Towards Adaptive Robust Control and Optimization for Constrained Uncertain Under-Actuated Mechanical Systems

For a specific class of under-actuated mechanical systems, non-holonomic servo constraints and model uncertainties are usually encountered. For such systems, this paper investigates the design of an adaptive robust controller with parameter optimization. A tighter link between the fuzzy set theory and the control of UMSs is bridged appropriately. Based on the UMSs with fuzzy information, an adaptive robust control method is then designed, and an analytical solution of the control input is determined, even if the servo constraints are non-holonomic. Furthermore, a concomitant parameter in the designed controller is analyzed, and a feasible controller admitting the optimal performance can be determined by minimizing a predefined performance index, such that the deterministic system performance can be ensured to be at a satisfying level. As supported by rigorous proofs, the existence and the uniqueness of the global solution to the optimization problem are presented. Finally, a numerical experiment is implemented to demonstrate the effectiveness of the proposed control design methodology.