Reachable Predictive Control: A Novel Control Algorithm for Nonlinear Systems with Unknown Dynamics and its Practical Applications

2025-10-02

AI Summary

How can piecewise-linear trajectory tracking be achieved for unknown nonlinear systems with time-varying dynamics—without prior system knowledge—while ensuring robustness against abrupt dynamic changes? Method: We propose a data-driven online control framework that (i) identifies local system dynamics in real time via small-perturbation excitation and local system identification; (ii) analytically derives the state reachable set without model assumptions, leveraging an upper bound on the local growth rate; and (iii) synthesizes a receding-horizon closed-loop controller based on reachable-set prediction. Contribution/Results: The approach avoids global modeling and parametric structural assumptions, enabling rapid adaptation to sudden dynamic shifts. Experimental validation across multiple unknown nonlinear systems demonstrates stable waypoint-sequence tracking, confirming strong robustness and generalization capability under unmodeled dynamics and disturbances.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Machine Learning: Online Learning & Bandits

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change in its dynamics, we demonstrate that it is possible to follow a set of waypoints comprised of states analytically proven to be reachable despite not knowing the system dynamics. The proposed algorithm first applies small perturbations to locally learn the system dynamics around the current state, then computes the set of states that are provably reachable using the locally learned dynamics and their corresponding maximum growth-rate bounds, and finally synthesizes a control action that navigates the system to a guaranteed reachable state.

Problem

• Controls nonlinear systems with unknown dynamics
• Follows trajectories without prior system knowledge
• Handles abrupt dynamic changes using reachable states

Innovation

• Learns system dynamics via local perturbations
• Computes provably reachable states from learned dynamics
• Synthesizes control actions for guaranteed reachable states