Boundary observer-based control for hyperbolic PDE–ODE cascade systems with stochastic jumps. (September 2020)

• Record Type: Journal Article
• Authors: Zhao, Yan; Qiu, Jianbin; Xu, Shengyuan; Li, Wenguo; Wu, Junli
• Is Part Of: Automatica. Volume 119(2020)
• Publication Date: 2020-09
• Subjects: Boundary observer-based control -- Hyperbolic PDE–ODE cascades -- Stochastic jumps; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.109089
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This work is concerned with the boundary observer-based control for a category of cascade systems with stochastic jumps. The cascade system consists of ordinary differential equations (ODEs) entering the hyperbolic partial differential equations (PDEs) through the boundary. A continuous-time, discrete-state homogeneous Markov process models the jumping parameters of the system, and its right continuous trajectory candidate values are taken from a finite set. A boundary observer is designed, which relies only on limited quantity of sensors at the boundary of the PDEs. Based on the Lyapunov functional approach, the observer-error system is firstly proved to be exponentially mean square stable. Then, the controller is presented by utilizing the estimated states of the ODEs as feedback variables. The evolution profiles of the PDEs in the closed-loop are proved to be exponentially mean square stable at the desired steady-state. The existence conditions of the boundary observer and the stability conditions of the PDEs in the closed-loop form are presented via a set of compact space-varying linear matrix inequalities (SVLMIs). The SVLMIs are then approximated by a finite number of LMIs, which guarantee the SVLMIs, and the computational cost is reduced greatly. Finally, the obtained theoretical results are applied to a traffic flow control system, which confirms that the proposed estimation and control methods are effective.