Data-Driven Tracking Control With Adaptive Dynamic Programming for a Class of Continuous-Time Nonlinear Systems

A data-driven adaptive tracking control approach is proposed for a class of continuous-time nonlinear systems using a recent developed goal representation heuristic dynamic programming (GrHDP) architecture. The major focus of this paper is on designing a multivariable tracking scheme, including the filter-based action network (FAN) architecture, and the stability analysis in continuous-time fashion. In this design, the FAN is used to observe the system function, and then generates the corresponding control action together with the reference signals. The goal network will provide an internal reward signal adaptively based on the current system states and the control action. This internal reward signal is assigned as the input for the critic network, which approximates the cost function over time. We demonstrate its improved tracking performance in comparison with the existing heuristic dynamic programming (HDP) approach under the same parameter and environment settings. The simulation results of the multivariable tracking control on two examples have been presented to show that the proposed scheme can achieve better control in terms of learning speed and overall performance.

I. Introduction

The tracking control problem is a challenging topic in the control system field as it aims to enable system states follow specific reference trajectories, rather than keep system states at the origin. The classical feedback control strategy is used for the tracking control based on the system model and all measured variables [1], [2], and the linearization technique is often used before the feedback control design for nonlinear systems. Therefore, such approach is based on enough system information and is usually effective on the specific operation point. The control performance would be deteriorated and even lose effect if the prior information of system model and parameter values has been changed. Although nonlinear control approaches have been proposed in the last several decades [3]–[5], such as backstepping control, sliding mode control, and observer-based nonlinear control, they still require the prior information of the system model. With the difficulty in the system description, the adaptive learning controllers were proposed and gradually developed [6]–[9]. This approach is better performance and has less limitation on models, parameter values, and disturbances [10], [11], hence this type of control design is very promising toward to the further control field and has attracted much attention on the topic.