CN116244888A - Hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization - Google Patents
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Abstract
The invention discloses a hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization, and belongs to the field of unmanned aerial vehicle energy management. The implementation method of the invention comprises the following steps: calculating the required power and the solar cell output power at the future moment according to the flight track of the unmanned aerial vehicle, distributing the residual required power except the solar cell output power to a fuel cell and a lithium cell, enabling the solar cell to be always kept at a maximum output power working point through a maximum power tracker (MPPT), establishing a hybrid energy system power distribution model, carrying out in-out convexity on the hybrid energy system power distribution model in a trust zone range, solving by adopting convexity optimization, obtaining a hybrid energy system power distribution result, and improving the flight endurance of the unmanned aerial vehicle; and an MPC rolling optimization strategy is further introduced, so that the energy management problem of the hybrid electric unmanned aerial vehicle is decomposed into a series of short-time-domain online optimization problems, the complexity of the energy management problem of the hybrid electric unmanned aerial vehicle is reduced, and the energy management efficiency of the hybrid electric unmanned aerial vehicle is improved.
Description
Technical Field
The invention relates to a hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization, and belongs to the field of unmanned aerial vehicle energy management.
Background
In recent years, unmanned aerial vehicles have been widely used in various aspects of production and life, and among them, solar cell fuel cell lithium cell hybrid electric unmanned aerial vehicles have attracted great attention. The solar cell can continuously convert solar energy in the environment into electric energy, but is greatly influenced by environmental factors; the energy density of the fuel cell is high, but the corresponding speed is relatively slow, and the electric characteristics are soft; the lithium battery has larger power density but smaller energy density, and the solar battery/fuel battery/lithium battery hybrid electric unmanned aerial vehicle can make up the deficiency of a single energy form and fully exert the advantages of combined energy. However, the combination of multiple energy forms makes the unmanned aerial vehicle energy system more complex, and efficient energy management is required to ensure efficient operation of the hybrid energy system.
The energy management strategies of the hybrid electric unmanned aerial vehicle are mainly divided into rule-based energy management strategies and optimization-based energy management strategies. The power distribution of the hybrid energy system is realized according to a preset rule based on a rule management strategy, so that the hybrid energy system has good real-time performance, but the optimality is generally poor; and the power distribution problem of the hybrid energy system is solved by adopting an optimization method based on an optimization management strategy. The power profile of the hybrid power system is determined by the maneuvering process of the hybrid electric unmanned aerial vehicle, the output power of the solar battery on the surface of the wing is also influenced by the flight attitude of the unmanned aerial vehicle, the state of the hybrid power system and the flight movement of the unmanned aerial vehicle have complex coupling relation, and the energy management is only carried out from the hybrid power system level, so that the high energy efficiency long-endurance flight of the hybrid electric unmanned aerial vehicle is difficult to meet. Therefore, in order to solve the problem of energy management of the solar cell/fuel cell/lithium cell hybrid electric unmanned aerial vehicle, a more efficient energy management strategy needs to be designed.
Disclosure of Invention
Aiming at the energy management problem of a solar cell fuel cell lithium cell hybrid electric unmanned aerial vehicle, the invention provides a hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization, which comprises the steps of firstly calculating the required power and the solar cell output power at the future moment according to the flight track of the unmanned aerial vehicle, distributing the residual required power except the solar cell output power to the fuel cell and the lithium cell, and the solar cell always keeps at the maximum output power working point through a maximum power tracker (MPPT), establishing a hybrid energy system power distribution model, carrying out convex optimization on the hybrid energy system power distribution model in the trust domain range, solving by adopting convex optimization, obtaining the hybrid energy system power distribution result, and improving the flight endurance of the unmanned aerial vehicle; and an MPC rolling optimization strategy is further introduced, so that the energy management problem of the hybrid electric unmanned aerial vehicle is decomposed into a series of short-time-domain online optimization problems, the complexity of the energy management problem of the hybrid electric unmanned aerial vehicle is reduced, and the energy management efficiency of the hybrid electric unmanned aerial vehicle is improved.
