Iterative Convex Optimization for Model Predictive Control with Discrete-Time High-Order Control Barrier Functions

TL;DR

This paper introduces an iterative convex optimization framework for model predictive control that efficiently enforces safety using high-order control barrier functions in discrete-time systems, applicable to any relative-degree.

Contribution

It proposes a novel iterative optimization approach that linearizes system dynamics and safety constraints at each step, enabling real-time safe control for high-order barrier functions.

Findings

Fast computational performance demonstrated

Applicable to any relative-degree control barrier functions

Ensures safety guarantees in real-time control

Abstract

Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as safety-critical requirements using discrete-time control barrier functions within a model predictive control (MPC) framework. Existing work usually focus on the feasibility or the safety for the optimization problem, and the majority of the existing work restrict the discussions to relative-degree one control barrier functions. Additionally, the real-time computation is challenging when a large horizon is considered in the MPC problem for relative-degree one or high-order control barrier functions. In this paper, we propose a framework that solves the safety-critical MPC problem in an iterative optimization, which is applicable for any relative-degree control barrier functions. In the proposed formulation, the nonlinear system dynamics as well as the safety constraints modeled as discrete-time high-order control barrier functions (DHOCBF) are linearized at each time step. Our formulation is generally valid for any control barrier function with an arbitrary relative-degree. The advantages of fast computational performance with safety guarantee are analyzed and validated with numerical results.