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

Shuping Tan; Ji-Feng Zhang

ESAIM: Control, Optimisation and Calculus of Variations (2009)

  • Volume: 15, Issue: 4, page 969-993
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Tan, Shuping, and Zhang, Ji-Feng. "Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises." ESAIM: Control, Optimisation and Calculus of Variations 15.4 (2009): 969-993. <http://eudml.org/doc/245338>.

@article{Tan2009,
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.},
author = {Tan, Shuping, Zhang, Ji-Feng},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {sampling control system; Markov jump parameter; adaptive control; double-step approach; stochastic noise; least matching error estimation},
language = {eng},
number = {4},
pages = {969-993},
publisher = {EDP-Sciences},
title = {Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises},
url = {http://eudml.org/doc/245338},
volume = {15},
year = {2009},
}

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
PB - EDP-Sciences
VL - 15
IS - 4
SP - 969
EP - 993
AB - 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.
LA - eng
KW - sampling control system; Markov jump parameter; adaptive control; double-step approach; stochastic noise; least matching error estimation
UR - http://eudml.org/doc/245338
ER -

References

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