An automatic controller design method for cluster aircraft systems

Abstract

The present invention discloses a method for automatically designing a controller for a swarm aircraft system, comprising the following steps: 1. Initializing swarm parameters, establishing a kinematic model and a dynamic model for the swarm aircraft system, and clarifying the formation control objectives; 2. Performing theoretical analysis of the swarm aircraft system's formation control based on general Lyapunov function theory; 3. Combining the sum-of-squares optimization method in automated reasoning technology to transform the formation control problem into a corresponding sum-of-squares optimization problem for solution; and 4. Using a designed efficient optimization algorithm, integrating controller design with verification and parameter optimization, the method completes the automatic design of a collaborative controller for the swarm aircraft system. The method implemented by the present invention not only solves controller design challenges in the prior art but also significantly improves the control efficiency of the swarm aircraft system in intelligently completing its target tasks.

Description

Technical field:

[0001] The invention belongs to the field of collaborative control and optimization of cluster systems, and discloses an automatic design method for a controller of a cluster aircraft system. Background technology:

[0002] With the rapid development of automatic control, computer, and aerospace technology, swarm systems, typically represented by multi-aircraft, have been widely used in military and civilian applications, such as multi-aircraft formation control and multi-missile coordinated penetration. Intelligent aircraft swarm systems are centered around collaborative interaction within the swarm and based on individual autonomous control. Through close collaboration among swarm members, swarm systems exhibit superior coordination, intelligence, and autonomy. However, when faced with complex and ever-changing dynamic environments and control tasks, swarm systems often exhibit low autonomy and poor coordination. This is primarily due to the difficulty in designing high-performance controllers for complex swarm systems with demanding control tasks and multiple constraints. Existing methods, such as containment control and adaptive control, often rely heavily on empirical or trial-and-error design, relying heavily on human reasoning based on empirical knowledge. To address this issue, there is an urgent need to develop intelligent controller design methods for swarm aircraft systems that meet practical needs. This invention is dedicated to overcoming the control problems of traditional aircraft cluster systems. Based on the heuristic reasoning function in automatic reasoning technology, it integrates controller design and verification, and parameter optimization, making limited prior knowledge intelligent, thereby designing an efficient optimization algorithm to realize the automatic design of the collaborative controller of the aircraft cluster system, thereby improving the efficiency of the cluster aircraft system in completing tasks intelligently. Summary of the invention:

[0003] This invention proposes an intelligent design method for a controller of a swarm aircraft system, which can solve the problems existing in the prior art. The technical solution is as follows:

[0004] Step 1: Initialize cluster parameters, establish the kinematic and dynamic models of the cluster aircraft system, and clarify the formation control objectives;

[0005] Step 2: Conduct theoretical analysis of the formation control of cluster aircraft systems based on the general Lyapunov function theory;

[0006] Step 3: Combining the sum-of-squares optimization method in automated reasoning technology, the formation control problem is transformed into a corresponding sum-of-squares optimization problem for solution;

[0007] Step 4: Through the designed efficient optimization algorithm, controller design and verification, and parameter optimization are integrated to complete the automatic design of the collaborative controller of the cluster aircraft system.

[0008] This invention automates the deductive reasoning process through automated reasoning technology, transforming the constraint-solving problem in a high-dimensional continuous state space into a series of symbolic calculations that can be automatically implemented on a computer. This allows for the design of efficient optimization algorithms for the automated design of collaborative controllers. This invention not only addresses existing controller design challenges but also enhances the control efficiency of swarm aircraft systems in intelligently completing their missions. Description of the drawings:

[0009] Figure 1 This is an example diagram of the relative coordinate system of the leader-follower cluster aircraft system in the present invention;

[0010] Figure 2 This is an example diagram of the communication topology of the leader-follower cluster aircraft system of the present invention;

[0011] Figure 3 It is a control principle diagram of the leader-follower cluster aircraft system formation in the present invention. Specific implementation method:

[0012] In order to more clearly illustrate the purpose, technical solutions and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0013] Consider a multi-aircraft swarm system consisting of a leader aircraft (numbered 0) and N follower aircraft (numbered 1 to N). The kinematic model of the i-th aircraft can be expressed as:

[0014]

[0015] Among them, x i ,y i , z i is the position of the i-th aircraft in the inertial coordinate system, Represents x i 、y i 、z i The derivative of v represents the derivative with respect to time. i is the speed of the i-th aircraft, θ i The trajectory inclination angle of the i-th aircraft, ψ i The trajectory deviation angle of the i-th aircraft.

[0016] If we regard the aircraft as a mass point system, we can get the simplified dynamic model of the i-th aircraft as follows:

[0017]

[0018] Where g is the acceleration due to gravity, n xi, n yi , n zi is the component of the overload of the i-th aircraft in each coordinate axis in the ballistic coordinate system.

[0019] Let x i =[x i ,y i ,z i ,v i ,θ i ,ψ i ] T ,u i =[n xi ,n yi ,n zi ] T , then equations (1) and (2) can be uniformly expressed as:

[0020]

[0021] in,

[0022]

[0023] There are many different control strategies for multi-aircraft formation flight. The present invention adopts the leader-follower strategy. This formation strategy is the most convenient for the study of cluster control systems with a leader. The relative coordinate relationship is shown in Figure 1 .

