An optimized control system and method for a water-air amphibious vehicle

Abstract

The application discloses an optimization control system and method of a water-air amphibious vehicle, and relates to the field of water-air amphibious vehicle optimization control. The water-air amphibious vehicle is modeled as a four-rotor aircraft when flying in the air, and is modeled as an unmanned ship when sailing on the water. A variable-order switching system is used to represent the mode conversion of the water-air amphibious vehicle when sailing on the water and flying in the air, so as to obtain a heterogeneous switching system model of the water-air amphibious vehicle. A suitable performance index is constructed. An Actor-Critic controller is designed for the water-air amphibious vehicle by using a reinforcement learning optimization algorithm. Compared with a traditional control strategy, the application scheme starts from the perspective of a heterogeneous switching system, combines the reinforcement learning idea, reduces the complicated calculation amount, realizes the autonomous intelligent control of the water-air amphibious vehicle, and saves the cost of the water-air amphibious vehicle.

Description

Technical Field

[0001] This invention relates to the field of optimized control of amphibious vehicles, specifically to an optimized control system and method for amphibious vehicles. Background Technology

[0002] In recent years, with the rapid development of electronic, communication, materials, and automation technologies, significant progress has been made in the field of intelligent unmanned equipment. Unmanned surface vessels (USVs) and unmanned aerial vehicles (UAVs) have become increasingly mature and possess significant advantages in marine exploration and development. USVs are highly flexible and easy to integrate, and can be widely used in areas such as marine water quality monitoring, marine ranching monitoring, marine atmosphere forecasting, communication relay, and territorial sea surveillance. UAVs have the advantages of high mobility, high timeliness, and low cost, and can effectively compensate for the deficiencies in aerial, maritime, and ground-based detection capabilities, making them an indispensable remote sensing platform for marine environmental monitoring. However, with the expansion of the operating environment and application scope of unmanned equipment, in some application scenarios, neither a single USV nor a single UAV is sufficient for operation. This has prompted the development of unmanned aerial vehicles (UAVs) capable of amphibious operations, namely amphibious vehicles, by leveraging the advantages of both USVs and UAVs.

[0003] The prerequisite for deploying intelligent unmanned equipment is the realization of autonomous functions, and control technology is an essential and crucial element in achieving these functions. In completing designated tasks, amphibious vehicles first need to quickly reach their designated locations. Secondly, to maximize the vehicle's maximum operating radius while completing the mission, it's necessary to conserve power by selecting appropriate system input energy and rationally planning the number of switching operations. Furthermore, the limitations of the vehicle's rotor and propeller speeds, as well as the limits on maximum airspeed and maximum flight speed, must be considered. It's also important to note that before the vehicle prepares to land on the water, the pitch and roll angles must be controlled within a small range to ensure stability upon landing. In tasks such as search and rescue and reconnaissance, the system exhibits variable-order switching characteristics. As the system order increases and becomes more nonlinear, the complexity of the problem rises sharply. Even with a known model, the optimal solution is often difficult to calculate, thus preventing the amphibious vehicle from autonomously completing its designated tasks. Summary of the Invention

[0004] This invention provides an optimized control system and method for an amphibious vehicle, which addresses the variable-order switching characteristics of the system dynamics when an aircraft lands in water from the air or ascends from the water to the air.

[0005] In a first aspect, this application provides an optimized control method for an amphibious vehicle, the method comprising:

[0006] Step 1: Model the amphibious vehicle flying in the air as a quadcopter.

[0007] Step 2: Model the amphibious vehicle that navigates on the water as an unmanned surface vessel;

[0008] Step 3: Represent the mode transition of the amphibious vehicle in water surface navigation and air flight using a variable order switching system to obtain the heterogeneous switching system model of the amphibious vehicle.

[0009] Step 4: Considering the system's input-state constraints, construct appropriate performance metrics;

[0010] Step 5: Use reinforcement learning optimization algorithms to design an Actor-Critic controller for the amphibious vehicle.

[0011] Optionally, amphibious vehicles flying in the air may be modeled as quadcopter aircraft, including:

[0012]

[0013] Where {x,y,z} represent the position state of the quadcopter, {φ,θ,ψ} represent the pitch angle, roll angle, and yaw angle, respectively; m is the mass of the quadcopter, l is the distance from the rotor center to the center of gravity of the aircraft, g is the acceleration due to gravity, and J is the mass of the quadcopter. x J y J z These are the moments of inertia of the quadcopter about its three axes; The vector consisting of the lift resultant force, roll resultant force, pitch resultant force, and yaw resultant force of the four motors is the input of the system.

