Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework

This paper introduces a nonsmooth framework for global adaptive control of a significant class of nonlinearly parameterized systems with uncontrollable unstable linearization. While there may not exist any smooth static or dynamic stabilizer due to the violation of the well-known necessary condition, we give sufficient conditions for the existence of non-Lipschitz continuous adaptive regulators that achieve global stability with asymptotic state regulation. A constructive design method is developed based on an effective coupling of a new parameter separation technique and the tool of adding a power integrator, leading to C⁰ adaptive regulators with minimal parameterization. Indeed, the dimension of the proposed dynamic compensator can always be one, irrespective of the number of unknown parameters. The power of our continuous adaptive control strategy is demonstrated by solving a number of challenging adaptive stabilization problems that have remained open for more than a decade