L∞ Optimal control of SISO continuous-time systems

Ahatraet-In this paper we study the problem of designing a controller that minimizes the weighted amplitude of the time response due to a given, fixed input signal for SISO continuous-time systems. The main result of the paper shows that this problem admits a minimizing solution in 6p, and that the optimal closed-loop system has a special structure: a sum of delayed step functions, all having the same amplitude. Thus the optimal controller has a non-rational transfer function. Although in the general case finding this controller entails solving an infinite-dimensional linear-programming problem, we show that in some special cases the optimal solutions have closed-form expressions and can be found by solving a set of algebraic equations. Finally, we address the issue of selecting time and frequency domain weighting functions. This paper together with our paper ‘Rational Z-s&optimal controller for SISO continuous-time systems’ (IEEE Trans. Autom. Control. AC-41. 1358-1363 119%)). which deals with the design’ of rational 6p, suboptimal controllers for general systems, give a complete solution of the 2X control problem.