Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises

¹ National Laboratory of Space Intelligent Control, Beijing Institute of Control Engineering, P.O. Box 2729, Beijing 100190, P. R. China. sptan@amss.ac.cn
² Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China. jif@iss.ac.cn

Received: 7 January 2007
Revised: 9 June 2008

Abstract

This paper is concerned with the sampled-data based adaptive linear quadratic (LQ) control of hybrid systems with both unmeasurable Markov jump processes and stochastic noises. By the least matching error estimation algorithm, parameter estimates are presented. By a double-step (DS) sampling approach and the certainty equivalence principle, a sampled-data based adaptive LQ control is designed. The DS-approach is characterized by a comparatively large estimation step for parameter estimation and a sufficient small control step for control updating. Under mild conditions, the closed-loop system is shown to be stable. It is found that the key factor determining the performance index is the estimation step rather than the control step. When the estimation step becomes too small, the system performance will become worse. When the estimation step is fixed, the system performance can indeed be improved by reducing the control step, but cannot reach the optimal value. The index difference between the sampled-data based adaptive LQ control and the conventional LQ optimal control is asymptotically bounded by a constant depending on the estimation step and the priori information of the parameter set.