Finite-time partial stability for stochastic dynamical systems

2016 ◽  
Author(s):  
Tanmay Rajpurohit ◽  
Wassim M. Haddad
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
Stochastic Dynamical Systems ◽  
Partial Stability

scholarly journals Partial-State Stabilization and Optimal Feedback Control for Stochastic Dynamical Systems

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Tanmay Rajpurohit ◽  
Wassim M. Haddad
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Stochastic Dynamical Systems ◽  
Stochastic Stabilization ◽  
Stability In Probability ◽  
Optimal Feedback ◽  
Partial Stability ◽  
Optimal Linear ◽  
Linear And Nonlinear ◽  
Partial State

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for partial stability and partial-state stabilization of stochastic dynamical systems. Partial asymptotic stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state which can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation, and hence, guaranteeing both partial stability in probability and optimality. The overall framework provides the foundation for extending optimal linear-quadratic stochastic controller synthesis to nonlinear-nonquadratic optimal partial-state stochastic stabilization. Connections to optimal linear and nonlinear regulation for linear and nonlinear time-varying stochastic systems with quadratic and nonlinear-nonquadratic cost functionals are also provided. Finally, we also develop optimal feedback controllers for affine stochastic nonlinear systems using an inverse optimality framework tailored to the partial-state stochastic stabilization problem and use this result to address polynomial and multilinear forms in the performance criterion.

Coherent phenomena in stochastic dynamical systems

1999 ◽  
Vol 169 (2) ◽  
pp. 171 ◽  
Author(s):  
Valerii I. Klyatskin ◽  
D. Gurarie
Keyword(s):  
Dynamical Systems ◽  
Stochastic Dynamical Systems
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