Finite-Time Simultaneous Stabilization for Stochastic Port-Controlled Hamiltonian Systems over Delayed and Fading Channels

Yaping Tang,Weiwei Sun,Xiaodi Li,Dongqing Liu

doi:10.1155/2020/6387025

Abstract

In this paper, a finite-time simultaneous stabilization problem is investigated for a set of stochastic port-controlled Hamiltonian (PCH) systems over delayed and fading noisy channels. The feedback control signals transmitted via a communication network suffer from both constant transmission delay and fading channels which are modeled as a time-varying stochastic model. First, on the basis of dissipative Hamiltonian structural properties, two stochastic PCH systems are combined to form an augmented system by a single output feedback controller and then sufficient conditions are developed for the semiglobally finite-time simultaneous stability in probability (SGFSSP) of the resulting closed-loop systems. The case of multiple stochastic PCH systems is also considered and a new control scheme is proposed for the systems to save costs and achieve computational simplification. Finally, an example is provided to verify the feasibility of the proposed simultaneous stabilization method.

Highlights

Port-controlled Hamiltonian (PCH) systems are known as an important class of nonlinear systems ([1, 2])
Compared to the general nonlinear systems, an excellent benefit of PCH systems is that the Hamiltonian function in the systems can be used as a Lyapunov function candidate in stability analysis. anks to the special system structure and clear physical meaning, applications of PCH systems can be found in a variety of engineering systems including power systems, robotic systems, and irreversible thermodynamic systems ([6,7,8,9,10])
Summarizing the above discussion, in this paper, we try to solve the finite-time simultaneous stabilization problem of stochastic PCH systems over delayed and fading channels and propose some new results that serve for the design of feedback controllers. e fading noisy channels modeled as multiple independent and memoryless forms exist between the controller and the plant

Summary

Introduction

Port-controlled Hamiltonian (PCH) systems are known as an important class of nonlinear systems ([1, 2]). Summarizing the above discussion, in this paper, we try to solve the finite-time simultaneous stabilization problem of stochastic PCH systems over delayed and fading channels and propose some new results that serve for the design of feedback controllers. E contributions of this paper mainly lie in the following two aspects: (1) taking network-induced delay and fading noisy channels environment into consideration, a new single output feedback controller design method is raised to deal with the SGFSSP problem for stochastic PCH systems. In this way, the controller implementation costs can be greatly reduced, and the computational simplification of control can be achieved. For the probability space (Ω, F, P), Ω denotes the sample space, F denotes the σ-algebra of the observable random events, and P is the probability measure on Ω

Problem Formulation and Preliminaries

A15 A25 g2KgT1

Illustrative Example

Conclusion