Adaptive dynamic programming for optimal tracking control of unknown nonlinear systems with application to coal gasification

Abstract

In this paper, we establish a new data-based iterative optimal learning control scheme for discrete-time nonlinear systems using iterative adaptive dynamic programming (ADP) approach and apply the developed control scheme to solve a coal gasification optimal tracking control problem. According to the system data, neural networks (NNs) are used to construct the dynamics of coal gasification process, coal quality and reference control, respectively, where the mathematical model of the system is unnecessary. The approximation errors from neural network construction of the disturbance and the controls are both considered. Via system transformation, the optimal tracking control problem with approximation errors and disturbances is effectively transformed into a two-person zero-sum optimal control problem. A new iterative ADP algorithm is then developed to obtain the optimal control laws for the transformed system. Convergence property is developed to guarantee that the performance index function converges to a finite neighborhood of the optimal performance index function, and the convergence criterion is also obtained. Finally, numerical results are given to illustrate the performance of the present method. Note to Practitioners Dynamic programming is a useful technique for solving optimal control problems. However, in many cases, it is computationally difficult to apply it due to the backward-in-time calculation or the "curse of dimensionality." ADP is an effective tool for solving optimal control problems forward-in-time. For most ADP algorithms, the accurate system model, the accurate iterative control and the accurate iterative performance index function are required to obtain the optimal control law. These iterative ADP algorithms can be called "accurate iterative ADP algorithms." For many real-world control systems, such as coal gasification systems, the system model is very difficult to construct. The optimal control and optimal performance index function cannot analytically be obtained. These make the accurate iterative ADP algorithms difficult to apply in real-world industrial systems. In this paper, based on the system data, NNs are used to overcome these difficulties, where the approximation errors and control disturbance are both considered. System transformation is introduced that transforms the tracking control system into a two-person zero-sum control system. Iterative ADP algorithm with iteration errors is then established to obtain the optimal control scheme, where the convergence proof is developed.