Stochastic Semistability for Nonlinear Dynamical Systems With Application to Consensus on Networks With Communication Uncertainty
| Autor: | Xu Jin, Tanmay Rajpurohit, Wassim M. Haddad |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Lyapunov function
Equilibrium point 0209 industrial biotechnology Markov chain Dynamical systems theory Computer science Stochastic process Mathematics::Number Theory 02 engineering and technology Dynamical system Computer Science Applications symbols.namesake Mathematics::Algebraic Geometry 020901 industrial engineering & automation Exponential stability Control and Systems Engineering Control theory Converse symbols Applied mathematics Almost surely Electrical and Electronic Engineering |
| Zdroj: | IEEE Transactions on Automatic Control. 65:2826-2841 |
| ISSN: | 2334-3303 0018-9286 |
| Popis: | This article focuses on semistability and finite time semistability analysis and synthesis of stochastic dynamical systems having a continuum of equilibria. Stochastic semistability is the property whereby the solutions of a stochastic dynamical system almost surely converge to Lyapunov stable in probability equilibrium points determined by the system initial conditions. In this article, we extend the theories of semistability and finite-time semistability for deterministic dynamical systems to develop a rigorous framework for stochastic semistability and stochastic finite-time semistability. Specifically, Lyapunov and converse Lyapunov theorems for stochastic semistability are developed for dynamical systems driven by Markov diffusion processes. These results are then used to develop a general framework for designing semistable consensus protocols for dynamical networks in the face of stochastic communication uncertainty for achieving multiagent coordination tasks in finite time. The proposed controller architectures involve the exchange of generalized charge or energy state information between agents guaranteeing that the closed-loop dynamical network is stochastically semistable to an equipartitioned equilibrium representing a state of almost sure consensus consistent with basic thermodynamic principles. |
| Databáze: | OpenAIRE |
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