The invention aims at realizing the following technical scheme:
the invention discloses a hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization, which comprises the following steps:
step one: giving out the flight track of the hybrid unmanned aerial vehicle, giving out the equivalent coefficient sigma, the trust domain size epsilon, the convergence error zeta and the prediction time domain N p Boundary conditions s min ,s max ,u min ,u max ;
Step two: since the solar cell has the highest output priority, the remaining required power P is supplemented by the lithium cell and the fuel cell sd According to the flight path of the hybrid electric unmanned aerial vehicle, calculating the solar cell power P in the prediction time domain pv [k]Power demand P D [k]And the remaining required power P sd [k]Where k=1, …, N p For predicting time, calculating solar output power P in prediction time domain D [k]And the remaining required power P sd [k]Solar energy can be utilized to the maximum extent, so that the power distribution result is more reasonable and efficient; according to the initial electricity of the lithium battery at the beginning of the current electricity quantity initialization iteration of the lithium batteryQuantity SOC t The method comprises the steps of carrying out a first treatment on the surface of the Based on the output power of fuel cell and the residual power needed at the last moment, the reference sequence in the prediction time domainInitialization is performed.
The energy source form of the hybrid electric unmanned aerial vehicle comprises a solar battery, a fuel cell and a lithium battery.
Step three: cell hydrogen consumption by lithium cell power SOC and fuelEquivalent hydrogen consumption m of lithium battery eb As a state variable, output power P of lithium battery b And fuel cell output power P fc Constructing a state equation of the hybrid energy system for the control quantity; reference sequence obtained by initializing step two +.>The state equation of the hybrid energy system is convex, i.e. in the reference sequence +.>And (3) performing first-order Taylor polynomial expansion in the range of the trust zone to obtain a convex hybrid energy system state equation. Further with fuel cell hydrogen consumption +.>Equivalent hydrogen consumption m of lithium battery eb And for optimizing the target, constructing a power distribution model of the hybrid energy system by using the state equation, the boundary condition constraint and the initial condition constraint of the hybrid energy system after the salification.
The state equation of the hybrid energy system is that
In the formula (1), SOC is the electric quantity of a lithium battery; u (U) oc Is lithiumA battery open circuit voltage; r is R int Is the internal resistance of the lithium battery; p (P) b Output power for lithium battery; q (Q) b Is lithium battery capacity;hydrogen consumption for the fuel cell; n (N) cell The number of the polar plates of the fuel cell; />Is the molar mass of hydrogen; η (eta) DCDC Is the DCDC converter efficiency; p (P) fc Output power for the fuel cell; f is Faraday constant; u (U) bus Is the bus voltage; m is m eb Equivalent hydrogen consumption for lithium batteries; p (P) b Output power for lithium battery; c LHV Is hydrogen with low calorific value.
Constructing a power distribution model of a hybrid energy system as
N in formula (2) p To predict the time domain length;is N p Hydrogen consumption of the fuel cell at the moment; m is m eb [N p ]Is N p Equivalent hydrogen consumption of the lithium battery at the moment; sigma is an equivalent coefficient; SOC (State of Charge) t The method comprises the steps of (1) setting the electric quantity of a lithium battery at an iteration initial moment; s [ k ]]The state quantity is the state quantity of the energy management problem of the mixed energy system at the kth moment; u [ k ]]The control quantity of the energy management problem of the mixed energy system at the kth moment; />A reference sequence for predicting the kth moment in the time domain; />And respectively obtaining constant matrixes related to the reference sequence, and performing first-order Taylor polynomial expansion on the state equation of the energy management problem near the reference sequence to obtain the constant matrixes, so as to obtain the state equation of the protruding hybrid energy system.
Step four: and (3) carrying out hybrid electric unmanned aerial vehicle energy management iterative optimization on the hybrid energy system power distribution model constructed in the step (III) by utilizing a convex optimization method, terminating the iterative process if the power distribution result obtained by optimizing and solving meets a preset iterative convergence criterion in the iterative process, taking the current result as an optimal power distribution result, and turning to the step (V). Otherwise, returning to the third step and continuing iteration until the power distribution result converges; because all constraint conditions and objective functions in the hybrid energy system power distribution model constructed in the step three are convex, stable and efficient iterative optimization is performed in a trust domain based on a convex optimization method, and a hybrid energy system power distribution result is obtained; and the MPC rolling optimization strategy is introduced to optimize the power distribution model of the convex optimized hybrid energy system, so that the power distribution result of the hybrid energy system in the prediction domain is optimized, the operand and the complexity of the iterative optimization process are further reduced, and the online real-time optimization capacity of the hybrid electric unmanned aerial vehicle energy management is improved.
