Designing Robust Control for Mechanical Systems: Constraint Following and Multivariable Optimization

This paper proposes a novel robust control design for mechanical systems based on constraint following and multivariable optimization. The state of the concerned system is affected by (possibly fast) time-varying and bounded uncertainty. The objective is to drive the system to obey a set of prescribed constraints. A β-measure is defined to gauge the constraint following error; based on which, a robust control scheme, which invokes design parameters, is proposed. For the seeking of optimal design parameters, a multivariable constrained optimization problem is formulated. The problem is successfully solved: with the ${existence,\ uniqueness}$ , and ${analytical\ expression (i.e.,\ closed\ form)}$ of the optimal design parameters demonstrated. With the optimal parameters, the proposed robust control can render dual performance: guaranteed and optimal. As the guaranteed performance, the β-measure is assured to be uniform boundedness and uniform ultimate boundedness. As the optimal performance, the performance index is globally minimized.