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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.
《Journal of The Franklin Institute》2023,360(14):10564-10581
In this work, we investigate consensus issues of discrete-time (DT) multi-agent systems (MASs) with completely unknown dynamic by using reinforcement learning (RL) technique. Different from policy iteration (PI) based algorithms that require admissible initial control policies, this work proposes a value iteration (VI) based model-free algorithm for consensus of DTMASs with optimal performance and no requirement of admissible initial control policy. Firstly, in order to utilize RL method, the consensus problem is modeled as an optimal control problem of tracking error system for each agent. Then, we introduce a VI algorithm for consensus of DTMASs and give a novel convergence analysis for this algorithm, which does not require admissible initial control input. To implement the proposed VI algorithm to achieve consensus of DTMASs without information of dynamics, we construct actor-critic networks to online estimate the value functions and optimal control inputs in real time. At last, we give some simulation results to show the validity of the proposed algorithm.  相似文献   

3.
The terminal iterative learning control is designed for nonlinear systems based on neural networks. A terminal output tracking error model is obtained by using a system input and output algebraic function as well as the differential mean value theorem. The radial basis function neural network is utilized to construct the input for the system. The weights are updated by optimizing an objective function and an auxiliary error is introduced to compensate the approximation error from the neural network. Both time-invariant input case and time-varying input case are discussed in the note. Strict convergence analysis of proposed algorithm is proved by the Lyapunov like method. Simulations based on train station control problem and batch reactor are provided to demonstrate the effectiveness of the proposed algorithms.  相似文献   

4.
This paper deals with the problem of iterative learning control algorithm for a class of multi-agent systems with distributed parameter models. And the considered distributed parameter models are governed by the parabolic or hyperbolic partial differential equations. Based on the framework of network topologies, a consensus-based iterative learning control protocol is proposed by using the nearest neighbor knowledge. When the iterative learning control law is applied to the systems, the consensus errors between any two agents on L2 space are bounded, and furthermore, the consensus errors on L2 space can converge to zero as the iteration index tends to infinity in the absence of initial errors. Simulation examples illustrate the effectiveness of the proposed method.  相似文献   

5.
A general system of the time-dependent partial differential equations containing several arbitrary initial and boundary conditions is considered. A hybrid method based on artificial neural networks, minimization techniques and collocation methods is proposed to determine a related approximate solution in a closed analytical form. The optimal values for the corresponding adjustable parameters are calculated. An accurate approximate solution is obtained, that works well for interior and exterior points of the original domain. Numerical efficiency and accuracy of the hybrid method are investigated by two-test problems including an initial value and a boundary value problem for the two-dimensional biharmonic equation.  相似文献   

6.
In this paper, a novel tracking control scheme for continuous-time nonlinear affine systems with actuator faults is proposed by using a policy iteration (PI) based adaptive control algorithm. According to the controlled system and desired reference trajectory, a novel augmented tracking system is constructed and the tracking control problem is converted to the stabilizing issue of the corresponding error dynamic system. PI algorithm, generally used in optimal control and intelligence technique fields, is an important reinforcement learning method to solve the performance function by critic neural network (NN) approximation, which satisfies the Lyapunov equation. For the augmented tracking error system with actuator faults, an online PI based fault-tolerant control law is proposed, where a new tuning law of the adaptive parameter is designed to tolerate four common kinds of actuator faults. The stability of the tracking error dynamic with actuator faults is guaranteed by using Lyapunov theory, and the tracking errors satisfy uniformly bounded as the adaptive parameters get converged. Finally, the designed fault-tolerant feedback control algorithm for nonlinear tracking system with actuator faults is applied in two cases to track the desired reference trajectory, and the simulation results demonstrate the effectiveness and applicability of the proposed method.  相似文献   

7.
This paper studies the neural adaptive control design for robotic systems with uncertain dynamics under the existence of velocity constraints and input saturation. The control objective is achieved by choosing a control Lyapunov function using joint error variables that are restricted to linear growth and furthermore by introducing a secant type barrier Lyapunov function for constraining the joint rate variables. The former is exploited to bind the forward propagation of the position errors, and the latter is utilized to impose hard bounds on the velocity. Effective input saturation is expressed, and neural networks are employed to tackle the uncertainty problem in the system dynamics. Feasibility conditions are formulated, and the optimal design parameters are obtained by solving the constrained optimization problem. We prove that under the proposed method, semi-global uniform ultimate boundedness of the closed-loop system can be guaranteed. Tracking errors meanwhile converge to small neighborhoods of the origin, and violations of predefined velocity constraints are avoided. Finally, numerical simulations are performed to verify the effectiveness of the theoretical developments.  相似文献   

