different priorities affect the feasibility of the solution at time k and the feasibility of the solution at time k+1 for different times k and k+1. Two concepts are presented herein regarding the feasibility of a variable priority MPC.

Definition one: at priority p, if the feasibility of its p (j) layer optimization solution means that its p (j+1) layer optimization solution is feasible for j, where j ε [1: l-1], then the MPC controller optimization problem (1.6) is said to have hierarchical recursive feasibility at time k.

Definition two: if the feasibility of the problem (1.6) at time k can be deduced that it is feasible at the next time k+1, the MPC controller optimization problem (1.6) has a horizontal recursive feasibility.

The optimization problem of the MPC controller is hereinafter referred to as a problem.

Hierarchical recursive feasibility is defined for one priority p at the same time, but horizontal recursive feasibility needs to prove that all priorities are viable. Furthermore, hierarchical recursive feasibility describes the simultaneous feasibility between hierarchical sub-problems, while horizontal recursive feasibility describes the existence of feasible solutions for the whole problem at adjacent times. The hierarchical recursive feasibility and the horizontal recursive feasibility together constitute the recursive feasibility of the MPC controller proposed by the present invention.

The optimization objective was first demonstrated to have hierarchical recursive feasibility, given theorem 1 below.

Theorem 1: let the blood sugar state be a constant set X _N Consider that at time k, there is a priority p and a state X (k) ∈X _N For a given prediction horizon n.gtoreq.1, when x=x (k), if constraint set U is not an empty set, then problem (1.6) has hierarchical recursive feasibility at k.

And (3) proving: consider an initial state of the controller at time k, x=x (k). It is assumed that the i-th sub-problem of the whole problem (1.6) is feasible. Is provided withIs the optimal solution of the i-layer sub-problem.

We can then get the value at j e [1: i-1]

Let Γ be the feasible solution set for the target optimization, it is evident that Ω e Γ. Consider the constraint U (1.2) x (N+k|k) ∈Γ, and (1.3) x (N+k|k) ∈Ω.

Furthermore, the following conditions are also evident

Substituting (1.20) and (1.21) into the (i+1) layer sub-problem results in constraint (1.2) (1.3) and constraint x (n+k|k) ∈Γ therein having been satisfied. Because ofIs an objective function J _i (x (k), u (k)) in the set. Combining these means +.>All constraints in the (i+1) layer sub-problem are satisfied. Thus (S)>Is a viable solution to the (i+1) th layer sub-problem at time k, i.e., the (i+1) th layer sub-problem is viable at time k. />

Finally, when k is smaller, x (N+k|k) ∈Γ is proved. When k is → infinity,it is also evident that the constraint x (n+k|k) ∈Ω is satisfied.

The optimization objective is then proved to have a horizontal recursive feasibility, and the following theorem 2 is given considering the cases of the same and different priorities, respectively.

Theorem 2: for the constraint systems (1.1) - (1.3), the problem (1.6) is unchanged from the set X in the blood glucose state _N With horizontal recursive feasibility.

And (3) proving: let the controller priority be p at time k; at time k+1, the controller priority is q. Consider first the case of priority p=q.

From algorithm 1 we can learn that

u ^* (k)＝u ^l* (k) (1.23)

Wherein u is ^l* (k) Is the optimal solution to the layer 1 sub-problem of the whole problem (1.6).

It is assumed that the first layer sub-problem (1.2) is feasible at time k. By generalization, from theorem 1, it is known that the optimization problem (1.6) is feasible at the same time k.

Let u be ^* (k) Is the optimal solution of the entire problem (1.6) at time k.

In order to find a viable solution to the problem at time k+1, the following control sequence is set up

Assuming that the model is unchanged at times k and k+1, then for k in the control range N when n=n+1 ₁ (x (k+N|k)) must be a value, soCan be solved, i.e.)>Is a viable solution for the first layer at time k+1. So according to the hierarchical recursion feasibility, the last layer at time k+1 must also have a feasible solution, i.e. there is a feasible solution at time k+1. This shows that the sequence defined by (1.25) is a viable solution to the first layer sub-problem (1.5) at time k+1. By applying theorem 1 again we have obtained that the optimization problem is feasible at time k+2, and that all later times are feasible, i.e. the whole optimization problem satisfies the horizontal recursive feasibility.

