Multi-Rate Planning and Control of Uncertain Nonlinear Systems: Model Predictive Control and Control Lyapunov Functions

TL;DR

This paper proposes a multi-rate control framework combining MPC and CLFs with Bézier curves for constrained nonlinear systems, enabling hierarchical planning and control at multiple time scales with guarantees on constraint satisfaction.

Contribution

It introduces a novel multi-rate control architecture that integrates trajectory planning and tracking using convex optimization, Bézier curves, and hierarchical control for nonlinear systems.

Findings

Framework successfully enforces constraints in simulations

Convex optimization enables efficient computation

Hierarchical control improves system stability

Abstract

Modern control systems must operate in increasingly complex environments subject to safety constraints and input limits, and are often implemented in a hierarchical fashion with different controllers running at multiple time scales. Yet traditional constructive methods for nonlinear controller synthesis typically "flatten" this hierarchy, focusing on a single time scale, and thereby limited the ability to make rigorous guarantees on constraint satisfaction that hold for the entire system. In this work we seek to address the stabilization of constrained nonlinear systems through a \textit{multi-rate} control architecture. This is accomplished by iteratively planning continuous reference trajectories for a nonlinear system using a linearized model and Model Predictive Control (MPC), and tracking said trajectories using the full-order nonlinear model and Control Lyapunov Functions (CLFs). Connecting these two levels of control design in a way that ensures constraint satisfaction is achieved through the use of \textit{B\'{e}zier curves}, which enable planning continuous trajectories respecting constraints by planning a sequence of discrete points. Our framework is encoded via convex optimization problems which may be efficiently solved, as demonstrated in simulation.