Abstract
Two on-line adaptive control methods for minimum-time control of unknown plants are presented. In the methods, the switching surface of the control is represented by a polynomial switching function with hierarchical structure, and the structural parameters are iteratively modified according to the information obtained during the control process. The methods do not need to identify the plant dynamics, and furthermore they can determine the switching surfaces, which approximate the optimal ones well, in comparatively few steps.
Two algorithms, the gradient modification method and the location modification method, are derived for modifying the switching function based upon the state-transition patterns in the state space. They can be called the self-adaptation algorithms, as they require no external instruction for modifying the switching function parameters. The location modification method is simpler and has better adaptivity. This method was applied to many unknown plants under different conditions by a computer simulation technique. Some of the results are given in order to show that the proposed method can realize a quasi-optimal control of high quality for unknown plants. It is also noted that the algorithm has a function to stabilize the control systems.
