Game-Theoretic Optimal Fixed-Time Adaptive Control for Fuzzy Mechanical Systems With Prescribed Performance

An optimal prescribed performance control with fixed-time for fuzzy mechanical systems is explored. Specifically, a novel bounded performance function is proposed, which preassigns the convergence time, transient convergence trend (dynamic, variable and gentle initial stage) and steady-state tracking accuracy. More possibilities for transient performance of fuzzy systems are developed. Then, fuzzy set theory is introduced to describe system uncertainties. A fuzzy mechanical system with prescribed performance is constructed in the homeomorphism mapping space. An adaptive control method with finite-time stability is proposed. Thus, the preassigned performance is met through a two-layer collaborative convergence characteristic, rather than relying solely on performance constraint. High-order adaptive laws reduce control costs and avoid overcompensation. Control design is always deterministic rather than based on fuzzy rules. A more effective way is reflected in fuzzy-based optimization. Based on fuzzy sets to measure uncertainty, a cooperative game optimization strategy is designed to obtain the optimal decision for multiple objectives and control parameters. The best combination of performance and cost is solved. The effectiveness of the proposed method is verified via the steer-by-wire system.