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A game-theoretic approach to a finite-time disturbance attenuation problem

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2 Author(s)
Rhee, Ihnseok ; Dept. of Aerosp. Eng. & Eng. Mech., Texas Univ., Austin, TX, USA ; Speyer, J.L.

A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H norm bound

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Automatic Control, IEEE Transactions on  (Volume:36 ,  Issue: 9 )