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Design of optimal control systems with bounded control signals

The design of optimal controllers for systems subject to hard bounds on the control signal is considered. Optimality refers to the fact that we achieve the smallest possible worst case error (i.e. difference between reference signal and plant output) during runtime. The external reference signal is bounded in amplitude and rate, which encounters for many practical situations. Moreover, a conservative design is avoided by these assumptions. The resulting constrained and infinite dimensional optimisation problem is re-casted to an unconstrained and finite dimensional one by applying the notion of Pareto-optimal solutions and Ritz approximation. Moreover, the presented framework allows to assess feasibility of the constraint control problem, and to display the tradeoff between the two objectives. A simulation example illustrates the developed theory.