The preset iteration convergence criterion of the energy management problem of the hybrid energy system is that
|s q [k]-s q-1 [k]|≤ξ,k=0,1,...,K (3)
Step five: and (3) applying the power distribution result of the hybrid energy system obtained by optimizing in the step (IV) to the hybrid energy system, wherein the power distribution result in the prediction time domain is used for controlling the output power of the fuel cell, and the solar cell is always kept at the maximum output power working point through the MPPT controller, so that the solar energy is utilized to the maximum extent, the energy consumption is reduced, and the flight endurance is improved. And (3) the unmanned aerial vehicle flies forwards along the track, the state information of the unmanned aerial vehicle and the state information of the hybrid energy system are updated, the second step is returned, and rolling optimization solution is carried out until the unmanned aerial vehicle completes the flight task.
The beneficial effects are that:
1. according to the hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization, the required power and the solar cell output power at the future moment are calculated according to the flight track of the hybrid electric unmanned aerial vehicle, and the method is applied to the power distribution of a hybrid energy system, so that the energy management of the hybrid system is more reasonable and efficient, the efficiency of the hybrid energy system is improved, and the flight endurance of the unmanned aerial vehicle is increased.
2. The invention discloses a hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization, which aims at the problem of hybrid energy system energy management, establishes a hybrid energy system power distribution convex optimization model, performs convex processing in the range of the trust zone of a reference track, adopts the sequence convex optimization method to perform efficient solution, can quickly realize the power distribution of the hybrid energy system, and is beneficial to the online application of hybrid electric unmanned aerial vehicle hybrid energy system management.
3. The invention discloses a hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization, which aims at the problems of strong nonlinearity, large calculated amount, multiple optimization variables and the like in the energy management of a hybrid energy system, introduces an MPC strategy, converts the energy management problem of the hybrid electric unmanned aerial vehicle into a series of short time domain optimization problems, solves a hybrid electric unmanned aerial vehicle energy management model only in a prediction time domain, reduces the complexity of the energy management problem, improves the solving efficiency, and further increases the instantaneity of the energy management.
Drawings
FIG. 1 is a flow chart of a hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization;
FIG. 2 is a comparison of fuel cell output power profile versus hydrogen consumption, FIG. 2 (a) is a fuel cell output power profile, and FIG. 2 (b) is a fuel cell hydrogen consumption;
fig. 3 is a comparison between the output power profile of the lithium battery and the power variation, fig. 3 (a) is the output power profile of the lithium battery, and fig. 3 (b) is the power variation of the lithium battery.
Detailed Description
For a better description of the objects and advantages of the present invention, the following description will further explain the present invention by referring to the figures and simulation cases.
Example 1:
the main parameter of the hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization is sigma=1, epsilon= [0.001,0.005,0.005 ]],ξ=[0.0001,0.0001,0.0001]And N p =40; 120 solar cells are arranged on the surface of the wing of the unmanned aerial vehicle, and the irradiation intensity on the day of flight is 1200W/m 2 The unmanned aerial vehicle takes off at 9 points in the morning of the same day. The main parameters of the lithium battery and the fuel cell are shown in table 1. The simulation environment is a desktop computer loaded with MATLAB2019b and is configured as Windows10, intel (R) Core (TM) CPU i7-7500 2.93GHz, running 16GB.
Table 1 main parameters of lithium battery and fuel battery
In order to verify the feasibility and the beneficial effects of the hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization disclosed by the invention, the technical scheme of the invention is clearly and in detail described in the following case, and a flow chart is shown in figure 1.
The hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization disclosed by the embodiment comprises the following specific implementation steps:
step one: giving out the flight track of the hybrid unmanned aerial vehicle, giving out the equivalent coefficient sigma, the trust domain size epsilon, the convergence error zeta and the prediction time domain N p Boundary conditions s min ,s max ,u min ,u max ;
Step two: since the solar cell has the highest output priority, the remaining required power P is supplemented by the lithium cell and the fuel cell sd According to the flight track of the hybrid electric unmanned aerial vehicle, calculating the solar cell power in the prediction time domainRate P pv [k]Power demand P D [k]And the remaining required power P sd [k]Where k=1, …, N p For predicting time, calculating solar output power P in prediction time domain D [k]And the remaining required power P sd [k]Solar energy can be utilized to the maximum extent, so that the power distribution result is more reasonable and efficient; according to the initial electric quantity SOC of the lithium battery at the beginning of the electric quantity initialization iteration of the current lithium battery t The method comprises the steps of carrying out a first treatment on the surface of the Based on the output power of fuel cell and the residual power needed at the last moment, the reference sequence in the prediction time domainInitialization is performed.
The energy source form of the hybrid electric unmanned aerial vehicle comprises a solar battery, a fuel cell and a lithium battery.
Step three: battery hydrogen consumption m of fuel and electric quantity SOC of lithium battery H2 Equivalent hydrogen consumption m of lithium battery eb As a state variable, output power P of lithium battery b And fuel cell output power P fc Constructing a state equation of the hybrid energy system for the control quantity; using the reference sequence obtained by the initialization of the step twoThe state equation of the hybrid energy system is convex, i.e. in the reference sequence +.>And (3) performing first-order Taylor polynomial expansion in the range of the trust zone to obtain a convex hybrid energy system state equation. Further with fuel cell hydrogen consumption +.>Equivalent hydrogen consumption m of lithium battery eb And for optimizing the target, constructing a power distribution model of the hybrid energy system by using the state equation, the boundary condition constraint and the initial condition constraint of the hybrid energy system after the salification.
The state equation of the hybrid energy system is that
In the formula (4), SOC is the electric quantity of the lithium battery; u (U) oc Open circuit voltage for lithium battery; r is R int Is the internal resistance of the lithium battery; p (P) b Output power for lithium battery; q (Q) b Is lithium battery capacity;hydrogen consumption for the fuel cell; n (N) cell The number of the polar plates of the fuel cell; />Is the molar mass of hydrogen; η (eta) DCDC Is the DCDC converter efficiency; p (P) fc Output power for the fuel cell; f is Faraday constant; u (U) bus Is the bus voltage; m is m eb Equivalent hydrogen consumption for lithium batteries; p (P) b Output power for lithium battery; c LHV Is hydrogen with low calorific value.
Constructing a power distribution model of a hybrid energy system as
N in (5) p To predict the time domain length; m is m H2 [N p ]Is N p Hydrogen consumption of the fuel cell at the moment; m is m eb [N p ]Is N p Equivalent hydrogen consumption of the lithium battery at the moment; sigma is an equivalent coefficient; SOC (State of Charge) t The method comprises the steps of (1) setting the electric quantity of a lithium battery at an iteration initial moment; s [ k ]]The state quantity is the state quantity of the energy management problem of the mixed energy system at the kth moment; u [ k ]]The control quantity of the energy management problem of the mixed energy system at the kth moment;a reference sequence for predicting the kth moment in the time domain; />And respectively obtaining constant matrixes related to the reference sequence, and performing first-order Taylor polynomial expansion on the state equation of the energy management problem near the reference sequence to obtain the constant matrixes, so as to obtain the state equation of the protruding hybrid energy system.
Step four: and (3) carrying out hybrid electric unmanned aerial vehicle energy management iterative optimization on the hybrid energy system power distribution model constructed in the step (III) by utilizing a convex optimization method, terminating the iterative process if the power distribution result obtained by optimizing and solving meets a preset iterative convergence criterion in the iterative process, taking the current result as an optimal power distribution result, and turning to the step (V). Otherwise, returning to the third step and continuing iteration until the power distribution result converges; because all constraint conditions and objective functions in the hybrid energy system power distribution model constructed in the step three are convex, stable and efficient iterative optimization is performed in a trust domain based on a convex optimization method, and a hybrid energy system power distribution result is obtained; and the MPC rolling optimization strategy is introduced to optimize the power distribution model of the convex optimized hybrid energy system, so that the power distribution result of the hybrid energy system in the prediction domain is optimized, the operand and the complexity of the iterative optimization process are further reduced, and the online real-time optimization capacity of the hybrid electric unmanned aerial vehicle energy management is improved.