[0014] Optionally, amphibious vehicles navigating on the water's surface may be modeled as unmanned surface vessels, including:

[0015]

[0016] in, These represent the position relative to the ground and the yaw angle, respectively. These represent the yaw rate, the vertical yaw rate, and the yaw angle rate, respectively. Let M represent the control input, f(η,ν) represent the inertia matrix, f(η,ν) represent the unknown dynamics of the system, and R(ψ) represent the rotation matrix of the system. The expression for R(ψ) is:

[0017]

[0018] Optionally, a variable-order switching system is used to represent the mode transitions of an amphibious vehicle during surface navigation and air flight, resulting in a heterogeneous switching system model for the amphibious vehicle, including:

[0019] use Represents the total variables of the system when an amphibious vehicle is in flight. Let represent the total variables of the system when the amphibious vehicle is navigating on the water surface. The amphibious vehicle is modeled as a heterogeneous switching system as follows:

[0020]

[0021]

[0022] Where, σ(t): This indicates the system switching signal, where t0 is the start time; F σ(t) (·) and G σ(t) (·) represent the system's internal dynamic function and input gain function derived from equations (1) and (2), respectively; t k The time when the switch occurs. and These are the state transition matrix and pulse vector for the amphibious vehicle at the moments of landing and takeoff, respectively.

[0023] Optionally, construct appropriate system input state performance metrics, including:

[0024] Step 4-1: Construct the following performance indicators for the heterogeneous switching system of the amphibious vehicle:

[0025]

[0026] Where φ(·,·)>φ min >0 indicates switching cost; Δ represents an estimate of the performance index (value function) corresponding to the current joint action strategy; t The sampling interval for integral reinforcement learning is set to a value slightly larger than the minimum dwell time; It is a positive definite function of the system state; γ > 0 represents the attenuation coefficient;

[0027] Step 4-2: Considering the problems caused by the discontinuous value function as the input optimization of the subsystem, the Action-Dependent Heuristic Dynamic Programming (ADHDP) method in reinforcement learning is adopted, and equation (6) is further written as:

[0028]

[0029] Wherein, σ(t) + ), Indicates the joint action strategy selected at the switching moment;

[0030] Step 4-3: Considering the state-input constraints that exist in actual amphibious vehicles during operation, the following state-related obstacle function is designed:

[0031]

[0032] Among them, Q 1 Let Q represent the original system cost function. 2 The barrier function of the design, α i This represents the weighting constant.

[0033] Optionally, an Actor-Critic controller is designed for the amphibious vehicle using a reinforcement learning optimization algorithm, including:

[0034] Step 5-1: During each interval of integral reinforcement learning, the signal switching strategy is improved as follows:

[0035]

[0036] Step 5-2: Based on Step 5-1, optimize the subsystem control input according to the stationary point condition equation:

[0037]

[0038] Step 5-3, combined with Steps 5-1 and 5-2, yields the joint control decision for the amphibious vehicle:

[0039]

[0040] Secondly, this application provides an optimized control system for an amphibious vehicle, the system comprising:

[0041] The aerial flight model building unit is used to build a dynamic model of an amphibious vehicle during aerial flight.

[0042] The surface navigation model building unit is used to build a dynamic model of an amphibious vehicle when it navigates on the water.

[0043] The heterogeneous switching system model building unit for amphibious vehicles is used to represent the mode transitions of amphibious vehicles in water surface navigation and air flight using a variable-order switching system, thereby obtaining a heterogeneous switching system model for amphibious vehicles.

[0044] The performance index construction unit is used to construct appropriate system input state performance indices.

[0045] The Actor-Critic Controller Design Unit is used to design Actor-Critic controllers for amphibious vehicles using reinforcement learning optimization algorithms.

[0046] The effects described in the invention are merely those of the embodiments, and not all the effects of the invention. One of the above technical solutions has the following advantages or beneficial effects:

[0047] 1) The method of the present invention adopts a reinforcement learning action-dependent heuristic dynamic programming method, which reduces the dependence on system model knowledge and solves the problem caused by the optimization of discontinuous value functions as inputs to switching subsystems.

[0048] 2) In this invention, reinforcement learning optimization control is a novel optimization control strategy with significant optimization effect, greatly improving the mission execution efficiency of amphibious vehicles, saving power energy, and realizing autonomous intelligent control of amphibious vehicles.

