Reference
S. Lin, D. Li, and B. De Schutter, "Optimizing the performance of the feedback
controller for state-based switching bilinear systems,"
Optimal Control Applications and Methods, Special Issue on
Control for Hybrid Systems: Applications and Methods for Adaptation and
Optimality, vol. 41, no. 6, pp. 1844-1853, Nov.-Dec. 2020.
Abstract
This paper is concerned with the design and performance optimization of
feedback controllers for state-based switching bilinear systems, where
subsystems take the form of bilinear systems in different state space
polyhedra. First, by further dividing the subregions into smaller regions and
designing region dependent feedback controllers in the resulting regions, the
switching bilinear systems can be transformed into corresponding switching
linear systems. Then, for these switching linear systems, by imposing
contractility conditions on the Lyapunov functions, an upper bound on the
infinite horizon quadratic cost can be obtained. Optimizing this upper bound
yields the controller design. The optimization problem is formulated as an LMI
optimization problem, which can be solved efficiently. Finally, the stability
of the close-loop system under the proposed controller is established step by
step through a decreasing overall Lyapunov function.
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BibTeX
@article{LinDeS:20-009,
author = {Lin, Shu and Li, Dewei and De Schutter, Bart},
title = {Optimizing the Performance of the Feedback Controller for
State-Based Switching Bilinear Systems},
journal = {Optimal Control Applications and Methods, \textnormal{Special
Issue on Control for Hybrid Systems: Applications and Methods for
Adaptation and Optimality}},
volume = {41},
number = {6},
pages = {1844--1853},
month = nov # {--} # dec,
year = {2020}
}