A neuro-optimal control method of modular robot manipulators based on nonzero-sum game strategy

Major challenges of controlling human-robot collaboration (HRC)-oriented modular robot manipulators (MRMs) include the estimation of human motion intention while cooperating with a robot and performance optimization. This article proposes a cooperative game-based approximate optimal control method of MRMs for HRC tasks. A harmonic drive compliance model-based human motion intention estimation method is developed using robot position measurements only, which forms the basis of the MRM dynamic model. Based on the cooperative differential game strategy, the optimal control problem of HRC-oriented MRM systems is transformed into a cooperative game problem of multiple subsystems. By taking advantage of the adaptive dynamic programming (ADP) algorithm, a joint cost function identifier is developed via the critic neural networks, which is implemented for solving the parametric Hamilton-Jacobi-Bellman (HJB) equation and Pareto optimal solutions. The trajectory tracking error under the HRC task of the closed-loop MRM system is proved to be ultimately uniformly bounded (UUB) by the Lyapunov theory. Finally, experiment results are presented, which reveal the advantage of the proposed method.

In this paper, an on-line adaptive dynamic programming (ADP) algorithm is presented to solve the optimal control problem for continuous-time nonlinear systems with control constraints. First, a suitable non-quadratic performance function is introduced to confront control constraints, and then we present an on-line ADP algorithm in which dynamic programming techniques and neural networks are used to solve the optimal control problem for nonlinear systems with control constraints, which is completely different with the traditional ADP algorithm using off-line training, and the corresponding convergence proof is given. Finally, a simulation examples is given to demonstrate the convergence and feasibility of the proposed algorithm.

In this paper, an optimal tracking control approach based on adaptive dynamic programming (ADP) algorithm is proposed to solve the linear quadratic regulation (LQR) problems for unknown discrete-time systems in an online fashion. First, we convert the optimal tracking problem into designing infinite-horizon optimal regulator for the tracking error dynamics based on the system transformation. Then we expand the error state equation by the history data of control and state. The iterative ADP algorithm of policy iteration (PI) and value iteration (VI) are introduced to solve the value function of the controlled system. It is shown that the proposed ADP algorithm solves the LQR without requiring any knowledge of the system dynamics. The simulation results show the convergence and effectiveness of the proposed control scheme.

In this paper, a finite-horizon ε-optimal control for a class of nonlinear systems with state delay is proposed by Adaptive Dynamic Programming (ADP) algorithm. First of all, the performance index function is defined and the Hamilton-Jacobi-Bellman (HJB) equation is obtained for the problem, the convergence of the iterative algorithm is also presented. Then, ADP algorithm for finite-horizon optimal control is introduced with an ε-error bound so as to get the ε-optimal control, and BP neural network is used to implement ADP algorithm. At last, an example is given to demonstrate the effectiveness of the proposed algorithm.

This paper studies an online adaptive dynamic programming (ADP) algorithm for linear fixed-time impulse systems. The ADP algorithm follows the value iteration method, updating the value approximation and the control law iteratively. In the algorithm, a single network structure is adopted. The single critic network approximates the objective value function. Online training of the value function and the control laws are implemented at each iteration. The network approximated value function converges to the optimal one of the impulse system. Simulations are also presented for the validity of the presented algorithm.

This paper is concerned with a new iterative adaptive dynamic programming (ADP) algorithm to solve optimal control problems for infinite horizon discrete-time nonlinear systems using a numerical controller. The convergence conditions of the iterative ADP are developed considering the errors by the numerical controller which show that the iterative performance index functions can converge to the greatest lower bound of all performance indices within a finite error bound. Neural networks and digital computer are used to approximate the iterative performance index function and compute the numerically iterative control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, a simulation example is given to illustrate the performance of the present method.

Optimal control of Markovian jump systems via a neural network-based ADP iterative algorithm

In this paper, we propose a new approach to address robust control problem of nonlinear systems with uncertainties based on an adaptive dynamic programming (ADP) algorithm. After reformulating the robust control problem as an optimal control problem, we propose a modified ADP method to solve the derived Hamilton-Jacobi-Bellman (HJB) equation, where the optimal cost function is approximated by online training a critic neural network (NN). Then the approximated optimal control action can be derived to guarantee the stability of the controlled system with uncertainties. The closed-loop system stability and convergence have been proved. A simulation example is provided to illustrate the effectiveness of the method.