The preset iteration convergence criterion of the energy management problem of the hybrid energy system is that
|s q [k]-s q-1 [k]|≤ξ,k=0,1,...,K (6)
Step five: and (3) applying the power distribution result of the hybrid energy system obtained by optimizing in the step (IV) to the hybrid energy system, wherein the power distribution result in the prediction time domain is used for controlling the output power of the fuel cell, and the solar cell is always kept at the maximum output power working point through the MPPT controller, so that the solar energy is utilized to the maximum extent, the energy consumption is reduced, and the flight endurance is improved. And (3) the unmanned aerial vehicle flies forwards along the track, the state information of the unmanned aerial vehicle and the state information of the hybrid energy system are updated, the second step is returned, and rolling optimization solution is carried out until the unmanned aerial vehicle completes the flight task.
The results obtained by the hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization disclosed by the invention are shown in fig. 2 and 3. Fig. 2 shows the comparison of the output power profile and the hydrogen consumption of the fuel cell obtained by the method of the present invention with the typical energy management strategy Nonlinear Model Predictive Control (NMPC) and the Fuzzy Logic State Machine (FLSM), and the results show that the output power and the hydrogen consumption rate of the fuel cell obtained by the method of the present invention have smaller fluctuation ranges, and the three strategies consume 9.83g,10.16g and 10.79g of hydrogen respectively, and compared with NMPC and FLSM, the method of the present invention saves 6.3% and 9.7% of hydrogen consumption respectively under the same conditions. Fig. 3 shows that the output power profile and the electric quantity change condition of the lithium battery obtained by the method of the invention are compared with those of the NMPC and the FLSM, and under the same initial electric quantity condition, the residual electric quantity of the lithium battery under three energy management strategies is 58.19%,59.63% and 61.98%, and the result shows that the method of the invention has better control performance in the aspect of effectively utilizing the battery compared with the NMPC and the FLSM.
The foregoing detailed description is provided for the purpose of illustrating the invention in further detail and is to be understood that this invention is not limited to the particular embodiments disclosed, but is intended to cover all modifications, equivalents, alternatives, and improvements as fall within the spirit and scope of the invention.
Claims (4)
1. The hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization is characterized in that: comprises the steps of,
step one: giving out the flight track of the hybrid unmanned aerial vehicle, giving out the equivalent coefficient sigma, the trust domain size epsilon, the convergence error zeta and the prediction time domain N p Boundary conditions s min ,s max ,u min ,u max ;
Step two: since the solar cell has the highest powerPriority is given to the supplement of the residual required power P by the lithium battery and the fuel battery sd According to the flight path of the hybrid electric unmanned aerial vehicle, calculating the solar cell power P in the prediction time domain pv [k]Power demand P D [k]And the remaining required power P sd [k]Where k=1, …, N p For predicting time, calculating solar output power P in prediction time domain D [k]And the remaining required power P sd [k]Solar energy can be utilized to the maximum extent, so that the power distribution result is more reasonable and efficient; according to the initial electric quantity SOC of the lithium battery at the beginning of the electric quantity initialization iteration of the current lithium battery t The method comprises the steps of carrying out a first treatment on the surface of the Based on the output power of fuel cell and the residual power needed at the last moment, the reference sequence in the prediction time domainInitializing;
the energy forms of the hybrid electric unmanned aerial vehicle comprise a solar battery, a fuel cell and a lithium battery;
step three: cell hydrogen consumption by lithium cell power SOC and fuelEquivalent hydrogen consumption m of lithium battery eb As a state variable, output power P of lithium battery b And fuel cell output power P fc Constructing a state equation of the hybrid energy system for the control quantity; reference sequence obtained by initializing step two +.>The state equation of the hybrid energy system is convex, i.e. in the reference sequence +.>Performing first-order Taylor polynomial expansion in the range of the trust zone to obtain a state equation of the hybrid energy system after the convexity; further with fuel cell hydrogen consumption +.>Equivalent hydrogen consumption m of lithium battery eb For optimizing the target, constructing a power distribution model of the hybrid energy system by using a state equation, boundary condition constraints and initial condition constraints of the hybrid energy system after the salification;
