# Lyapunov-based Stochastic Nonlinear Model Predictive Control: Shaping the State Probability Density Functions

arXiv: https://arxiv.org/abs/1505.02871 · HTML: https://mlsanity.com/paper/1505.02871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2015.

## Built on by (most cited first, 1 of 1)

- [Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive control](https://mlsanity.com/paper/2103.05441/) (2021)

## Abstract (arXiv)

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.