[0024] The formation control goal of the cluster aircraft system is: for any initial formation condition, there exists T0>0, so that the cluster system (3) satisfies

[0025]

[0026]

[0027] Then the cluster system (3) is said to realize formation flight under the leader-follower strategy, where p0 = [x0, y0, z0] T and p i =[x i ,y i ,z i ] T Represent the position vectors of the leading aircraft and the i-th follower aircraft, d i represents the desired relative position vector between the leader and the ith follower, and Represent the velocity vectors of the leading aircraft and the i-th follower aircraft respectively. For convenience, let the error vector be expressed as That is, when e i→At 0:00, the leader-follower cluster aircraft system achieved formation flight.

[0028] In order to achieve the above control objectives, the present invention adjusts the overload u of the aircraft by feeding back the error vector of the cluster aircraft system. i , the designed nonlinear control protocol is as follows:

[0029]

[0030] in, is the Laplace matrix, which describes the communication topology between aircraft (see Figure 2 , the arrow’s head receives the information transmitted by the arrow’s tail), and h(·) is the nonlinear coupling function to be designed. It is worth noting that the leader aircraft, as a signal generator, will generate a reference trajectory for the follower aircraft to track. Therefore, the leader aircraft can access the follower aircraft’s information, but the follower aircraft cannot access the leader aircraft’s information, that is, L 0j = 0 for any j = 1, ..., N, so u0 ≡ 0. N is the number of follower aircraft. Based on formula (6), during the flight of the cluster aircraft system, the required overload u for each follower aircraft is calculated. i , used to control each follower aircraft.

[0031] The required overload u of each follower aircraft will be calculated i The device (such as software, hardware, firmware or a combination thereof) is called a controller to be implemented, and the controller is optionally further configured to convert the calculated overload u i Applied to each following aircraft. Still optionally, the controller also obtains the error vector e of each aircraft i .

[0032] To achieve automatic controller design, we use the general Lyapunov function to prove the convergence of the trajectory (i.e., the control protocol (6) is designed so that all the follower aircraft in the cluster system perfectly track the trajectory of the leader aircraft). Let where V(·) is a continuously differentiable, radially unbounded positive definite function that satisfies the following equation:

[0033]

[0034]

[0035]

[0036] in, represents the partial derivative of the function V(·), F q (a,b)=q(a)-q(b),H q,W(a,b)=(q(a)-q(b)) T W(q(a)-q(b)), q(·) is a continuous function, W is a positive semidefinite matrix, Γ=BB T is a positive semidefinite diagonal matrix.

[0037] By solving the above constraints, we can find the desired Lyapunov function V(·) and nonlinear coupling function h(·) to realize the automatic design of control protocol (6). However, constraints (7), (8) and (9) are inherently complex, because even checking the non-negativity of a fourth-order polynomial is an NP-hard problem. Since the sum of squares (SOS) polynomial has the property of complete non-negativity, for the system described by the polynomial vector field, we can use the sum of squares decomposition method in the automatic reasoning technology to perform algebraic characterization and reasoning analysis on the formation control problem of the aircraft cluster system, and transform it into a sum of squares optimization problem on a semi-algebraic set that can be solved by a computer, as follows:

[0038]

[0039]

[0040]

[0041] where V(·) is a continuously differentiable positive definite square sum polynomial function, is a known monomial vector function (for example, is a 2nd order monomial vector function, then is the semi-positive definite matrix to be solved. Furthermore, the semi-algebraic set condition (8) still involves a bilinear non-convex optimization problem, which has high computational complexity. Therefore, we can transform it into a corresponding convex optimization problem, thereby simplifying the automatic solution process of the polynomial Lyapunov function V(·) and the coupling function h(·).

[0042] choose

[0043]

[0044] and

[0045]

[0046] Among them, a j (·) is a monomial function (j = 1,…,m, and m represents the number of monomial functions), k j (j=0,…,m) are real coefficients to be determined; b j(·) is a monomial vector function, (j = 1,…,n, and n represents the number of monomial vector functions), l j (j=0,…,n) are real coefficients to be determined.

[0047] First, solve the following optimization problem 1:

[0048] find

[0049] st

[0050]

[0051]

[0052] This gives a set of coefficients k0, k1, ..., k m , that is, the initial solution of the Lyapunov function is obtained, which is expressed as V′(·).

[0053] Then, substitute it into the following optimization problem 2:

[0054] find

[0055] st

[0056]

[0057]

[0058]

[0059] If there exists a feasible solution l0,l1,…,l n , the polynomial coupling function h(·) can be obtained, and then the control protocol (6) can be obtained; if there is no feasible solution, the order of V(·) in the optimization problem 1 can be adjusted, that is, the number of monomial functions m can be changed (for example, in the 2D state, the 2nd order V(·) satisfies m=5, and the 3rd order V(·) satisfies m=9). Thus, through continuous iterative updates, the desired polynomial Lyapunov function V(·) and coupling function h(·) can be solved, and the automatic design of the controller can be completed while achieving the formation control goal. The control principle diagram can be seen in Figure 3 .

