Minimax robust optimal control of multiscale linear-quadratic systems

With a growing system complexity in the IoT framework, many networked cyber-physical systems work in a hierarchical fashion. Layers of information outputs and command inputs are available. An active area of research is in optimizing the design of policies and control command that influence information flow for such multi-layered systems. Our focus in current research is to first formulate the control command flow for hierarchical systems in the form of multiscale state-space models on a tree, and then the design of an optimal control law under constraints that relate the states of information across the system layers. We propose a game-theoretic formulation of a robust optimal controller for the broad class of multiscale systems having underlying hierarchical structure. The optimization gives an H∞ controller similar to that for a discrete-time system but with scale as the horizon. We motivate the usage of this work using a layered building temperature control example, and discuss steady-state behavior, convergence, and finally a comparison of our method with the standard LQR control formulation giving supportive simulation results.