Reachable Predictive Control: A Novel Control Algorithm for Nonlinear Systems with Unknown Dynamics and Its Practical Applications
Taha Shafa, Yiming Meng, Melkior Ornik
AI summary
Problem
Conventional control strategies fail when system dynamics are unknown or undergo abrupt changes, leaving autonomous systems vulnerable to safety violations. There is a critical need for a control framework that guarantees safe navigation without relying on prior models or extensive pre-collected data.
Approach
The algorithm iteratively applies small control perturbations to estimate local system dynamics, computes a Guaranteed Reachable Set using known Lipschitz bounds, and synthesizes control actions to steer the system toward provably safe waypoints.
Key results
- Formal derivation of a Guaranteed Reachable Set underapproximation for underactuated nonlinear systems
- Iterative control synthesis algorithm guaranteeing trajectory tracking and reach-avoidance without a nominal model
- Simulation validation of an autonomous vehicle navigating unknown terrain while respecting payload safety constraints
- Extension of prior myopic control methods to provide formal safety guarantees for practical systems
Why it matters
Provides a theoretically grounded, model-free safety framework for autonomous systems operating in unpredictable or failure-prone environments.
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.