Multi-model LQ-constrained min‐max control

This paper deals with the designing of a min–max controller that provides the minimum value of maximal (among a finite number of linear models) quadratic functional under a simple constraint for a control amplitude. Using the Lagrange multipliers approach, we show that the consideration of this constraint implies the existence of a new adjoint variable (treated as a time‐varying Lagrange multiplier), providing the closed‐form solutions for the considered multi‐model LQ‐constrained min–max control problem. The method is illustrated by three numerical examples.