When p+.q. In this case, the priority of the control target changes at k+1. By theorem 1, at time k, any state X (k) ∈X _N Can all makeAs the optimal solution of problem (1.6) at k, form (1.24).

When k approaches infinity, the applicationFor time k+1, a control sequence u is easily constructed _q (x ⁺ (k) For a given frame) is

Wherein x is ⁺ (k) =ax (k) +bu (k) +ke (k), and due to the constraint of (1.3)

x(k+N-1|k)＝x(k+N|k) (1.27)

We can then obtain

At time k+1, u will be due to the condition of (1.27) _q (x ⁺ (k) Is applicable to the system and can be obtained

x(k+1+N-1|k+1)＝x(k+1+N|k+1) (1.29)

Therefore, the constraint in (1.3) is satisfied at time k+1 and is not empty, and according to model (1.1), u _q (x ⁺ (k) (1.5) is a feasible solution at k+1. Next, applying theorem 1, obtaining that at least one solution u exists _q(l) (x ⁺ (k) To satisfy the constraint at k+1 of the q (l) layer sub-problem in (1.6). Under this constraint, the target priority becomes q. Thus, problem (1.6) is unchanged from set X in blood glucose state _N The inner demonstrated horizontal recursive feasibility. This completes the demonstration of theorem 2 as k approaches infinity.

When the controller run time k is relatively small, there is no (1.27) formula as constraint, and we can only use the default individual value u _q As the u value when the control k+n is predictively controlled, it is assumed that it is possible.

According to the model (1.1)

x ⁺ (k+N|k)＝Ax(k+N|k)+Bu(k+N|k) (1.31)

At this time we assume u _q (k+1+N-1|k+1)) exists, and is abbreviated as u _q (k+1)

x ⁺ (k+N|k)＝Ax(k+N|k)+Bu _q (k+1) (1.32)

According to (1.1) the relationship of observer y to state x

x ⁺ (k+N|k)＝C ^-1 r(k+N|k) (1.33)

Can be calculated out

u _q (k+1)＝B ^-1 [C ^-1 r(k+N|k)-Ax(k+N|k)] (1.34)

x (k+n|k) can also be estimated continuously from the generalization of (1.33). So u _q (k+1+N-1|k+1)) is found. I.e. when k is relatively small, u _q (x ⁺ (k) With a feasible solution). The problem (1.6) proved to be horizontally recursive viable. Thus, the controller system proves to have a horizontal recursive feasibility, whether or not priorities p and q are the same, at any time k.

According to the above demonstration, the controller satisfies both the horizontal recursive feasibility and the hierarchical recursive feasibility, and the controller has feasibility.

2. Stability demonstration

First, stability issues of the controller need to be discussed at different instances of time k. When k is large, i.e., k→infinity, it is desirable that the controller gradually stabilize at the equilibrium point d _p . When k is relatively small, it is desirable that the controller can converge y (k) to the control target r (k) to ensure that the patient is not at risk while ensuring that the patient is under safety from the effects of pulsatility.

First, the control system stability when k→infinity is discussed.

The stability of the dictionary MPC is determined only by the first objective function, i.e. the most important objective function. In general, the objective function is required to be positive, which is widely used to ensure the feasibility and stability of conventional MPCs. From the three cost functions of (1.13), L ₁ ，L ₂ And L ₃ The function may guarantee its positive nature. Then for L ₁ The function, i.e. the most important objective function, isTo prove that it converges to the equilibrium point d _p 。

This is the dictionary stable value function V proposed by the present invention _p (x)

Wherein the method comprises the steps ofIs the dictionary optimal solution of problem (1.6).

At this time, it is necessary to prove V _p (x) Is positive and converges to d _p An axicon 1 is given.

Lemma 1: for constraint systems (1.1) - (1.3), for any X (k) ∈X _N ，V _p (x) Is positive and converges to d _p 。

And (3) proving: first, through J _p(1) From formulas (1.5) and (1.13), it can be seen that V _p (x) And (5) being more than or equal to 0, and ensuring the positive determination. For convergence to d _p It needs to be proved if and only if x=r ₀ V at the time of _p (x)＝0。

First of all, it is necessary to prove V _p (r ₀ )＝0。

Under the condition of k → infinity, let us let

x(k|k)＝r ₀ (1.36)

Assume thatIs V _p (x) Is the optimal solution of->And is J _p(1) Is a solution to the optimization of (3).Is the dictionary optimal solution of problem (1.6).