[0049] 3) This invention comprehensively considers factors such as convergence rate, constraints, control input cost, and switching cost, and establishes performance indicators that are both practically significant and can guide the achievement of optimization goals, thus possessing high engineering practical value. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the optimized control method for an amphibious vehicle according to the present invention;

[0051] Figure 2 This is a structural diagram of the amphibious vehicle of the present invention;

[0052] Figure 3 This is an optimized control structure diagram of an amphibious vehicle according to the present invention;

[0053] Figure 4 This is a schematic diagram of the integral reinforcement learning algorithm for the continuous-time heterogeneous switching system of the present invention;

[0054] Figure 5 This is a schematic diagram of the hardware system of the amphibious vehicle of the present invention;

[0055] Figure 6 A schematic diagram of the optimized control system structure of an amphibious vehicle according to the present invention. Detailed Implementation

[0056] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0057] Figure 1A schematic flowchart of an optimized control method for an amphibious vehicle according to the present invention is shown.

[0058] Reference Figure 1 The method of this invention includes the following steps:

[0059] Step 1: Model the amphibious vehicle flying in the air as a quadcopter.

[0060] Step 2: Model the amphibious vehicle that navigates on the water as an unmanned surface vessel;

[0061] Step 3: Represent the mode transition of the amphibious vehicle in water surface navigation and air flight using a variable order switching system to obtain the heterogeneous switching system model of the amphibious vehicle.

[0062] Step 4: Considering the system's input-state constraints, construct appropriate performance metrics;

[0063] Step 5: Using reinforcement learning optimization algorithms, design an Actor-Critic controller for the amphibious vehicle. Next, taking the team's self-developed amphibious vehicle as an example, the implementation process of the above-mentioned method will be explained in detail.

[0064] like Figure 2 As shown, this is the amphibious vehicle independently developed by the team. 1—quadcopter, 2—catamaran-like hull, 3—internal electronic control system, 4—multi-functional payload, 5—twin-propeller propulsion. The amphibious vehicle's parameters are as follows: weight: 3 kg, effective payload: 2 kg, main body length: 0.93 m, maximum airspeed: 36 km / h, maximum flight time: 25 min, ideal maximum operating time: 60 min, multi-functional payload: 2, maximum speed: 3 knots.

[0065] like Figure 3 , 4As shown, the optimized control algorithm design in this embodiment can be implemented using the following steps: First, an Actor-Critic control structure is adopted. The Critic network approximator approximates the value function (i.e., performance index) of the amphibious vehicle system. The number of Critic networks is the same as the number of subsystems. The inputs of the Critic networks include the system state, the current subsystem, and the inputs of the Actor networks. The Actor networks optimize the system input by minimizing the value of the Critic networks. Second, the concept of reinforcement learning is introduced. An integral reinforcement learning algorithm is used to design the switching law and control law of the amphibious vehicle based on the policy evaluation equation (value function). The neural network is trained online and offline using system data to improve the approximation effect. Finally, at the sampling update time, the minimum value function is compared to obtain the optimal switching and control inputs of the heterogeneous switching system of the amphibious vehicle, thereby achieving autonomous intelligent control of the amphibious vehicle.

[0066] In the above embodiments of the present invention, an optimized control method for an amphibious vehicle is provided, the method comprising the following steps:

[0067] In step 1, the amphibious vehicle is modeled as a quadcopter when it is flying in the air. The specific model is as follows:

[0068]

[0069] Where {x,y,z} represent the position state of the quadcopter, {φ,θ,ψ} represent the pitch angle, roll angle, and yaw angle, respectively; m is the mass of the quadcopter, l is the distance from the rotor center to the center of gravity of the aircraft, g is the acceleration due to gravity, and J is the mass of the quadcopter. x J y J z These are the moments of inertia of the quadcopter about its three axes; The vector consisting of the lift resultant force, roll resultant force, pitch resultant force, and yaw resultant force of the four motors is considered as the input of the system.

