Robust Optimal Control for Discrete-Time LTI Systems Over Multiple Additive White Gaussian Noise Channels

Unlike the traditional point-to-point control structure, control system design through network media introduces additional constraints due to limited capacities of the used communication channels. In this article, we address the optimal performance control problem for linear uncertain discrete-time systems over multiple additive white Gaussian noise channels, where mean power constraints are imposed on the actuator side. The desired controller is aimed to robustly stabilize the plant, to minimize the linear quadratic cost, and to satisfy diverse prespecified mean power limits associated with individual elements of the control law, simultaneously. Within the framework of system-level synthesis, the performance objective and power constraints, together with relevant upper bounds, over all admissible uncertainties are characterized in terms of system responses of the closed-loop system and statistics of the communication channels. Based on this characterization, numerically tractable algorithms are proposed for controller synthesis. The counterpart for deterministic systems is also discussed as a special case with corresponding algorithms being provided. Moreover, the relative performance loss incurred by the size of model uncertainties and the finite truncation is explicitly established. An example is also included to show the effectiveness of the present results.