Control Lyapunov-Barrier Function Based Model Predictive Control for Stochastic Nonlinear Affine Systems

TL;DR

This paper introduces a stochastic model predictive control framework for nonlinear affine systems using a novel control Lyapunov-barrier function, ensuring stability, feasibility, and improved performance with event-triggering mechanisms.

Contribution

It develops a new stochastic control Lyapunov-barrier function combining CLF and barrier functions, and integrates it into a sampled-data MPC with event-triggering for nonlinear systems.

Findings

Validated via obstacle avoidance example

Guarantees stability and feasibility

Enhanced performance with event-triggering

Abstract

A stochastic model predictive control (MPC) framework is presented in this paper for nonlinear affine systems with stability and feasibility guarantee. We first introduce the concept of stochastic control Lyapunov-barrier function (CLBF) and provide a method to construct CLBF by combining an unconstrained control Lyapunov function (CLF) and control barrier functions. The unconstrained CLF is obtained from its corresponding semi-linear system through dynamic feedback linearization. Based on the constructed CLBF, we utilize sampled-data MPC framework to deal with states and inputs constraints, and to analyze stability of closed-loop systems. Moreover, event-triggering mechanisms are integrated into MPC framework to improve performance during sampling intervals. The proposed CLBF based stochastic MPC is validated via an obstacle avoidance example.