[0070] Furthermore, in step 2, when the amphibious vehicle is navigating on the water, it is modeled as an unmanned surface vessel. This model has six degrees of freedom: sway, pitch, bow, heave, roll, and pitch. For simplicity, only the first three degrees of freedom are considered here, so the specific model is as follows:

[0071]

[0072] in, These represent the position relative to the ground and the yaw angle, respectively. These represent the yaw rate, the vertical yaw rate, and the yaw angle rate, respectively. Let M represent the control input, f(η,ν) represent the inertia matrix, f(η,ν) represent the unknown dynamics of the system, and R(ψ) represent the rotation matrix of the system. Its expression is:

[0073]

[0074] Furthermore, in step 3, a variable-order switching system is used to represent the mode transitions of the amphibious vehicle during surface navigation and air flight, resulting in a heterogeneous switching system model for the amphibious vehicle. The steps are as follows:

[0075] Since actual amphibious vehicles typically employ rapid descent and rapid ascent during mode transitions, the dynamic process of the transition is ignored and considered an instantaneous switch. A heterogeneous controlled switching system design method is adopted. When the amphibious vehicle is preparing to descend from the air into the water, assuming an altitude z and a pitch angle... The roll angle θ and its velocity states disappear (in practice, they can be considered to become 0), leaving only the horizontal position [x, y] and yaw angle ψ as the three degrees of freedom. Furthermore, at the switching moment, the three variables x, y, and ψ remain unchanged, while their velocities... A pulse jump occurs, reaching 0. Similarly, when the amphibious vehicle prepares to ascend from the water into the air, the three variables x, y, and ψ remain unchanged. The pulse jumps to 0. And z, The three variables θ will appear, and their state and velocity information can be set with reasonable initial values ​​or determined by the feedback signal measured by the sensor in practice.

[0076] use Represents the total variables of the system when an amphibious vehicle is in flight. Let the total variables of the system represent the amphibious vehicle's system when it is navigating on the water. Based on the above analysis, the amphibious vehicle can be modeled as a heterogeneous switching system as follows:

[0077]

[0078]

[0079] Where, σ(t): This indicates the system switching signal, where t0 is the start time; F σ(t) (·) and G σ(t) (·) represent the system's internal dynamic function and input gain function derived from equations (12) and (13), respectively; t k The time when the switch occurs. and These are the state transition matrix and pulse vector for the amphibious vehicle at the moments of landing and takeoff, respectively.

[0080] Furthermore, step 4 considers system input-state constraints and constructs suitable performance metrics, including the following steps:

[0081] Step 4-1: For the heterogeneous switching system of the amphibious vehicle obtained in Step 3, construct the following performance indicators:

[0082]

[0083] Where φ(·,·)>φ min >0 indicates switching cost; Δ represents an estimate of the performance index (value function) corresponding to the current joint action strategy; t The sampling interval for integral reinforcement learning is typically set to a value slightly larger than the minimum dwell time. It is a positive definite function of the system state; γ > 0 represents the attenuation coefficient.

[0084] Step 4-2: Considering the problems caused by discontinuous value functions in optimizing subsystem inputs, the Action-Dependent Heuristic Dynamic Programming (ADHDP) method in reinforcement learning is adopted. Equation (17) is further written as:

[0085]

[0086] Wherein, σ(t) + ), This indicates the joint action strategy selected at the switching moment.

[0087] Step 4-3: To complete water rescue missions, amphibious vehicles need to quickly reach designated locations. To maximize the vehicle's maximum operating radius while completing the mission, it's necessary to conserve power, select appropriate system input energy, and rationally plan the number of switching operations. Furthermore, the limitations of the vehicle's rotor and propeller speeds, as well as the limits of maximum airspeed and maximum flight speed, must be considered. It's also important to note that before the vehicle prepares to land in the water, the pitch and roll angles need to be controlled within a small range to ensure stability after landing. To meet these mission requirements, the optimization control problem of the amphibious vehicle is transformed into an optimization control problem considering multiple factors and constraints. Therefore, the following state-dependent obstacle function is designed and incorporated into the cost function of the performance index:

[0088]

[0089] Among them, Q 1 Let Q represent the original system cost function. 2 The barrier function of the design, αi This represents the weighting constant.