8.
This paper proposes adaptive iterative learning control schemes for robot manipulator systems with iteration-varying lengths. To prove the asymptotical convergence of the joint position tracking error along the iteration axis, this paper develops a new composite energy function based on the newly introduced auxiliary variables for the analysis. Moreover, the traditional assumption of identical initialization condition is relaxed to be arbitrarily varying and then an initial rectifying mechanism is introduced to tackle initial shift problem of robotic systems. Illustrative simulations on a two degree-of-freedom robot manipulator are provided to verify the theoretical results.  相似文献   

9.
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10.
《Journal of The Franklin Institute》2023,360(14):10745-10765
For nonlinear discrete-time systems with non-uniform iteration lengths and random initial state shifts, this paper developed a feedback higher-order iterative learning control (ILC) approach. To compensate the absent information of last iteration caused by non-uniform iteration lengths, the tracking information in both iteration domain and time domain is included in ILC design with the help of higher-order control and feedback control, respectively, while the general ILC schemes just adopt the information in iteration domain. A sufficient condition based on the higher-order ILC gains is derived. It is guaranteed that as the iteration number goes to infinity, the asymptotic bound of tracking error is proportional to random initial state shifts in mathematical expectation sense. Specifically, as the expectation of initial state shifts is zero, the ILC tracking error can be controlled to zero along the iteration direction. Two examples with different initial conditions are provided to validate the proposed ILC approach.  相似文献   

11.
In this paper, a numerical method to solve nonlinear optimal control problems with terminal state constraints, control inequality constraints and simple bounds on the state variables, is presented. The method converts the optimal control problem into a sequence of quadratic programming problems. To this end, the quasilinearization method is used to replace the nonlinear optimal control problem with a sequence of constrained linear-quadratic optimal control problems, then each of the state variables is approximated by a finite length Chebyshev series with unknown parameters. The method gives the information of the quadratic programming problem explicitly (The Hessian, the gradient of the cost function and the Jacobian of the constraints). To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented.  相似文献   

12.
This paper is concerned with the distributed formation control problem of multi-quadrotor unmanned aerial vehicle (UAV) in the framework of event triggering. First, for the position loop, an adaptive dynamic programming based on event triggering is developed to design the formation controller. The critic-only network structure is adopted to approximate the optimal cost function. The merit of the proposed algorithm lies in that the event triggering mechanism is incorporated the neural network (NN) to reduce calculations and actions of the multi-UAV system, which is significant for the practical application. What’s more, a new weight update law based on the gradient descent technology is proposed for the critic NN, which can ensure that the solution converges to the optimal value online. Then, a finite-time attitude tracking controller is adopted for the attitude loop to achieve rapid attitude tracking. Finally, the efficiency of the proposed method is illustrated by numerical simulations and experimental verification.  相似文献   

13.
This paper considers a nonsmooth constrained distributed convex optimization over multi-agent systems. Each agent in the multi-agent system only has access to the information of its objective function and constraint, and cooperatively minimizes the global objective function, which is composed of the sum of local objective functions. A novel continuous-time algorithm is proposed to solve the distributed optimization problem and effectively characterize the appropriate gain of the penalty function. It should be noted that the proposed algorithm is based on an adaptive strategy to avoid introducing the primal-dual variables and estimating the related exact penalty parameters. Additional, it is demonstrated that the state solution of the proposed algorithm achieves consensus and converges to an optimal solution of the optimization problem. Finally, numerical simulations are given and the proposed algorithm is applied to solve the optimal placement problem and energy consumption problem.  相似文献   

14.
The main challenges of modular robot manipulators (MRMs) with the environmental constraints include the avoidance of catastrophic collision and the precious contacting in the whole interaction process. Consequently, an event-triggered optimal interaction control method of MRMs under the complex multi-task constraints is presented in this paper. Firstly, on the basis of the joint torque feedback (JTF) technique, the dynamic model of constrained MRM subsystem is established. Secondly, the sensorless-based decentralized nonlinear disturbance observer (NDOB) is proposed to detect and identify the sudden external collision for each joint. Then, the performance index function is improved to achieve the interaction control, which contains the fusion state variable function, the influence of external collision, the known model term, and the estimation of model uncertainties through the radial basis function neural network (RBFNN) identifier. Further, based on event-triggered mechanism and adaptive dynamic programming (ADP) algorithm, the approximate event-triggered optimal interaction control strategy is acquired by the critic neural network (NN). Next, the closed-loop MRM system is demonstrated to be uniformly ultimately bounded (UUB) through the Lyapunov stability theorem. Finally, the experiments are achieved effectively for each joint on the platform, such that the feasibility and universality of the proposed interaction control approach are testified by the experimental results.  相似文献   

