Understanding disturbance attenuation problems with unknown input time-delays: A game-theoretic approach with performance risk aversion

The main contribution is the application of a zero-sum game-theoretic framework and performance-measure statistics that can help robust control design to obtain a certain level of performance robustness in presence of adversarial process and measurement disturbances starting from the assumptions of linear stochastic dynamics, unknown input time-delays, a finite-horizon integral-quadratic cost and noisy output observations. A disturbance attenuation problem is based on a saddle-point equilibrium associated with the controller with performance risk aversion in competing with persistent process and measurement disturbances. The resulting saddle-point strategies are in turn supported by: i) a Kalman-like estimator for both unknown time-delays and noisy states and ii) a custom dynamical set of mathematical statistics associated with the underlying random cost of the chi-squared type.