Next, it can be deduced that

We select one possible solution u of the first layer (1.7) _p(1) (r ₀ )

u _p(1) (r ₀ )＝{u ₀ ，...，u ₀ } (1.38)

Substituting (1.38) into (1.5) and (1.13) to obtain

J _p(1) (r ₀ ，u _p(1) (r ₀ ))＝0 (1.39)

Obviously, the objective function value of the optimal solution is less than or equal to the objective function value of the feasible solution, so

Because of V _p (x) 0 or more is established, thus can be obtained

V _p (r ₀ )＝0 (1.41)

Next, it needs to be proved that when V _p (x) When=0, x=r ₀ 。

First, let x (k|k) =x,is the dictionary optimal solution of problem (1.6).

Substituting the conditions into the objective function formula (1.5) to obtain

Since k→infinity, according to (1.3), it is available at any i ε [0: n-2]

x(k+i|k)＝x(k+N-1|k) (1.43)

And x (n|k) =r ₀ Therefore, it is

x＝x(k|k)＝x(k+N|k)＝r ₀ (1.44)

From the index 1, it is easy to know that the controller is asymptotically stable to d _p . In summary, the MPC controller provided by the invention has stability and can be gradually stabilized at d _p 。

To sum up, V _p (x) Is positive and definiteAnd converge to the balance point d _p . Also easily push out J _p(1) (x) Is also converged to d _p And is positive.

A demonstration of the stability of the closed loop system (1.12) is given below.

Theorem 3: considering constraint systems (1.1) - (1.3) with priority p, if constraint set U is non-empty, x=x (k) at initial time k=0, closed loop system (1.12) is at X _N Internally asymptotically stable optimal steady state d _p 。

And (3) proving: assume thatIs the dictionary optimal solution of the controller objective function J at time k, k+1. Is obtained by a model (1.1)

Wherein u is _p(1) (x ⁺ (k) Is the optimal solution to the first layer optimization problem (1.5). In the previous evidence, a viable solution to the first layer optimization problem at time k+1 can be obtained

It is obvious that the process is not limited to,

J _p(1) (x ⁺ (k)，u _p(1) (x ⁺ (k)))≤J _p(1) (x(k)，u _p (x ⁺ (k))) (1.47)

thus closed loop system V _p (x ⁺ (k) V) and V _p The difference of (x (k)) is

According to the model (1.1), the observer y is a linear function, and according to the reference objective rule function disclosed in the invention, Δy (k) is greater than or equal to Δy (k+n+1), i.e. for the volatility parameter

Δy(k)-Δy(k+N+1)≥0 (1.49)

So V _p (x ⁺ (k))-V _p (x (k)) is 0 or less, function V _p (x) Along the trajectory of the closed loop system. V in combination with the results of the theory 1 _p (x (k)) is the Lyapunov function of the closed loop system, and stability is demonstrated.

Another case when time k is discussed next. When k is not large, then approach the steady state r for y ₀ Less urgent, it is desirable that the controller converge y (k) to the trajectory of r (k), where stability needs to be determined.

For the problem (1.6), the output sequence at time k+1 and the control target sequences (1.50) and (1.51) can be easily calculated for the model (1.1)

/>

The above sequence is brought into an objective function (1.6), and the corresponding objective function value J is calculated _k+1

Since (1.1) is assumed to be a time-invariant system, we let r ^* (k+1+N|k)＝αr ^* (k+1+i|k)+(1-α)r ₀ Y ^* (k+1+N|k)＝Cx ^* (k+N|k) to obtain

Can be pushed to

Then according to (1.49) it is possible to obtain

From the previous evidence, it can be found that for any k.gtoreq.0, there isFrom formula (1.55)>Is monotonically decreasing and ∈>At d _p Where the minimum value is taken. Therefore, the value function of the optimization problem (1.6)>Is a Lyapunov function of a closed loop system. It can also prove that the controller has stability for the case where the time k is small, so that y (k) converges to r (k).

