Model Predictive Control of Hybrid Dynamical Systems

2026-04-23

AI Summary

This work proposes a hybrid time-domain model predictive control (MPC) framework for hybrid dynamical systems subject to both continuous and discrete dynamics as well as state-input constraints. By integrating hybrid equation modeling, control Lyapunov functions, and terminal cost design, the approach formulates a structurally optimized MPC problem and establishes verifiable conditions for asymptotic stability. The method coherently links stage cost, terminal cost, and a static state feedback law, thereby theoretically guaranteeing asymptotic stability of the closed-loop system with respect to a target set. The efficacy and broad applicability of the proposed framework are demonstrated through multiple representative case studies.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid equations, involving a differential equation and a difference equation with inputs and constraints. The proposed hybrid MPC algorithm uses a suitable prediction and control horizon construction inspired by hybrid time domains. Structural properties of the hybrid optimization problem, its feasible set, and its value function are provided. Checkable conditions to guarantee asymptotic stability of a set are provided. These conditions are given in terms of properties on the stage cost, terminal cost, and the existence of static state-feedback laws, related through a control Lyapunov function condition. Examples illustrate the results throughout the paper.

Problem

• Model Predictive Control
• Hybrid Dynamical Systems
• Asymptotic Stability
• Hybrid Equations
• Control Lyapunov Function

Innovation

• Hybrid Dynamical Systems
• Model Predictive Control
• Asymptotic Stability
• Control Lyapunov Function
• Hybrid Time Domains