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1.
In this paper, the optimal consensus control problem of nonlinear multi-agent systems(MASs) with completely unknown dynamics is considered. The problem is formulated in a differential graphical game approach which can be solved by Hamilton-Jacobi (HJ) equations. The main difficulty in solving the HJ equations lies in the nonlinear coupling between equations. Based on the Adaptive Dynamic Programming (ADP) technique, an VI-PI mixed HDP algorithm is proposed to solve the HJ equations distributedly. With the PI step, a suitable iterative initial value can be obtained according to the initial policies. Then, VI steps are run to get the optimal solution with exponential convergence rate. Neural networks (NNs) are applied to approximate the value functions, which makes the data-driven end-to-end learning possible. A numerical simulation is conducted to show the effectiveness of the proposed algorithm.  相似文献   

2.
This paper studies the verification of multi-potential games with a given partition, and proposes a kind of multi-potential equation based on semi-tensor product of matrices. Firstly, the basis of each player’s potential function is constructed, based on which, a new formula is established for the calculation of each player’s potential function. Secondly, a new potential equation is proposed for the verification of potential games via each player’s potential function. Using the new potential equation, a kind of multi-potential equation is constructed for the verification of multi-potential games with a given partition. It is proved that a finite game is a multi-potential game with a given partition if and only if the multi-potential equation has solution. In addition, all possible potential functions are obtained for each group of the partition. An illustrative example is worked out to show the effectiveness of the obtained new results.  相似文献   

3.
At present, gradient iteration methods have been used to solve various Sylvester matrix equations and proved effective. Based on this method, we generalize the factor gradient iterative method (FGI) for solving forward periodic Sylvester matrix equations (FPSME) and backward periodic Sylvester matrix equations (BPSME). To accelerate the convergence of the iterative method, we refer to Gauss-Seidel and Jacobi iterative construction ideas and use the latest matrix information in the FGI iterative method to obtain the modified factor gradient iterative (MFGI) method. Then, the convergence of the proposed methods and the selection of optimal factors are proved. The last numerical examples illustrate the effectiveness and applicability of the iterative methods.  相似文献   

4.
This paper focuses on constructing a conjugate gradient-based (CGB) method to solve the generalized periodic coupled Sylvester matrix equations in complex space. The presented method is developed from a point of conjugate gradient methods. It is proved that the presented method can find the solution of the considered matrix equations within finite iteration steps in the absence of round-off errors by theoretical derivation. Some numerical examples are provided to verify the convergence performance of the presented method, which is superior to some existing numerical algorithms both in iteration steps and computation time.  相似文献   

5.
The purpose of this paper is to present an iterative algorithm for solving the general discrete-time periodic Sylvester matrix equations. It is proved by theoretical analysis that this algorithm can get the exact solutions of the periodic Sylvester matrix equations in a finite number of steps in the absence of round-off errors. Furthermore, when the discrete-time periodic Sylvester matrix equations are consistent, we can obtain its unique minimal Frobenius norm solution by choosing appropriate initial periodic matrices. Finally, we use some numerical examples to illustrate the effectiveness of the proposed algorithm.  相似文献   

6.
By means of the real linear operator, we establish an iterative algorithm for solving a class of complex generalized coupled Sylvester matrix equations. The finite termination of the proposed algorithm is proved. By representing a complex matrix as a larger real matrix, we present a new method to prove that the minimum-norm solution or minimum-norm least squares solution of the complex generalized coupled Sylvester matrix equations can be obtained by an appropriate selection for the initial matrices, which has not been found in the existing work. Numerical experiments on some randomly generated data and practical image restoration problem show that the proposed algorithm is feasible and effective.  相似文献   

7.
In this paper, the stabilization is studied for a complex dynamic model which involves nonlinearities, uncertainty, and Lévy noises. This paper also discusses the controller discretization and presents a new algorithm to obtain the upper bound for the sample interval through which the exponential stability of the discrete system can still be guaranteed. Firstly, an integral sliding surface is designed to obtain the sliding mode dynamics for the considered stochastic Lévy process. By using Lyapunov theory, generalized Itô formula and some inequality techniques, the exponential stability is proved in the sense of mean square for sliding mode dynamics. The reachability of the sliding mode surface is also ensured by designing a sliding mode control law. Secondly, the continuous-time controller is discretized from the point of control cost, and the squared difference is analyzed for the states before and after the discretization. Different from those classical stochastic differential equations driven by Brownian motions, the noise is supposed to be Lévy type and the squared difference is analyzed in different cases. Furthermore, we obtain the largest sampling interval through which the discretized controller can still stabilize the Lévy process driven stochastic system. Finally, a simulation for a drill bit system is given to demonstrate the results under the algorithms.  相似文献   

