Hard and soft Sub-Time-Optimal Controllers for a Mechanical System with Uncertain Mass

An essential limitation in using the classical optimal control has been its limited robustness to modeling inadequacies and perturbations. This paper presents conceptions of two practical control structures based on the time-optimal approach: hard and soft ones. The hard structure is defined by parameters selected in accordance with the rules of the statistical decision theory; however, the soft structure allows additionally to eliminate rapid changes in control values. The object is a basic mechanical system, with uncertain (also non-stationary) mass treated as a stochastic process. The methodology proposed here is of a universal nature and may easily be applied with respect to other elements of uncertainty of time-optimal controlled mechanical systems.