Nonlinear-nonquadratic optimal and inverse optimal control for stochastic dynamical systems

作者：Rajpurohit Tanmay; Haddad Wassim M^*

来源：International Journal of Robust and Nonlinear Control, 2017, 27(18): 4723-4751.

DOI：10.1002/rnc.3829

• stochastic stability
• Lyapunov functions
• inverse optimal control
• stochastic Hamilton-Jacobi-Bellman equation
• polynomial cost functionals
• multilinear forms

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for nonlinear stochastic dynamical systems. Specifically, we provide a simplified and tutorial framework for stochastic optimal control and focus on connections between stochastic Lyapunov theory and stochastic Hamilton-Jacobi-Bellman theory. In particular, we show that asymptotic stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton-Jacobi-Bellman equation and, hence, guaranteeing both stochastic stability and optimality. In addition, we develop optimal feedback controllers for affine nonlinear systems using an inverse optimality framework tailored to the stochastic stabilization problem. These results are then used to provide extensions of the nonlinear feedback controllers obtained in the literature that minimize general polynomial and multilinear performance criteria.

• 出版日期2017-12-1