Tracking Control Of Continuous-time Systems Research Articles

Adaptive optimal output tracking of continuous-time systems via output-feedback-based reinforcement learning

Reinforcement learning provides a powerful tool for designing a satisfactory controller through interactions with the environment. Although off-policy learning algorithms were recently designed for tracking problems, most of these results either are full-state feedback or have bounded control errors, which may not be flexible or desirable for engineering problems in the real world. To address these problems, we propose an output-feedback-based reinforcement learning approach that allows us to find the optimal control solution using input–output data and ensure the asymptotic tracking control of continuous-time systems. More specifically, we first propose a dynamical controller revised from the standard output regulation theory and use it to formulate an optimal output tracking problem. Then, a state observer is used to re-express the system state. Consequently, we address the rank issue of the parameterization matrix and analyze the state re-expression error that are crucial for transforming the off-policy learning into an output-feedback form. A comprehensive simulation study is given to demonstrate the effectiveness of the proposed approach.

Comments on “On-line optimal tracking control of continuous-time systems”

In this note, we discuss a previously published paper by Chou et al. [Chou JH, Hsieh CH, Sun JH. On-line optimal tracking control of continuous-time systems. Mechatronics 2004;14:587–97]. The method proposed by authors is based on a sequential on-line identification and optimal control idea. We show that the identification part is not correct in the suggested form and we modify the identification part by suggesting a version of recursive least-squares algorithm. In addition, the identifiability of an arbitrary system is questioned and a counter-example is given. Next, we show that the application of optimal control to the identified linear moving model is not based on any theoretical basis and we present reasons why the method will not work for general systems. In summary, it is shown that the combined on-line identification and control method will not work in general as claimed. Finally, we propose an alternative control method to be applied for dimensionally restricted systems.

On-line optimal tracking control of continuous-time systems

An on-line optimal tracking control with a quadratic performance index is developed for nonlinear continuous-time systems under control constraints. The systems are represented by a linear sequential model which is derived by using the orthogonal functions. This approach permits the linear feedback control law to be applied to nonlinear continuous-time systems. The on-line optimal tracking control of a two-link robot arm system with control constraints is presented to illustrate the considerable promise that the proposed method exhibits.