Cooperative game-theoretic optimization of adaptive robust constraint-following control for fuzzy mechanical systems under inequality constraints

For servo mechanical systems, it is typically desirable to consider a series of equality and inequality constraints in the control analysis. While constraint-following control strategies based on the Udwadia-Kalaba (U-K) equation efficiently tackle equality constraints, the handling of inequality constraints remains underexplored, particularly in the presence of time-varying uncertainties. In this paper, an adaptive robust constraint-following control scheme is herein established based on fuzzy description of uncertainty and cooperative game theory. Leveraging the diffeomorphism approach tailored for the inequality constraint, we reformulate the constraint equation and the dynamical model, thereby appropriately incorporating both equality and inequality constraints into a unified constraint-following problem. Subsequently, a robust control strategy with the leakage-type adaptive law is proposed to render the constraint-following error uniformly bounded and uniformly ultimately bounded. Furthermore, to search for the optimal selection for control parameters, this optimization problem is presented as a two-player cooperative game by formulating the fuzzy performance index (i.e., the cost function), with the index being influenced by the tunable parameter (i.e., the player). As supported by rigorous proofs, the existence of the Pareto optimality is guaranteed and its solution is effectively attained, leading to enhanced control system performance. Lastly, a numerical example of an active roll control system (ARCS) is presented to validate the effectiveness of the proposed approach.