Generalized Bang-Bang Control for Multivariable Feedforward Regulation

In control engineering, effective implementations require to take into account the constraints for both the inputs and the outputs of the controlled system. A feedforward regulation problem is then set out to achieve a minimum-time rest-to-rest output transition for square MIMO (multi-input multi-output) linear time-invariant systems. The found time-optimal solution extends the well-known bang-bang control to a generalized bang-bang control in which some amplitude constraints on the outputs are active. A straightforward sufficient condition to have a solution is provided. The structure of the time-optimal input-output pair is also investigated. A feasibility linear programming approach to compute an approximate solution is proposed. An example highlights the found results.