Adaptive Robust Model Predictive Control for Mechanical Systems Under Time‐Varying Uncertainties With Unknown Bounds

ABSTRACT Time‐varying uncertainties, often with unknown bounds, are ubiquitous in mechanical systems. The lack of a priori knowledge of these uncertainties impedes the evaluation of their effects on system performance, leading to deteriorating control precision and potential instability. To address this challenge, this study presents an adaptive robust model predictive control (ARMPC) strategy and a control switching mechanism to tackle such uncertainties, whether from internal or external origins. First, the nominal system is decoupled from the uncertain components. A feedforward compensation term based on Udwadia‐Kalaba approach and an optimal feedback term from the receding horizon control framework are elaborated to achieve rapid convergence, coupled with an uncertainty rejection component to guarantee the uniform boundedness and uniform ultimate boundedness of the closed‐loop system. Second, an adaptive robust controller satisfying the input saturation constraint is proposed, serving as a viable alternative when the optimization problem is infeasible. Finally, the efficacy of the ARMPC scheme is demonstrated through simulations of a two‐link R‐R mechanical manipulator system and a path tracking example, showcasing its superior performance in terms of convergence rate, overshoot, and steady‐state error under different levels of uncertainties.