H∞-optimal boundary control of hyperbolic systems with sampled measurements

This paper studies the finite-horizon H^∞-optimal control problem for linear hyperbolic systems when only time-sampled values of the state are available, with control acting on the boundary. The problem is formulated in a differential game framework by associating a zero-sum differential game with the original disturbance attenuation problem. The minimizing player´s minimax strategy in this game corresponds to the optimal controller in the disturbance attenuation problem, which is linear and is characterized in terms of the solution of a particular generalized Riccati evolution equation. The optimum achievable performance is determined by the condition of existence of a solution to another family of generalized Riccati evolution equations. The formulation allows for the control to be time-varying between two consecutive sampling times, and in this respect the paper presents optimum choices for these waveforms as functions of sampled values of the state