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For linear time-invariant systems having a state matrix with uncertain sign,we formulate a minimax adaptive control problem as a zero sum dynamic game.Explicit expressions for the optimal value function and the optimal control laware given in terms of a Riccati equation. The optimal control law is adaptivein the sense the past data is used to estimate the uncertain sign forprediction of future dynamics. Once the sign has been estimated, the controllerbehaves like standard H-infinity optimal state feedback.

Minimax Adaptive Control for State Matrix with Unknown Sign