Neuro-optimal tracking control for a class of discrete-time nonlinear systems via generalized value iteration adaptive dynamic programming approach

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.

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.

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.

Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach

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.

An iterative adaptive dynamic programming algorithm for optimal control of unknown discrete-time nonlinear systems with constrained inputs

Adaptive dynamic programming for security of networked control systems with actuator saturation

In this chapter, differential games are studied for continuous-time linear and nonlinear systems, including two-player zero-sum games, multi-player zero-sum games, and multi-player nonzero-sum games, via a series of adaptive dynamic programming (ADP) approaches. First, an integral policy iteration algorithm is developed to learn online the Nash equilibrium of two-player zero-sum differential games with completely unknown continuous-time linear dynamics using the state and control data. Second, multi-player zero-sum differential games for a class of continuous-time uncertain nonlinear systems are solved by using a novel iterative ADP algorithm. Via neural network modeling for the system dynamics, the ADP technique is employed to obtain the optimal control pair iteratively so that the iterative value function reaches the optimal solution of the zero-sum differential games. Finally, an online synchronous approximate optimal learning algorithm based on policy iteration is developed to solve multi-player nonzero-sum games of continuous-time nonlinear systems without the requirement of exact knowledge of system dynamics.

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.

Adaptive Dynamic Programming (ADP) is a new way for the complex nonlinear system optimal controller design. But the iteration step requires infinite ensure to find the optimal control law. In this paper, the greed iterative ADP algorithm was improved by adopting-approximate method. Further, the strict mathematical analysis and proof is given. The improved algorithm based in initial state points iterative limited steps to find approximate optimal control law. So reduces the computational complexity, and beneficial to outcome of the project. Simulation illustrate to the algorithm is effective to overcome the difficulty of the infinite iteration.

Neural-network-based output-feedback control with stochastic communication protocols

A neural-network-based finite-horizon optimal tracking control scheme for a class of unknown nonlinear discrete-time systems is developed. First, the tracking control problem is converted into designing a regulator for the tracking error dynamics under the framework of finite-horizon optimal control theory. Then, with convergence analysis in terms of cost function and control law, the iterative adaptive dynamic programming algorithm is introduced to obtain the finite-horizon optimal controller to make the cost function close to its optimal value within an ε-error bound. Furthermore, in order to implement the algorithm via dual heuristic dynamic programming technique, three neural networks are employed to approximate the error dynamics, the cost function, and the control law, respectively. In addition, a numerical example is given to demonstrate the validity of the present approach.

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

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.

Robust oxygen excess ratio control of PEMFC systems using adaptive dynamic programming