Partial-state stabilization and optimal feedback control for stochastic dynamical systems

2016 ◽  
Author(s):  
Tanmay Rajpurohit ◽  
Wassim M. Haddad
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Optimal Feedback Control ◽  
Stochastic Dynamical Systems ◽  
Optimal Feedback ◽  
Partial State

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.

Optimal feedback control for fractional neutral dynamical systems

Optimization ◽  
2018 ◽  
Vol 67 (5) ◽  
pp. 549-564 ◽  
Author(s):  
Zhenhai Liu ◽  
Xuemei Li ◽  
Biao Zeng
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Optimal Feedback Control ◽  
Optimal Feedback

Universal Feedback Controllers and Inverse Optimality for Nonlinear Stochastic Systems

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Wassim M. Haddad ◽  
Xu Jin
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Stochastic Control ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Optimal Feedback Control ◽  
Control Law ◽  
Stochastic Dynamical Systems ◽  
Control Lyapunov Function ◽  
Inverse Optimality

Abstract In this paper, we develop a constructive finite time stabilizing feedback control law for stochastic dynamical systems driven by Wiener processes based on the existence of a stochastic control Lyapunov function. In addition, we present necessary and sufficient conditions for continuity of such controllers. Moreover, using stochastic control Lyapunov functions, we construct a universal inverse optimal feedback control law for nonlinear stochastic dynamical systems that possess guaranteed gain and sector margins. An illustrative numerical example involving the control of thermoacoustic instabilities in combustion processes is presented to demonstrate the efficacy of the proposed framework.

Partial-state stabilization and optimal feedback control

2015 ◽  
Vol 26 (5) ◽  
pp. 1026-1050 ◽  
Author(s):  
Andrea L'Afflitto ◽  
Wassim M. Haddad ◽  
Efstathios Bakolas
Keyword(s):  
Feedback Control ◽  
Optimal Feedback Control ◽  
Optimal Feedback ◽  
Partial State
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