Variable-Exponent Lyapunov Function-Based Attracting-Manifold Adaptive Control Design with Application to Ground Vehicle Lateral Guidance

We introduce a new control framework crafted to enhance the transient performance of the adaptive vehicle lateral guidance system. This framework, for the first time, systematically and synergistically alloys two elements, variable-exponent Lyapunov function and attracting-manifold design, together. It offers a dual set of benefits. Firstly, we propose a novel nonquadratic Lyapunov function design with a variable exponent. Compared to conventional quadratic Lyapunov function-based designs, this approach accelerates the dissipation of tracking-error energy globally, thus fostering improved transient performance. Secondly, the attracting-manifold design provides a noncertaintyequivalence method to further enhance transient performance by promptly mitigating the perturbation induced by parametric uncertainty. This strategic fusion leverages the strengths of both elements, elevating transient performance beyond what either design could achieve independently. The new control framework is established in a general context, making it applicable to a class of control-affine systems in Brunovsky's canonical form. We apply it to develop an adaptive vehicle lateral guidance system and show its improved transient performance through experiments conducted on a high-fidelity, moving-base, driving simulator.