Minimization of the worst-case peak to peak gain via dynamic programming: State feedback case

The problem of designing a controller that minimizes the worst-case peak to peak gain of the closed loop system was considered. The principle of optimality was applied and derived a dynamic programming formulation of the optimization problem was described. At each step of the dynamic program, the cost to go has the form of a gauge function and can be recursively determined through simple transformations. The formulation allows to consider, together with the worst case inputs, fixed known inputs and it can naturally incorporate actuator saturation constraints. A computational scheme that allows to compute the exact value of the worst-case peak to peak gain for any finite horizon is presented.