[0090] Furthermore, step 5 employs a reinforcement learning optimization algorithm to design an Actor-Critic controller for the amphibious vehicle, including the following steps:

[0091] Step 5-1: During each interval of integral reinforcement learning, the signal switching strategy is improved as follows:

[0092]

[0093] Step 5-2: Based on Step 5-1, optimize the subsystem control input according to the stationary point condition equation:

[0094]

[0095] Step 5-3, combining steps 5-1 and 5-2, yields the joint control decision (switching decision and control input) for the amphibious vehicle:

[0096]

[0097] Based on the obstacle function terms in steps 4 and 5, the optimized controller designed using reinforcement learning can strike a balance between control cost and system performance. Furthermore, as long as the obstacle function is bounded, the state constraints of the amphibious vehicle can be guaranteed to remain within a certain range. To implement the control algorithm proposed in step 5, the Guoyun Industrial Control J1900 shipborne computer was selected for the self-developed amphibious vehicle to meet the computational requirements of the reinforcement learning algorithm. Figure 5 The diagram shown is a schematic of the hardware system of the amphibious vehicle developed by the team. The control algorithm of this invention was applied to the team's self-developed amphibious vehicle and tested in different waters, thus verifying the effectiveness of the algorithm.

[0098] In embodiments of the present invention, such as Figure 6 As shown, another aspect provides an optimized control system for an amphibious vehicle, the system comprising:

[0099] The aerial flight model building unit is used to build a dynamic model of an amphibious vehicle during aerial flight.

[0100] The surface navigation model building unit is used to build a dynamic model of an amphibious vehicle when it navigates on the water.

[0101] The heterogeneous switching system model building unit for amphibious vehicles is used to represent the mode transitions of amphibious vehicles in water surface navigation and air flight using a variable-order switching system, thereby obtaining a heterogeneous switching system model for amphibious vehicles; the performance index construction unit is used to construct appropriate performance indexes for the system.

[0102] Actor-Critic controller design unit, used to design Actor-Critic controllers for air amphibious vehicles using reinforcement learning optimization algorithms;

[0103] The controller verification unit conducts experimental tests on the self-developed amphibious vehicle to verify the effectiveness of the optimized controller designed for the amphibious vehicle.

[0104] This method employs a reinforcement learning action-dependent heuristic dynamic programming approach to reduce reliance on system model knowledge and address the problem of optimizing inputs to switching subsystems using discontinuous value functions.

[0105] In this application, reinforcement learning optimization control is presented as a novel optimization control strategy. It has significant optimization effects, greatly improving the mission execution efficiency of amphibious vehicles while saving power energy and realizing autonomous intelligent control of amphibious vehicles.

[0106] This application comprehensively considers factors such as convergence rate, constraints, control input cost, and switching cost, and establishes performance indicators that are both practically significant and can guide the achievement of optimization goals, thus possessing high engineering practical value.

[0107] For details not described in the optimized control system of an amphibious vehicle provided in the embodiments of this application, please refer to the above-described invention and the optimized control method of an amphibious vehicle provided in the embodiments, which will not be repeated here.

[0108] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, any modifications, improvements and equivalent substitutions made without departing from the principle of the present invention are included within the protection scope of the present invention.

Claims

1. An optimization control method of a water-air amphibious vehicle, characterized by, The method comprises: Step 1, modeling the water-air amphibious vehicle flying in the air as a quadrotor; Step 2, modeling the water-air amphibious vehicle sailing on the water surface as an unmanned ship; Step 3, representing the mode conversion of the water-air amphibious vehicle sailing on the water surface and flying in the air by a variable-order switching system to obtain a heterogeneous switching system model of the water-air amphibious vehicle; Step 4, considering the system input-state limitation, constructing a suitable performance index; Step 5, using a reinforcement learning optimization algorithm to design an Actor-Critic controller for the water-air amphibious vehicle; The heterogeneous switching system model of the water-air amphibious vehicle is obtained by representing the mode conversion of the water-air amphibious vehicle sailing on the water surface and flying in the air by a variable-order switching system, comprising: with denotes the full variables of the system of the water-air amphibious vehicle when flying in the air, denotes the full variables of the system of the water-air amphibious vehicle when sailing on the water, the water-air amphibious vehicle being modeled as a heterogeneous switched system as follows: (4)； (5)； wherein, is a switching signal of the system, is a start time; and are the internal dynamic function and input gain function derived from equation (1) and equation (2), respectively; is a switching time, and are the state transition matrix and impulse vector at the time of the water-air vehicle falling into water and taking off, respectively. Considering the system input-state limitation, constructing a suitable performance index, comprising: Step 4-1, for the heterogeneous switching system of the water-air amphibious vehicle, constructing a performance index as follows: (6)； wherein denotes a switching cost; denotes an estimate of the value function of the performance indicator corresponding to the current joint action policy; is the sampling interval time for integral reinforcement learning, set to a value slightly greater than the minimum dwell time; is a positive definite function on the system state; denotes a decay coefficient; Step 4-2, considering the problem of discontinuous value function optimization for subsystem input, using an Action-Dependent Heuristic Dynamic Programming (ADHDP) method in reinforcement learning to further write formula (6) as follows: (7)； wherein, represents the joint action policy for the switching time instant selection; Step 4-3, considering the phenomenon of state-input limitation of the actual water-air amphibious vehicle in the running process, designing a state-related barrier function as follows: (8)； wherein, represents the original system cost function, represents the designed barrier function, represents the weight constant.