In summary, at any time k, the controller has stability.

And all that is not described in detail in this specification is well known to those skilled in the art.

It is noted that in the present invention, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.

Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims

1. An artificial pancreas adaptive model predictive control system with variable priority, which is characterized in that: the system is a variable-priority adaptive MPC controller for controlling safety of blood sugar of a patient, and the control method of the variable-priority adaptive MPC controller specifically comprises the following steps:

s3, calculating insulin constraint u at k moment _min And u _max ；

S4, measuring a k moment state x (k);

s5, u is _min And u _max As constraint conditions, calculate U _p(l) (x (k)) optimization problem:

S7, returning to the step S2 when k=k+1, and recalculating;

u is calculated in the step S5 _p(l) (x (k)) comprising the following steps:

T2, willCalculating +.>

T3, willAnd->As constraint substitution optimization problem of the priority level three-stage p (3), calculating

In step S1, firstly, modeling the blood glucose into an amax time series model using weighted RLS fitting, and converting the amax model into a state space form more effectively through a stability criterion, wherein the conversion result from the time series model to the state space is as follows:

x(k)＝Ax(k-1)+Bu(k-1)+Ke(k)

y(k)＝Cx(k-1)+e(k)

wherein k is equal to or greater than 0 and is control time, x is E R ^N And u.epsilon.R ^N Respectively a system state and a control input, wherein N is a prediction control time domain;

the different objective functions in the step S2 are represented by L (x, u), the objective functions L (x, u) conflict with each other and have different orders of priority, defined as p, and the arrangement of L (x, u) is represented as L according to the order of priority p _p ＝{L _p(1) ，...，L _p(l) I is the total number of objective functions, L (x, u) is expressed as L from high to low according to the priority order p _p ＝{L _p(1) ，...，L _p(l) The j-th objective function L _p(j) (x, u) corresponding dictionary MPC level total objective function J _p(j) The definition is as follows:

wherein,is the i-th layer objective function J _p(o) (x, u) optimal value.

2. The variable priority artificial pancreas adaptive model predictive control system of claim 1, wherein: in the step S3, in the control system for blood glucose, the system is constrained by the control input by default at each moment, and then constraint conditions of the control input are defined; u default set minimum value u _min And maximum value u _max The method comprises the steps of carrying out a first treatment on the surface of the When the control time k is relatively short, the control does not reach equilibrium stability, and when the control time k is long, the default system is stable, where x (k+n|k) =x (k+n-1|k), and all are at the stable point,

U＝{u∈[u _min ，u _max ]|x(k|k)＝x}

wherein Ω is the balance set of the controller, and in glycemic control, the default balance point d _p Is (r) ₀ ，u ₀ )，r ₀ U is the average standard target blood sugar value for different people ₀ Assuming a number approaching 0 and present, the equilibrium point d _p Is attributed to the omega collection.

3. The variable priority artificial pancreas adaptive model predictive control system of claim 1, wherein: in the step S6, when the state x (k) is corresponding to the time k, the dictionary optimal solution of the optimization problem, that is, the optimization result of the last layer, is obtained

The disturbance e (k) is not taken into account by default when deriving the closed loop system.

Definition of DeltaU _k As a sequence of future control input increments,

4. a variable priority artificial pancreas adaptive model predictive control system in accordance with claim 3, wherein: assuming that the above-mentioned optimization problem has a solutionThe closed-loop control increment obtained according to the predictive control principle is

(1) Δu (k) is a function of x (k), N, k;

(2) Due to the existence of time domain constraints, the Δu (k) functional relationship is nonlinear;

thereby writing out the model predictive control closed loop system as

5. The variable priority artificial pancreas adaptive model predictive control system of claim 4, wherein: the observer y of the controller is made to approach an ideal control target r, as an important factor affecting the physical safety of the patient, the output quantity of the controller, namely the injected insulin quantity u and deltau, should be within a limit range, and the two magnitudes should be as small as possible under the condition of ensuring the blood sugar risk when solving, so the following three-layer objective function is designed for different patient conditions, the priority of the target can be changed, and the dictionary MPC is used for solving layer by layer as follows: