CN107942687B - Approximate dynamic programming optimization control method for attitude adjustment of underwater hot glider - Google Patents
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Abstract
The invention discloses an approximate dynamic planning optimization control method for underwater hot glider attitude adjustment, which comprises the following steps: s1, designing a cost function of an approximate dynamic programming controller, wherein the output end of the approximate dynamic programming controller is connected with a controlled object of the underwater hot glider; s2, designing a value function of the approximate dynamic programming controller; s3, calculating an optimized execution output equation of the approximate dynamic programming controller; s4, connecting two single-input single-output active-disturbance-rejection controllers in parallel before the approximate dynamic programming controller, and respectively controlling the two single-input single-output active-disturbance-rejection controllers to output two control signals; s5, the original control input signal is obtained by inverse transformation of the control signal obtained in step S4, and the optimized execution output is obtained. The nonlinear optimization approximate dynamic programming control law for attitude adjustment of the underwater hot glider can be obtained only through real-time state feedback.
Description
Technical Field
The invention relates to the technical field of optimization control and ship and ocean engineering, in particular to an approximate dynamic programming optimization control method for attitude adjustment of an underwater hot glider.
Background
The operation of an underwater thermal glider is so high in rate because most of its operation time is in a stable sawtooth-like gliding motion in the vertical plane. Under the premise, the displacement of the mass block at the longitudinal position in the underwater hot glider is adjusted, so that the floating or sinking pitch angle of the mass block is changed, and the net buoyancy change size and speed of the mass block are determined. Therefore, the key to the control of an underwater thermal glider is to ensure that its pitch angle and net buoyancy are maintained or varied at desired target values by control inputs to the displacement of the mass in its longitudinal direction. This is an optimization control problem of the single-input multiple-output under-actuated system.
The approximate dynamic programming solves the problem of dimension disaster of the dynamic programming, and is a mainstream and widely applied optimization control method for the multi-input multi-output dynamic system. Currently, the implementation of approximate dynamic programming is mainly based on artificial neural network approximation, or iterative approximation. Therefore, approximate dynamic planning is also often referred to as neurodynamic planning. However, approximate dynamic programming based on an artificial neural network requires a large amount of data to be successfully learned and trained offline, and is not suitable for practical application. Iterative convergence problems exist with iterative-based approximate dynamic planning. They have not been able to better solve the problem of optimal control of attitude adjustment for underwater hot gliders.
Therefore, an approximate dynamic programming optimization control method independent of an artificial neural network or iterative approximation is urgently needed, not only can self-adaptive feedback regulation be realized like a PID control method, but also the optimization control problem of multi-input multi-output coupling can be better solved, so that the optimization control problem of posture regulation of the underwater hot glider is better solved, and a real data-driven approximate dynamic programming method is invented.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an underwater hot glider attitude regulation control method which is not based on an artificial neural network or iterative approximation and adopts novel approximate dynamic programming optimization: the value function of the underwater thermal glider attitude regulation approximate dynamic programming optimization control method is designed to be in a quadratic form, a polynomial expression of the optimized execution output is deduced through a strategy improvement principle of the approximate dynamic programming method, then a two-input two-output coupling active disturbance rejection decoupling control method is introduced, variable coefficients in the optimized execution output expression are obtained through real-time feedback, and finally a nonlinear optimized approximate dynamic programming control law of the underwater thermal glider attitude regulation can be obtained only through real-time state feedback.
In order to achieve the purpose, the invention is realized by the following technical scheme:
an approximate dynamic programming optimization control method for attitude adjustment of an underwater hot glider is characterized by comprising the following steps:
s1, designing a cost function of an approximate dynamic programming controller, wherein the output end of the approximate dynamic programming controller is connected with a controlled object of the underwater hot glider;
s2, designing a value function of the approximate dynamic programming controller;
s3, calculating an optimized execution output equation of the approximate dynamic programming controller;
s4, connecting two single-input single-output active-disturbance-rejection controllers in parallel before the approximate dynamic programming controller, and respectively controlling the two single-input single-output active-disturbance-rejection controllers to output two control signals;
s5, the original control input signal is obtained by inverse transformation of the control signal obtained in step S4, and the optimized execution output is obtained.