2. The method of optimal control of a hydroair amphibious vehicle according to claim 1, characterized in that, The water-air amphibious vehicle flying in the air is modeled as a quadrotor, comprising: (1)； wherein, denotes the position state of the quadrotor, denote the pitch, roll and yaw angles, respectively; is the mass of the quadrotor, is the distance from the center of the rotor to the center of mass of the body, is the gravitational acceleration, are the moments of inertia of the quadrotor about the three axes, respectively; is the vector of the total lift force of the four motors, the total roll force, the total pitch force and the total yaw force, and is the input of the system.

3. The method of optimal control of a water-air amphibious vehicle according to claim 2, characterized in that, The water-air amphibious vehicle sailing on the water surface is modeled as an unmanned ship, comprising: (2)； wherein, respectively represent the position and the yaw angle, respectively represent the yaw direction velocity, the vertical yaw direction velocity and the yaw velocity, , represents the control input, represents the inertia matrix, represents the system unknown dynamics, represents the system rotation matrix (3)。 4. The method of optimal control of a hydroair amphibious vehicle according to claim 3, characterized in that, The reinforcement learning optimization algorithm is used to design an Actor-Critic controller for the water-air amphibious vehicle, comprising: Step 5-1, in each integral reinforcement learning interval, the switching signal strategy is improved as follows: (9)； Step 5-2, on the basis of step 5-1, the subsystem control input is optimized according to the stationary point condition equation: (10)； Step 5-3, combining step 5-1 and step 5-2, the joint control decision of the water-air amphibious vehicle is obtained: (11)。 5. An optimized control system for a water-air amphibious vehicle, characterized in that, The system comprises: An air flight model establishing unit is configured to establish a dynamic model of the water-air amphibious vehicle flying in the air; A water surface sailing model establishing unit is configured to establish a dynamic model of the water-air amphibious vehicle sailing on the water surface; A water-air amphibious vehicle heterogeneous switching system model establishing unit is configured to represent the mode conversion of the water-air amphibious vehicle sailing on the water surface and flying in the air by a variable-order switching system to obtain a heterogeneous switching system model of the water-air amphibious vehicle; A performance index constructing unit is configured to construct a suitable performance index; An Actor-Critic controller designing unit is configured to use a reinforcement learning optimization algorithm to design an Actor-Critic controller for the water-air amphibious vehicle; The water-air amphibious vehicle heterogeneous switching system model establishing unit is specifically configured to: with denotes the full variables of the system of the water-air amphibious vehicle when flying in the air, denotes the full variables of the system of the water-air amphibious vehicle when sailing on the water, the water-air amphibious vehicle being modeled as a heterogeneous switched system as follows: (4)； (5)； wherein, is a switching signal of the system, is a start time; and are the internal dynamic function and input gain function derived from equation (1) and equation (2), respectively; is a switching time, and are the state transition matrix and impulse vector at the time of water landing and take-off of the amphibious vehicle, respectively. The performance index constructing unit is specifically configured to: Step 4-1, for the heterogeneous switching system of the water-air amphibious vehicle, constructing a performance index as follows: (6)； wherein denotes a switching cost; denotes an estimate of the value function of the performance indicator corresponding to the current joint action policy; is the sampling interval time for integral reinforcement learning, set to a value slightly greater than the minimum dwell time; is a positive definite function on the system state; denotes a decay coefficient; Step 4-2, To solve the problem of discontinuous value function optimization for subsystem input, the Action-Dependent Heuristic Dynamic Programming (ADHDP) method in reinforcement learning is adopted. Equation (6) is further written as: (7)； wherein, represents the joint action policy selected at the switching time instant; Step 4-3, Considering the phenomenon of state-input constraints in the actual water-air amphibious vehicle during operation, the following state-dependent barrier function is designed: (8)； wherein, represents the original system cost function, represents the designed barrier function, represents the weight constant.

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