step four: performing hybrid electric unmanned aerial vehicle energy management iterative optimization on the hybrid energy system power distribution model constructed in the step three by utilizing a convex optimization method, terminating the iterative process if a power distribution result obtained by optimizing and solving meets a preset iterative convergence criterion in the iterative process, taking a current result as an optimal power distribution result, and turning to the step five; otherwise, returning to the third step and continuing iteration until the power distribution result converges; because all constraint conditions and objective functions in the hybrid energy system power distribution model constructed in the step three are convex, stable and efficient iterative optimization is performed in a trust domain based on a convex optimization method, and a hybrid energy system power distribution result is obtained; and the MPC rolling optimization strategy is introduced to optimize the power distribution model of the convex optimized hybrid energy system, so that the power distribution result of the hybrid energy system in the prediction domain is optimized, the operand and the complexity of the iterative optimization process are further reduced, and the online real-time optimization capacity of the hybrid electric unmanned aerial vehicle energy management is improved.
2. The hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization of claim 1, wherein: the method further comprises the step five of applying the power distribution result of the hybrid energy system obtained by optimizing in the step four to the hybrid energy system, and using the power distribution result in the prediction time domain to control the output power of the fuel cell, wherein the solar cell always keeps the maximum output power working point through the MPPT controller, so that the solar energy is utilized to the maximum extent, the energy consumption is reduced, and the flight time is improved; and (3) the unmanned aerial vehicle flies forwards along the track, the state information of the unmanned aerial vehicle and the state information of the hybrid energy system are updated, the second step is returned, and rolling optimization solution is carried out until the unmanned aerial vehicle completes the flight task.
3. The hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization according to claim 1 or 2, wherein: in the third step, the first step is performed,
the state equation of the hybrid energy system is that
In the formula (1), SOC is the electric quantity of a lithium battery; u (U) oc Open circuit voltage for lithium battery; r is R int Is the internal resistance of the lithium battery; p (P) b Output power for lithium battery; q (Q) b Is lithium battery capacity;hydrogen consumption for the fuel cell; n (N) cell The number of the polar plates of the fuel cell; />Is the molar mass of hydrogen; η (eta) DCDC Is the DCDC converter efficiency; p (P) fc Output power for the fuel cell; f is Faraday constant; u (U) bus Is the bus voltage; m is m eb Equivalent hydrogen consumption for lithium batteries; p (P) b Output power for lithium battery; c LHV Is hydrogen with low heat value;
constructing a power distribution model of a hybrid energy system as
N in formula (2) p To predict the time domain length;is N p Hydrogen consumption of the fuel cell at the moment; m is m eb [N p ]Is N p Equivalent hydrogen consumption of the lithium battery at the moment; sigma is an equivalent coefficient; SOC (State of Charge) t The method comprises the steps of (1) setting the electric quantity of a lithium battery at an iteration initial moment; s [ k ]]Is the kth timeState quantity of energy management problem of hybrid energy system; u [ k ]]The control quantity of the energy management problem of the mixed energy system at the kth moment; />A reference sequence for predicting the kth moment in the time domain; />And respectively obtaining constant matrixes related to the reference sequence, and performing first-order Taylor polynomial expansion on the state equation of the energy management problem near the reference sequence to obtain the constant matrixes, so as to obtain the state equation of the protruding hybrid energy system.
4. The hybrid electric unmanned aerial vehicle energy management method based on MPC sequence convex optimization of claim 3, wherein: in the fourth step, the first step is performed,
the preset iteration convergence criterion of the energy management problem of the hybrid energy system is that
|s q [k]-s q-1 [k]|≤ξ,k=0,1,...,K (3)。
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