[0060] It should be noted that the mathematical model (3) of the swarm aircraft system contains non-polynomial terms, namely sin(·), cos(·), and therefore cannot be solved directly using the square sum optimization tool. We can use mathematical methods such as Taylor series expansion to mathematically approximate the non-polynomial terms; we can also use the following variable replacement method, namely ζ i = sinθ i , ηi =cosθ i ,λ i =sinψ i , μ i =cosψ i , while optimizing Problems 1 and 2 will be accompanied by equality constraints and

[0061] According to the method of the embodiment of the present invention, we integrate controller design and verification with parameter optimization, which not only realizes the automatic design of the collaborative controller of the cluster aircraft system, but also greatly improves the control efficiency of the cluster aircraft system in intelligently completing the target task.

[0062] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for automatically designing a controller for a swarm aircraft system, wherein the swarm aircraft system includes a leader aircraft and N follower aircraft, the method comprising the following steps: Step 1: Obtain the parameters of the cluster aircraft system, establish the kinematic model and dynamic model of the cluster aircraft system, and use the cluster aircraft system to realize the trajectory error e between all follower aircraft and the leader aircraft during formation flight. i Establish a formation control target and a control protocol for achieving the formation control target; wherein the kinematic model and dynamic model of the swarm aircraft system are uniformly expressed as: x i represents the state vector of the i-th aircraft, u i represents the control vector of the i-th aircraft; Step 2: Construct a general Lyapunov function for the trajectory errors of all follower aircraft and the leader aircraft based on the formation control target in is the error vector, p0 and p i Represent the position vectors of the leading aircraft and the i-th follower aircraft, d i represents the desired relative position vector between the leader and the ith follower, and Represent the velocity vectors of the leading aircraft and the i-th follower aircraft respectively; V(·) is a continuously differentiable, radially unbounded positive definite function that satisfies the first set of formulas; in, represents the partial derivative of the function V(·), F q (a,b)=q(a)-q(b),H q,W (a,b)=(q(a)-q(b)) T W(q(a)-q(b)), q(·) is a continuous function, W is a positive semidefinite matrix, Γ=BB T is a positive semidefinite diagonal matrix; Step 3: Convert the first set of formulas satisfied by V(·) into a sum-of-squares SOS optimization problem on a semi-algebraic set as follows: where V(·) is a continuously differentiable positive definite square sum polynomial function, is a known monomial function, is the positive semidefinite matrix to be solved; In step 3, let as well as Among them, a j (·) is a monomial function, k j is the real coefficient to be determined, b j (·) is a monomial vector function, l j is the real coefficient to be determined, and solve the following optimization problem 1: find k0,k1,…,k m , st This gives a set of coefficients k0, k1, ..., k m , that is, the initial Lyapunov function V′(·) is obtained and substituted into the optimization problem 2: st Solve optimization problem 2 and obtain feasible solutions l0,l1,…,l n , and then obtain h(·) and the designed control protocol; Step 4: Generate a controller for the swarm aircraft system according to the control protocol.

2. The automatic controller design method for a swarm aircraft system according to claim 1, characterized in that: In step 1, x i =[x i ,y i ,z i ,v i ,θ i ,ψ i ] T represents the state vector, u i =[n xi ,n yi ,n zi ] T represents the control vector, x i ,y i , z i is the position of the ith aircraft in the cluster aircraft system in the inertial coordinate system, v i is the speed of the i-th aircraft, θ i The trajectory inclination angle of the i-th aircraft, ψ i The trajectory angle of the i-th aircraft, g is the acceleration of gravity, n xi , n yi , n zi is the component of the overload of the i-th aircraft in each coordinate axis in the ballistic coordinate system, 3. The automatic controller design method for a swarm aircraft system according to claim 2, characterized in that: In step 2, when e i →0, the cluster aircraft system realizes formation flight, where p0 = [x0, y0, z0] T , p i =[x i ,y i ,z i ] T , and 4. The automatic controller design method for a swarm aircraft system according to claim 3, characterized in that: The control protocol in step 1 is in, is the Laplace matrix, which describes the communication topology between the aircraft in the cluster aircraft system, and h(·) is the nonlinear coupling function to be designed.

5. The automatic controller design method for a swarm aircraft system according to claim 4, characterized in that: In step 3, In solving the optimization problem 2, if there is no feasible solution, it is necessary to adjust the order of V(·) in the optimization problem 1, and re-solve the optimization problem 1 to obtain the initial V′(·), which is then inserted into the optimization problem 2 and solved. Through cyclic iterative updates, the desired polynomial Lyapunov function V(·) and coupling function h(·) are solved.

6. The automatic controller design method for a swarm aircraft system according to claim 5, characterized in that: In step 3, the Taylor series expansion method is used to calculate f(x i ) and sin(·) and cos(·) in B are mathematically approximated; or Using the variable replacement method, let ζ i = sinθ i , η i =cosθ i ,λ i =sinψ i , μ i =cosψ i , and the optimization problem to be solved will be accompanied by equality constraints and 7. An information processing device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 6 is implemented.

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