The cost function of the approximate dynamic programming controller in step S1 is defined as:
γ[x(t),u(t),t]＝a1Δθ2(t)+a2Δm0 2(t)+a3u2(t) (1)
wherein γ [ x (t), u (t), t]A cost function representing time t, wherein the cost function is related to the state x (t) of the underwater hot glider, the control input u (t) and the current time t, and delta theta (t) represents the difference between the pitch angle of the current time and the control target value; Δ m0(t) represents the difference between the net buoyancy at the current time and its control target value; u (t) represents the control input at the current time; a is1,a2And a3The optimized weighting coefficients, which represent the variables to which they are multiplied, can each be taken to be 1 here.
In step S2, an equivalent quadratic form is adopted, and the value function of the approximate dynamic programming controller is designed as follows:
wherein α is a discount factor; u (t) represents the control input at the current time; p (t) is the upper triangular weight matrix of the quadratic valued function, whose element r11(t),r12(t),r13(t),r22(t),r23(t),r33(t) is a variable coefficient over time.
In step S3, the principle equation (4) is improved according to the strategy of the approximate dynamic programming method, and the evaluation function Q (θ (t), m) is used0(t), u (t) partial derivatives of the control input signal u (t) to derive a polynomial expression of the optimization execution output u (t) of the variable coefficients, equation (6):
wherein u is*(t) represents an optimization control input at the current time; θ (t) represents a pitch angle at the present time; m is0(t) represents the net buoyancy at the current time; l1(t)，l2(t) represents a new representation of the variable coefficients used for the approximation.
The step S4 includes:
the method comprises the steps that a first single-input single-output active-disturbance-rejection controller and a second single-input single-output active-disturbance-rejection controller are connected in parallel before an approximate dynamic programming controller, the input of the first single-input single-output active-disturbance-rejection controller is the difference between a pitch angle at the current moment and a control target value of the first single-input single-output active-disturbance-rejection controller, and the input of the second single-input single-output active-disturbance-rejection controller is the difference between a net buoyancy force at the current moment and the control target value of the second single-; the system equation is as follows:
controlling the amplification factor of the input signal to be:
wherein the content of the first and second substances,
is an unknown model of an underwater hot glider object; y is1,y2Is the pitch angle and net buoyancy output state of the underwater hot glider;
substituting the optimization execution output u (t) in equation (6) into the above equation (7) can obtain:
then in equation (9) the new control input signal becomes l1(t),l2(t), and equation (9) controls the input signal amplification factor to become:
the equation (9) is decoupled into the following two single-input single-output systems, the first and second single-input single-output active disturbance rejection controllers are used for respectively controlling and can respectively output a control signal U1,U2：
In step S5, the control signal U output by the first and second single-input single-output active-disturbance-rejection controllers1,U2Through inverse transformation, the original control input signal can be obtained, the original control input signal is the variable coefficient l of the optimized execution output u (t) polynomial expression of the approximate dynamic programming controller1(t),l2(t)：
If C-1Singularity, which can be set to 1, and the optimization execution output u (t) of the approximate dynamic programming controller is:
after step S5, the method further includes:
and S6, adjusting the controlled object of the underwater hot glider to move through the optimized execution output obtained in the step S5, comparing the pitch angle and the net buoyancy value of the controlled object of the underwater hot glider at the moment with the target values of the pitch angle and the net buoyancy value, obtaining the difference between the pitch angle and the control target value at the current moment and the difference between the net buoyancy and the control target value at the current moment, feeding back the difference to the two single-input single-output active disturbance rejection controllers in the step S4, and circulating until the optimum state is reached.
