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.Downloads:
Bibtex entry: