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.

Keywords: sampling control system, Markov jump parameter, adaptive control, double-step approach, stochastic noise, least matching error estimation

@article{COCV_2009__15_4_969_0, author = {Tan, Shuping and Zhang, Ji-Feng}, title = {Double-stepped adaptive control for hybrid systems with unknown {Markov} jumps and stochastic noises}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {969--993}, publisher = {EDP-Sciences}, volume = {15}, number = {4}, year = {2009}, doi = {10.1051/cocv:2008057}, mrnumber = {2567254}, zbl = {1175.93247}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2008057/} }

TY - JOUR AU - Tan, Shuping AU - Zhang, Ji-Feng TI - Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 969 EP - 993 VL - 15 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008057/ DO - 10.1051/cocv:2008057 LA - en ID - COCV_2009__15_4_969_0 ER -

%0 Journal Article %A Tan, Shuping %A Zhang, Ji-Feng %T Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 969-993 %V 15 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008057/ %R 10.1051/cocv:2008057 %G en %F COCV_2009__15_4_969_0

Tan, Shuping; Zhang, Ji-Feng. Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises. ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 4, pp. 969-993. doi : 10.1051/cocv:2008057. http://archive.numdam.org/articles/10.1051/cocv:2008057/

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