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.