Decision Function-Based Adaptive Control of Uncertain Systems Subject to Irregular Output Constraints

While barrier Lyapunov function-based approach has been successfully used in adaptive control of uncertain systems with output/state constraints, it is nontrivial to use this method to deal with systems with irregular constraints (where the constraints may appear, disappear, or alternate during system operation). It is in fact an open interesting problem to develop a control method capable of coping with the irregular constraints uniformly. In this note, a unified adaptive control strategy is developed for uncertain systems subject to irregular output constraints. First, we introduce the concept of link function, with which we transform the nondifferentiable constraint into a smooth one. Second, by using several function transformations, and the decision function in particular that bridges the irregular output constraints and the barrier function, we recast the problem of maintaining irregular constraints into the stabilization of the barrier function, which allows different constraint forms to be addressed under a fixed control structure wherein one only needs to select the appropriate decision function and design parameters, eliminating the need for control redesign and stability reanalysis. The effectiveness of the proposed scheme is validated by numerical simulations.