Lyapunov-based Stochastic Nonlinear Model Predictive Control: Shaping the State Probability Density Functions
Abstract
Stochastic uncertainties in complex dynamical systems lead to variability of system states, which can in turn degrade the closed-loop performance. This paper presents a stochastic model predictive control approach for a class of nonlinear systems with unbounded stochastic uncertainties. The control approach aims to shape probability density function of the stochastic states, while satisfying input and joint state chance constraints. Closed-loop stability is ensured by designing a stability constraint in terms of a stochastic control Lyapunov function, which explicitly characterizes stability in a probabilistic sense. The Fokker-Planck equation is used for describing the dynamic evolution of the states' probability density functions. Complete characterization of probability density functions using the Fokker-Planck equation allows for shaping the states' density functions as well as direct computation of joint state chance constraints. The closed-loop performance of the stochastic control approach is demonstrated using a continuous stirred-tank reactor.
Cite
@article{arxiv.1505.02871,
title = {Lyapunov-based Stochastic Nonlinear Model Predictive Control: Shaping the State Probability Density Functions},
author = {Edward A. Buehler and Joel A. Paulson and Ali Akhavan and Ali Mesbah},
journal= {arXiv preprint arXiv:1505.02871},
year = {2016}
}
Comments
Submitted to the 54th IEEE Conference on Decision and Control, Osaka, Japan, December 2015