Optimal Adaptive Robust Control for Uncertain Mechanical Systems: A Nash Game-Oriented Approach

作者：Zheng, Yunjun^*; Zhao, Han; He, Chunsheng; Wu, Qilin

来源：International Journal of Fuzzy Systems, 2022, 24(7): 3226-3243.

DOI：10.1007/s40815-022-01333-9

• System uncertainty
• Constraint following
• Fuzzy set theory
• Adaptive robust control
• Multi-parameter optimization

This paper investigates a novel Nash game-oriented optimal adaptive robust control with the fuzzy evidence theory to deal with the constraint-following control problem for the uncertain mechanical system. This paper's innovations are composed of three parts. First, the uncertainty is nonlinear and time-varying in practice with little knowledge about it but considered bounded. This paper provides a fuzzy evidence theory to describe the uncertainty within a fuzzy evidence number. Second, we design a new adaptive robust control with a leakage-type self-correcting adaptive law to render the constrained mechanical system to follow the specified constraints accurately. It is shown that the designed adaptive law can compensate for the uncertainty and avoid overcompensation. The control is deterministic other than IF-THEN fuzzy rule-based and guarantees uniform boundedness and uniform ultimate boundedness. Third, we introduce the Nash game theory into the multi-parameter optimization design to optimize the two tunable control parameters. We choose the two control parameters as two players with cost functions relevant to the control cost and performance. Then we obtain the optimal control parameters in Nash equilibrium which is proved to exist and can be analytically obtained. Ultimately, the numerical simulations on the 2DOF robot manipulator are presented to demonstrate the proposed control scheme's effectiveness.