8.
Riccati differential equations are a class of first-order quadratic ordinary differential equations and have various applications in systems and control theory. In this study, we analyzed a switched Riccati differential equation driven by a Poisson-like stochastic signal. We specifically focused on computing the mean escape time of the switched Riccati differential equation. The contribution of this study is twofold. We first show that, under the assumption that the subsystems described as deterministic Riccati differential equations escape in finite time regardless of their initial state, the mean escape time of the switched Riccati differential equation admits a power series expression. To further expand the applicability of this result, we then present an approximate formula to compute the escape time of deterministic Riccati differential equations. Numerical simulations were performed to illustrate the obtained results.  相似文献   

9.
In this study, a robust fractional-order controller design methodology for a type of fractional-order or integer-order model with dead time is proposed using phase and gain margin specifications. The delayed Bode’s ideal transfer function is used as a reference model to design the controller analytically. The delay term in delayed Bode’s ideal transfer function provides the exact determination of these frequency domain specifications when the system owns a dead time. The analytical robust controller design problem is transformed to solving four nonlinear equations with four unknown variables, two of which are the desired specifications; namely, phase and gain margins. The remaining two are the phase and gain cross-over frequencies. Next, some conditions are set based on the desired specifications so that nonlinear equations provide a unique solution. The proposed method is compared with the other existing robust controller methods based on the same frequency domain specifications. The simulation results reveal that the proposed method outperforms the other methods and also gives closer outcomes to the desired specifications.  相似文献   

10.
There are many hybrid stochastic differential equations (SDEs) in the real-world that don’t satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory.  相似文献   

11.
The paper studies the iterative solutions of the generalized coupled Sylvester transpose matrix equations over the reflexive (anti-reflexive) matrix group by the generalized conjugate direction algorithm. The convergence analysis shows that the solution group can be obtained within finite iterative steps in the absence of round-off errors for any initial given reflexive (anti-reflexive) matrix group. Furthermore, we can get the minimum-norm solution group by choosing special kinds of initial matrix group. Finally, some numerical examples are given to demonstrate the algorithm considered is quite effective in actual computation.  相似文献   

12.
An Impact Angle, Speed and Acceleration Control Guidance (IASAG) law against the stationary target is proposed, which is critical for the effectiveness of the air-to-surface guided weapons. It is hard to address multiple terminal constraints problem for unpowered missile, especially including terminal speed constraint, which is uncontrollable state. Based on Line-of-Sight (LOS) angle, a fourth-order polynomial function is designed to make the number of coefficients of the function equal to number of boundary conditions. Through analytic calculation and transformation, the relation between the specified boundary conditions and the coefficients are established. The coefficient equations are reduced to a univariate nonlinear equation whose solution is determined by terminal speed constraint. Based on the characteristic of the nonlinear equation, we propose a Particle Swarm Optimization(PSO) method to find the coefficient that satisfies terminal speed constraint. According to Lyapunov stability theory, an asymptotically stable trajectory tracking controller is designed to track the reference leading angle with respect to range-to-go to guarantee the impact angle, speed and acceleration constraints. The effectiveness of the proposed guidance law is verified through numerical simulations.  相似文献   

13.
This paper considers a trilayer Stackelberg game problem for nonlinear system with three players. A novel performance function is defined for each player, which depends on the coupling relationships with the other two players. The coupled Hamilton–Jacobi–Bellman (HJB) equations are built from the performance functions, and the optimal control polices of three players are obtained based on the Bellman’s principle of optimality. Because of the nonlinearity and coupling characteristics, a policy iteration (PI) algorithm with a three-layer decision-making framework is developed to online learn the coupled HJB equations. In order to implement the algorithm, we construct a critic-action neural network (NN) structure and design a NN approximation-based iteration algorithm. Finally, a simulation example is presented to verify the effectiveness of the proposed method.  相似文献   

14.
This paper addresses the synchronization problem of fractional-order complex spatiotemporal networks (CSNs) based on partial differential equations with delays via boundary control. First, fractional-order CSNs with time-invariant and time-varying delays are studied separately due to the widespread existence of time delays in complex networks. Moreover, two boundary controllers are proposed to solve the synchronization issue of fractional-order CSNs, in which nodes communicate with each other only on the spatial boundary. Furthermore, according to the fractional-order inequality, the synchronization criteria of fractional-order CNSs with multiple delays are obtained. Finally, the numerical simulations are given to verify the feasibility of the presented results. A case provides the application of CSNs in image encryption.  相似文献   

15.
Sylvester quaternion tensor equations have a wide range of applications in image processing and system and control theory. In this paper, by the Kronecker product and vectorization operator and the properties of quaternion tensors, we focus mainly on proposing the tensor form of the generalized product-type biconjugate gradient method for solving generalized Sylvester quaternion tensor equations. As an application, we apply the proposed method to restore a blurred and noisy-free color video. The obtained numerical results illustrate the effectiveness of our method compared with some existing methods.  相似文献   

