A Verification Theorem and Application to the Linear Quadratic Regulator for Minimax Control Problems

Sufficient conditions for a function to be an optimal minimax control are given for the general problem. Then attention is turned to the control problem with a minimax quadratic value function [formula] and linear state equation dξ/dτ = A(τ) ξ(τ) + B(τ) ζ(τ), ξ(t) = x ∈ Rn. The Bellman equation for the function V is derived and a lower bound for the value function is given. Finally, the scalar case is completely solved with some numerical results given.