Statistical and theoretical analysis of the soft-constrained time-optimal control of stable linear plants

The soft-constrained time-optimal control (SCTO) of a general strictly stable linear system whose dominant pole has a distinct real part is considered. A detailed analytical study of the asymptotic saturation properties of the control amplitude and duration is presented. These properties are qualitatively different from those of a marginally stable linear system and can be deduced analytically from the eigenstructure of the plant. The analysis shows that, under some (reasonable) hypotheses, the control amplitude is bounded by an inequality constraint. Since the validity of the hypotheses cannot be rigorously shown, a statistical analysis is used to show that these hypotheses are statistically valid. Numerical and statistical results agree well with theoretical predictions