In this paper, a new generalized policy iteration (GPI) based adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite horizon discrete-time nonlinear systems. The GPI algorithm is a general idea of interacting policy and value iteration algorithms of ADP. There are two iteration indices, which iterate for policy improvement and policy evaluation, respectively, in the GPI algorithm. The convergence properties of the GPI algorithm are developed. Finally, simulation results are presented to illustrate the performance of the developed algorithm.

In this paper, a novel iterative adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. When the iterative control law and iterative performance index function in each iteration cannot be accurately obtained, it is shown that the iterative controls can make the performance index function converge to within a finite error bound of the optimal performance index function. Stability properties are presented to show that the system can be stabilized under the iterative control law which makes the present iterative ADP algorithm feasible for implementation both on-line and off-line. Neural networks are used to approximate the iterative performance index function and compute the iterative control policy, respectively, to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

In this paper, a new iterative optimal learning control scheme for discrete-time nonlinear systems using iterative adaptive dynamic programming (ADP) approach is developed to obtain the optimal control law for coal gasification control systems. For the unknown coal gasification process, neural networks (NNs) are introduced to reconstruct the dynamics of the gasification process, where the approximation errors of the reconstruction dynamics are considered. Via system transformation, the optimal tracking control problem with approximation errors is transformed into a two-person zero-sum optimal control problem. A new iterative ADP algorithm is then developed to obtain the optimal control law for the transformed system with convergence analysis. Finally, numerical results are given to illustrate the performance of the present method.

An optimal control strategy based on adaptive dynamic programming (ADP) algorithm is proposed for the typical optimal control problem of missile interceptor with control constraints. This method is based on ADP algorithm control architecture and using BP neural network has great advantages in approximating nonlinear systems to approach the cost function and optimal control strategy by on-line iteration. Experimental results show that: Compared with the traditional control policy, this controller improves the control accuracy of missile interception process, and the system robustness is also significantly enhanced, and the control performance is better.

This paper presents a functional model predictive control (MPC) approach based on an adaptive dynamic programming (ADP) algorithm with the abilities of handling control constraints and disturbances for the optimal control of nonlinear discrete-time systems. In the proposed ADP-based nonlinear MPC (NMPC) structure, a neural-network-based identification is established first to reconstruct the unknown system dynamics. Then, the actor-critic scheme is adopted with a critic network to estimate the index performance function and an action network to approximate the optimal control input. Meanwhile, as the MPC strategy can effectively determine the current control by solving a finite horizon open-loop optimal control problem, in the proposed algorithm, the infinite horizon is decomposed into a series of finite horizons to obtain the optimal control. In each finite horizon, the finite ADP algorithm solves the optimal control problem subject to the terminal constraint, the control constraint, and the disturbance. The uniform ultimate boundedness of the closed-loop system is verified by the Lyapunov approach. Finally, the ADP-based NMPC is conducted on two different cases and the simulation results demonstrate the quick response and strong robustness of the proposed method.

This paper deals with optimal tracking control problems for a class of discrete-time nonlinear systems using a generalized policy iteration adaptive dynamic programming (ADP) algorithm. First, by system transformation, the optimal tracking control problem is transformed into an optimal regulation problem. Then the generalized policy iteration ADP algorithm is employed to obtain the optimal tracking controller with convergence and optimality analysis. The developed algorithm uses the idea of two iteration procedures to obtain the iterative tracking control laws and the iterative value functions. Three neural networks, including model network, critic network and action network, are used to implement the developed algorithm. At last, an simulation example is given to demonstrate the effectiveness of the developed method.

In this paper, an innovative adaptive dynamic programming (ADP) algorithm with fast convergence speed is designed for the optimal containment control problem of discrete‐time linear multi‐agent systems. Precisely, a quadratic input energy cost function, including local containment error information and actuator information in the neighborhood, is designed for each follower. Solving the stationary condition of the cost function, the optimal containment controllers are obtained. Traditional ADP methods use actor–critic neural networks to approximate optimal costs and control strategies, it is time‐consuming to solve large‐scale multi‐agent problems due to the computational complexity of neural networks. In order to seek faster convergence speed of optimal containment control without knowing the model information, the fast ADP algorithm framework is designed, it is proved theoretically that the convergence speed is determined by some configurable parameters, and the whale optimization algorithm is employed to globally optimize the parameters of given spaces to derive the optimal configuration. Finally, numerical simulation results are given to verify the effectiveness of the designed algorithm.