Compared with the prior art, the invention has the following advantages:
the invention designs a novel approximate dynamic programming optimization control method for underwater hot glider attitude adjustment, which is characterized in that a quadratic value function and extreme value derivation thereof are designed, and an approximate dynamic programming optimization execution output expression of a variable coefficient is obtained by combining two-input and two-output active disturbance rejection decoupling control, so that a nonlinear optimal approximate dynamic programming control law for underwater hot glider attitude adjustment can be obtained only by real-time state feedback. The method does not depend on an artificial neural network or an iterative approximation approximate dynamic programming optimization control method, can realize self-adaptive feedback regulation like a PID control method, and can also better realize the optimization control of multi-input multi-output coupling, thereby better solving the optimization control problem of the attitude regulation of the underwater hot glider and inventing a real data-driven approximate dynamic programming method.
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FIG. 1 is a flow chart of an approximate dynamic programming optimization control method of attitude adjustment for an underwater hot glider of the present invention;
fig. 2 is a schematic structural and schematic principle diagram of the novel approximate dynamic programming optimization control method for attitude adjustment of the underwater hot glider.
Detailed Description
The present invention will now be further described by way of the following detailed description of a preferred embodiment thereof, taken in conjunction with the accompanying drawings.
As shown in fig. 1, an approximate dynamic programming optimization control method for attitude adjustment of an underwater hot glider includes the following steps:
s1, designing a cost function of an approximate dynamic programming controller, wherein the output end of the approximate dynamic programming controller is connected with a controlled object of the underwater hot glider;
s2, designing a value function of the approximate dynamic programming controller;
s3, calculating an optimized execution output equation of the approximate dynamic programming controller;
s4, connecting two single-input single-output active-disturbance-rejection controllers in parallel before the approximate dynamic programming controller, and respectively controlling the two single-input single-output active-disturbance-rejection controllers to output two control signals;
s5, the original control input signal is obtained by inverse transformation of the control signal obtained in step S4, and the optimized execution output is obtained.
The cost function of the approximate dynamic programming controller in step S1 is defined as:
γ[x(t),u(t),t]＝a1Δθ2(t)+a2Δm0 2(t)+a3u2(t) (1)
wherein γ [ x (t), u (t), t]A cost function representing time t, wherein the cost function is related to the state x (t) of the underwater hot glider, the control input u (t) and the current time t, and delta theta (t) represents the difference between the pitch angle of the current time and the control target value; Δ m0(t) represents the difference between the net buoyancy at the current time and its control target value; u (t) represents the control input at the current time; a is1,a2And a3An optimized weight coefficient representing a variable multiplied therewith,here, both can be taken to be 1.
In step S2, an equivalent quadratic form is adopted, and the value function of the approximate dynamic programming controller is designed as follows:
wherein α is a discount factor; u (t) represents the control input at the current time; p (t) is the upper triangular weight matrix of the quadratic valued function, whose element r11(t),r12(t),r13(t),r22(t),r23(t),r33(t) is a variable coefficient over time.
In step S3, the principle equation (4) is improved according to the strategy of the approximate dynamic programming method, and the evaluation function Q (θ (t), m) is used0(t), u (t) partial derivatives of the control input signal u (t) to derive a polynomial expression of the optimization execution output u (t) of the variable coefficients, equation (6):
wherein u is*(t) represents an optimization control input at the current time; θ (t) represents a pitch angle at the present time; m is0(t) represents the net buoyancy at the current time; l1(t)，l2(t) represents a new representation of the variable coefficients used for the approximation.
FIG. 2 is a new approximate dynamic for underwater hot glider attitude adjustmentThe structure and the principle schematic diagram of the planning optimization control method are shown, wherein 1, a first single-input single-output active disturbance rejection controller; 2-a second single-input single-output active-disturbance-rejection controller; 3-approximate dynamic programming controller; 4-controlled object of underwater hot glider; v. ofθ-a set target value for underwater hot glider pitch control;
setting a target value for net buoyancy control of the underwater hot glider; l1(t) outputting the variable coefficients of the first term of the u (t) polynomial expression for the approximate dynamic programming optimization execution; l2(t) outputting the variable coefficients of the second term of the u (t) polynomial expression for approximate dynamic programming optimization execution; u (t) is the output of the optimization execution of the approximate dynamic programming; theta (t) is an actual output value of a pitch angle of the underwater hot glider at the time t; m is0And (t) is the net buoyancy actual output value at the moment t of the underwater hot glider.
