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

TL;DR

A stochastic model predictive control (MPC) framework is presented in this paper for nonlinear affine systems with stability and feasibility guarantee and event‐triggering mechanisms are integrated into MPC framework to improve performance during sampling intervals.

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.

Figures (6)

• Figure 1: Control structure of sampled-data SMPC with event-triggering mechanisms
• Figure 2: $k_{Bi}$’s influence on $B_i$
• Figure 3: The feasible regions $X_\phi$ with $\rho=0.005$ (the former) and $X_L$ (the later). The green surfaces are boundaries of $X_i$ and $D_i$ while the red region is outside $X_\phi$ or $X_L$.
• Figure 4: 20 simulations with same conditions. Red, blue and green circles denote $X_i$, $D_i$ and $X_g$ respectively. The right one considers auxiliary Lyapunov controller and event-triggering mechanisms while the left does not.
• Figure 5: States and control inputs of the wheeled mobile robot

Theorems & Definitions (19)

• definition 1
• definition 2
• definition 3
• proposition 1
• proof
• theorem 1
• proof
• proposition 2
• proof
• proposition 3