Control Lyapunov–Barrier function based model predictive control for stochastic nonlinear affine systems

Weijiang Zheng, Bing Zhu

2023International Journal of Robust and Nonlinear Control19 citationsDOI

Abstract

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.

Topics & Concepts

Control theory (sociology)Model predictive controlLyapunov functionAffine transformationNonlinear systemLinearizationControl-Lyapunov functionComputer scienceLyapunov redesignStability (learning theory)MathematicsMathematical optimizationControl (management)Artificial intelligencePure mathematicsMachine learningPhysicsQuantum mechanicsAdvanced Control Systems OptimizationFault Detection and Control SystemsControl Systems and Identification