With reference to fig. 2, the step S4 includes:
a first single-input single-output active-disturbance-rejection controller 1 and a second single-input single-output active-disturbance-rejection controller 2 are connected in parallel before the approximate dynamic programming controller, the input of the first single-input single-output active-disturbance-rejection controller 1 is the difference between the pitch angle at the current moment and the control target value of the pitch angle, and the input of the second single-input single-output active-disturbance-rejection controller 2 is the difference between the net buoyancy at the current moment and the control target value of the net buoyancy; the final output of the first and second single-input single-output active disturbance rejection controllers is the variable coefficient l of the polynomial expression of the optimized execution output u (t) of the approximate dynamic programming controller 31(t)，l2(t) the system equation is as follows:
controlling the amplification factor of the input signal to be:
wherein the content of the first and second substances,
is an unknown model of an underwater hot glider object; y is1,y2Is the pitch angle and net buoyancy output state of the underwater hot glider;
substituting the optimization execution output u (t) in equation (6) into the above equation (7) can obtain:
then in equation (9) the new control input signal becomes l1(t),l2(t), and equation (9) controls the input signal amplification factor to become:
the equation (9) is decoupled into the following two single-input single-output systems, the first and second single-input single-output active disturbance rejection controllers are used for respectively controlling and can respectively output a control signal U1,U2：
In step S5, the control signal U output by the first and second single-input single-output active-disturbance-rejection controllers1,U2Through inverse transformation, the original control input signal can be obtained, the original control input signal is the variable coefficient l of the optimized execution output u (t) polynomial expression of the approximate dynamic programming controller1(t),l2(t)：
If C-1Singularity, which can be set to 1, and the optimization execution output u (t) of the approximate dynamic programming controller is:
after step S5, the method further includes:
and S6, adjusting the controlled object action of the underwater thermal glider through the optimized execution output obtained in the step S5, comparing the pitch angle and the net buoyancy value of the controlled object of the underwater thermal glider at the moment with the target values of the pitch angle and the net buoyancy value of the controlled object of the underwater thermal glider by using the control signal obtained in the equation (13), obtaining the difference between the pitch angle and the control target value at the current moment and the difference between the net buoyancy and the control target value at the current moment, feeding back the difference to the two single-input single-output active disturbance rejection controllers in the step S4, and circulating until the optimum is achieved. Therefore, the complete optimization control of the attitude adjustment of the underwater hot glider based on the novel approximate dynamic programming method is realized.