15.
In this paper, an iterative learning control strategy is presented for a class of nonlinear pure-feedback systems with initial state error using fuzzy logic system. The proposed control scheme utilizes fuzzy logic systems to learn the behavior of the unknown plant dynamics. Filtered signals are employed to circumvent algebraic loop problems encountered in the implementation of the existing controllers. Backstepping design technique is applied to deal with system dynamics. Based on the Lyapunov-like synthesis, we show that all signals in the closed-loop system remain bounded over a pre-specified time interval [0,T]. There even exist initial state errors, the norm of tracking error vector will asymptotically converge to a tunable residual set as iteration goes to infinity and the learning speed can be easily improved if the learning gain is large enough. A time-varying boundary layer is introduced to solve the problem of initial state error. A typical series is introduced in order to deal with the unknown bound of the approximation errors. Finally, two simulation examples show the feasibility and effectiveness of the approach.  相似文献   

16.
In this paper, the subspace identification based robust fault prediction method which combines optimal track control with adaptive neural network compensation is presented for prediction the fault of unknown nonlinear system. At first, the local approximate linear model based on input-output of unknown system is obtained by subspace identification. The optimal track control is adopted for the approximate model with some unknown uncertainties and external disturbances. An adaptive RBF neural network is added to the track control in order to guarantee the robust tracking ability of the observation system. The effect of the system nonlinearity and the error caused by subspace modeling can be overcome by adaptive tuning of the weights of the RBF neural network online without any requisition of constraint or matching conditions. The stability of the designed closed-loop system is thus proved. A density function estimation method based on state forecasting is then used to judge the fault. The proposed method is applied to fault prediction of model-unknown fighter F-8II of China airforce and the simulation results show that the proposed method can not only predict the fault, but has strong robustness against uncertainties and external disturbances.  相似文献   

17.
This paper proposes a novel model free adaptive iterative learning control scheme for a class of unknown nonlinear systems with randomly varying iteration lengths. By applying the dynamic linearization technique along the iteration axis, such systems can be transformed into iteration-depended time varying linear systems. Then, an improved model free adaptive iterative learning control scheme can be constructed only using input and output data of the system. From the rigorous theoretical analysis, it is shown that the mathematical expectation of tracking errors converge to zero as iteration increases. This design does not require any dynamic information of the ILC systems and prior information of randomly varying iteration lengths. An illustrative example verifies the effectiveness of the proposed design.  相似文献   

18.
在大型线性方程组的超松弛迭代法求解中,加速因子经常难以确定.应用BP神经网络对其进行训练学习,经过对比分析,得到最佳模型,应用该模型可快速确定加速因子.将该方法应用于石家庄市栾城水文试验基地,计算结果表明,BP人工神经网络有效地解决了地下水数值模拟中加速因子难以确定的问题.  相似文献   

19.
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   

20.
This paper investigates distributed convex optimization problems over an undirected and connected network, where each node’s variable lies in a private constrained convex set, and overall nodes aim at collectively minimizing the sum of all local objective functions. Motivated by a variety of applications in machine learning problems with large-scale training sets distributed to multiple autonomous nodes, each local objective function is further designed as the average of moderate number of local instantaneous functions. Each local objective function and constrained set cannot be shared with others. A primal-dual stochastic algorithm is presented to address the distributed convex optimization problems, where each node updates its state by resorting to unbiased stochastic averaging gradients and projects on its private constrained set. At each iteration, for each node the gradient of one local instantaneous function selected randomly is evaluated and the average of the most recent stochastic gradients is used to approximate the true local gradient. In the constrained case, we show that with strong-convexity of the local instantaneous function and Lipschitz continuity of its gradient, the algorithm converges to the global optimization solution almost surely. In the unconstrained case, an explicit linear convergence rate of the algorithm is provided. Numerical experiments are presented to demonstrate correctness of the theoretical results.  相似文献   

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