Supervisory adaptive safety control for uncertain nonlinear systems

Abstract

This paper investigates the supervisory adaptive safety control problem for uncertain nonlinear systems with unmeasurable states. In order to estimate unknown parameters and unmeasurable states, a supervisory observer framework consisting of a multi-observer bank and a supervisor unit, is proposed based on a dividing rectangles (DIRECT) algorithm. Under a desired accuracy, the parameter estimates converge to near the true parameters within finite-time while the estimation error of the system state converges to a small neighborhood near the origin. Also, an observer robust adaptive control barrier function is constructed to ensure safety for uncertain nonlinear systems by guaranteeing controlled invariance of a time-varying auxiliary set. By adjusting some parameters in the DIRECT algorithm, the time-varying auxiliary set approaches the original safe set, which reduces the conservatism generated by the compression of the safe set. Finally, two examples, including an adaptive cruise control system, are given to demonstrate the effectiveness of the proposed method.