16.
This paper focuses on the numerical solution of a class of generalized coupled Sylvester-conjugate matrix equations, which are general and contain many significance matrix equations as special cases, such as coupled discrete-time/continuous-time Markovian jump Lyapunov matrix equations, stochastic Lyapunov matrix equation, etc. By introducing the modular operator, a cyclic gradient based iterative (CGI) algorithm is provided. Different from some previous iterative algorithms, the most significant improvement of the proposed algorithm is that less information is used during each iteration update, which is conducive to saving memory and improving efficiency. The convergence of the proposed algorithm is discussed, and it is verified that the algorithm converges for any initial matrices under certain assumptions. Finally, the effectiveness and superiority of the proposed algorithm are verified with some numerical examples.  相似文献   

17.
This study presents a new framework for merging the Adaptive Fuzzy Sliding-Mode Control (AFSMC) with an off-policy Reinforcement Learning (RL) algorithm to control nonlinear under-actuated agents. In particular, a near-optimal leader-follower consensus is considered, and a new method is proposed using the framework of graphical games. In the proposed technique, the sliding variables’ coefficients are considered adaptively tuned policies to achieve an optimal compromise between the satisfactory tracking performance and the allowable control efforts. Contrary to the conventional off-policy RL algorithms for consensus control of multi-agent systems, the proposed method does not require partial knowledge of the system dynamics to initialize the RL process. Furthermore, an actor-critic fuzzy methodology is employed to approximate optimal policies using the measured input/output data. Therefore, using the tuned sliding vector, the control input for each agent is generated which includes a fuzzy term, a robust term, and a saturation compensating term. In particular, the fuzzy system approximates a nonlinear function, and the robust part of the input compensates for any possible mismatches. Furthermore, the saturation compensating gain prevents instability due to any possible actuator saturation. Based on the local sliding variables, the fuzzy singletons, the bounds of the approximation errors, and the compensating gains are adaptively tuned. Closed-loop asymptotic stability is proved using the second Lyapunov theorem and Barbalat's lemma. The method's efficacy is verified by consensus control of multiple REMUS AUVs in the vertical plane.  相似文献   

18.
This paper discusses the fixed-time leader-following consensus problem for multiple uncertain nonholonomic systems, which are widely used in engineering models. According to our literature review, either the system is assumed to be known, or the uncertainty only contains state information, which does not meet the actual requirements. For this reason, this paper investigates more general nonholonomic systems with uncertainties driven by inputs and states. First, a fixed-time adaptive distributed observer is proposed to estimate the leader’s state and structural parameters, which ensures that the estimation errors converge to zero within a fixed time. Second, two regulator equations based on the idea of cooperative output regulation are constructed, and a novel observer-based distributed switching control law is proposed. This control law overcomes the nonholonomic constraints and appropriately relaxes the assumptions of uncertain functions in the existing references. Finally, the simulation results verify the effectiveness of the proposed control scheme.  相似文献   

19.
通过调查和分析的方式了解当前高职院校对各级各类技能竞赛成果的学时量认定标准和转换规则,发现存在学时量认定标准不统一,学分转换规则过于笼统等问题。提出建立以下三个规则的建议:由赛项组织单位制定和提交申请、国家学分银行审核的成果认定标准确定规则,由个人用户提出申请、国家学分银行审核和储存的成果积累规则,由个人用户申请、职业院校审核和反馈、国家学分银行备案的成果转换规则。  相似文献   

20.
This paper proposes an adaptive data-driven fault-tolerant control scheme using the Koopman operator for unknown dynamics subjected to nonlinearities, time-varying loss of effectiveness, and additive actuator faults. The main objective of this method is to design a virtual actuator to hide actuator faults from the view of the system’s nominal controller without having any prior knowledge about the system’s underlying dynamics. The designed virtual actuator is placed between the faulty plant and the nominal controller of the system to keep the dynamical system’s performance consistent before and after the occurrence of actuator faults. Based on the Koopman operator theory, an equivalent Koopman predictor is first obtained using the process data only, without knowing the governing equations of the underlying dynamics. Koopman operator is an infinite-dimensional, linear operator which takes the nonlinear process data into an infinite-dimensional feature space where the dynamic data correlations have linear behavior. Next, based on the approximated system’s Koopman operator, a virtual actuator is designed and implemented without knowing the system’s nominal controller. Needless to use a separate fault detection, isolation, and identification module to perform fault-tolerant control, the current method leverages the adaptive framework to keep the system’s desired performance in facing time-varying additive and loss of effectiveness actuator faults. Finally, the approach’s efficacy is demonstrated using simulation on a two-link manipulator benchmark, and a comparison study is presented.  相似文献   

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