Decentralized Control of Stochastically Switched Linear System with Unreliable Communication

We consider a networked control system (NCS)consisting of two plants, a global plant and a local plant,and two controllers, a global controller and a local controller.The global (resp. local) plant follows discrete-time stochasticallyswitched linear dynamics with a continuous global (resp. local)state and a discrete global (resp. local) mode. We assume thatthe state and mode of the global plant are observed by bothcontrollers while the state and mode of the local plant areonly observed by the local controller. The local controller caninform the global controller of the local plant’s state and modethrough an unreliable TCP-like communication channel wheresuccessful transmissions are acknowledged. The objective ofthe controllers is to cooperatively minimize a modes-dependentquadratic cost over a finite time horizon. Following the methoddeveloped in [1] and [2], we construct a dynamic program basedon common information and a decomposition of strategies, anduse it to obtain explicit optimal strategies for the controllers.In the optimal strategies, both controllers compute a commonestimate of the local plant’s state. The global controller’s actionis linear in the state of the global plant and the commonestimated state, and the local controller’s action is linear inthe actual states of both plants and the common estimatedstate. Furthermore, the gain matrices for the global controllerdepend on the global mode and its observation about the localmode, while the gain matrices for the local controller dependon the actual modes of both plants and the global controller’sobservation about the local mode.