In conclusion, the approximate dynamic programming optimization control method for underwater hot glider attitude adjustment is independent of an artificial neural network or an iterative approximation approximate dynamic programming optimization control method, can realize self-adaptive feedback adjustment like a PID (proportion integration differentiation) control method, and can also better realize the optimization control of multi-input multi-output coupling, so that the optimization control problem of underwater hot glider attitude adjustment is better solved, and a real data-driven approximate dynamic programming method is invented.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (2)
1. An approximate dynamic programming optimization control method for attitude adjustment of an underwater hot glider is characterized by comprising the following steps:
s1, designing a cost function of an approximate dynamic programming controller, wherein the output end of the approximate dynamic programming controller is connected with a controlled object of the underwater hot glider;
s2, designing a value function of the approximate dynamic programming controller;
s3, calculating an optimized execution output equation of the approximate dynamic programming controller;
s4, connecting two single-input single-output active-disturbance-rejection controllers in parallel before the approximate dynamic programming controller, and respectively controlling the two single-input single-output active-disturbance-rejection controllers to output two control signals;
s5, inverse transforming the control signal obtained in step S4 to obtain the original control input signal, and further obtaining the optimized execution output;
the cost function of the approximate dynamic programming controller in step S1 is defined as:
γ[x(t),u(t),t]＝a1Δθ2(t)+a2Δm0 2(t)+a3u2(t) (1)
wherein γ [ x (t), u (t), t]A cost function representing time t, wherein the cost function is related to the state x (t) of the underwater hot glider, the control input u (t) and the current time t, and delta theta (t) represents the difference between the pitch angle of the current time and the control target value; Δ m0(t) represents the difference between the net buoyancy at the current time and its control target value; u (t) represents the control input at the current time; a is1,a2And a3Optimized weighting coefficients representing the variables multiplied by them, which may each be taken to be 1 here;
in step S2, an equivalent quadratic form is adopted, and the value function of the approximate dynamic programming controller is designed as follows:
wherein α is a discount factor; u (t) represents the control input at the current time; p (t) is the upper triangular weight matrix of the quadratic value functionOf the element r11(t),r12(t),r13(t),r22(t),r23(t),r33(t) is a variable coefficient over time;
in step S3, the principle equation (4) is improved according to the strategy of the approximate dynamic programming method, and the evaluation function Q (θ (t), m) is used0(t), u (t) partial derivatives of the control input signal u (t) to derive a polynomial expression of the optimization execution output u (t) of the variable coefficients, equation (6):
wherein u is*(t) represents an optimization control input at the current time; θ (t) represents a pitch angle at the present time; m is0(t) represents the net buoyancy at the current time; l1(t)，l2(t) representing a new representation of the variable coefficients used for the approximation;
the step S4 includes:
the method comprises the steps that a first single-input single-output active-disturbance-rejection controller and a second single-input single-output active-disturbance-rejection controller are connected in parallel before an approximate dynamic programming controller, the input of the first single-input single-output active-disturbance-rejection controller is the difference between a pitch angle at the current moment and a control target value of the first single-input single-output active-disturbance-rejection controller, and the input of the second single-input single-output active-disturbance-rejection controller is the difference between a net buoyancy force at the current moment and the control target value of the second single-; the system equation is as follows:
controlling the amplification factor of the input signal to be:
wherein the content of the first and second substances,
is an unknown model of an underwater hot glider object; y is1,y2Is the pitch angle and net buoyancy output state of the underwater hot glider;
substituting the optimization execution output u (t) in equation (6) into the above equation (7) can obtain:
then in equation (9) the new control input signal becomes l1(t),l2(t), and in the equation (9), the new control input signal amplification factor becomes:
the equation (9) is decoupled into the following two single-input single-output systems, the first and second single-input single-output active disturbance rejection controllers are used for respectively controlling and can respectively output a control signal U1,U2：
In step S5, the control signal U output by the first and second single-input single-output active-disturbance-rejection controllers1,U2Through inverse transformation, the original control input signal can be obtained, and the original control input signal is the optimized execution output u (t) polynomial expression of the approximate dynamic programming controllerCoefficient of variation l1(t),l2(t)：
If C-1Singularity, which can be set to 1, and the optimization execution output u (t) of the approximate dynamic programming controller is:
2. the approximate dynamic programming optimization control method for attitude adjustment of an underwater hot glider according to claim 1, wherein the step S5 is followed by further comprising:
and S6, adjusting the controlled object of the underwater hot glider to move through the optimized execution output obtained in the step S5, comparing the pitch angle and the net buoyancy value of the controlled object of the underwater hot glider at the adjusting moment with the target values of the pitch angle and the net buoyancy value of the controlled object of the underwater hot glider, obtaining the difference between the pitch angle and the control target value at the current moment and the difference between the net buoyancy and the control target value at the current moment, feeding back the difference to the two single-input single-output active disturbance rejection controllers in the step S4, and circulating until the optimum state is reached.
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