Passivity-exploiting stabilization of semilinear single-track vehicle models with distributed tire friction dynamics

TL;DR

This paper introduces a passivity-based backstepping control method for stabilizing semilinear single-track vehicle models with distributed tire friction dynamics, ensuring exponential convergence and robustness through Lyapunov-based analysis.

Contribution

It presents a novel passivity-exploiting backstepping control design for coupled ODE-PDE vehicle models, including both state and output feedback with observer integration.

Findings

Effective stabilization of oversteer vehicles at high speeds.

Robust control performance under external disturbances.

Theoretical guarantees of exponential convergence.

Abstract

This paper addresses the local stabilization problem for semilinear single-track vehicle models with distributed tire friction dynamics, represented as interconnections of ordinary differential equations (ODEs) and hyperbolic partial differential equations (PDEs). A passivity-exploiting backstepping design is presented, which leverages the strict dissipativity properties of the PDE subsystem to achieve exponential stabilization of the considered ODE-PDE interconnection around a prescribed equilibrium. Sufficient conditions for local well-posedness and exponential convergence are derived by constructing a Lyapunov functional combining the lumped and distributed states. Both state-feedback and output-feedback controllers are synthesized, the latter relying on a cascaded observer. The theoretical results are corroborated with numerical simulations, considering non-ideal scenarios and accounting for external disturbances and uncertainties. Simulation results confirm that the proposed control strategy can effectively and robustly stabilize oversteer vehicles at high speeds, demonstrating the relevance of the approach for improving the safety and performance in automotive applications.