Non-Cooperative Game-Oriented Optimal Prescribed Performance Control for Underactuated Mechanical Systems with Asymmetric Constraints

This paper explores the application of non-cooperative game theory in achieving optimal prescribed performance control for uncertain underactuated mechanical systems. The study addresses scenarios characterized by time-varying (potentially rapid) and bounded uncertainties. Utilizing a constraint-following control design approach., we apply the prescribed transient and steady-state performance (TSSP) criteria to the constraint-following error. Additionally., we employ state transformation techniques to implement the prescribed performance control. We introduce a prescribed performance control methodology with two adjustable parameters and demonstrate the process of determining the optimal design for these parameters through Nash games. Our findings indicate a significant enhancement in the overall system performance., thus confirming the efficacy of the optimization method grounded in non-cooperative game theory.