UC Berkeley

Stochastic uncertainties in complex systems lead to variability of system states, which can degrade the closed-loop performance. This paper presents a model predictive control approach for a class of nonlinear systems with unbounded stochastic uncertainties. The control approach aims at shaping the probability distribution function of 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 evolution of the probability distribution function of states. Constructing the probability distribution functions using the Fokker-Planck equation allows for shaping the states' distribution functions as well as direct computation of the joint state chance constraints. The closed-loop performance of the stochastic optimal control approach is demonstrated on a benchmark continuous bioreactor.