Optimal Co-Design of Scheduling and Control for Networked Systems

Robots using distributed sensors in smart environments and smart infrastructure systems such as traffic and power systems are examples of networked cyber-physical systems where communication and/or computational resources are constrained. The scientific challenge is to design scheduling and control schemes taking into account such resource constraints and to preferably include fair resource sharing mechanisms among different control applications. In this talk we present a novel framework for the optimal co-design of scheduling and control for networked systems with resource constraints. In particular we consider multiple control loops, which transmit their measurements over a shared communication channel. Only a limited number of those control loops may close their feedback loop at a time. As a result the dynamics of the individual control loops are coupled through the resource constraint. The scientific question is, when a control loop should schedule the transmission of a measurement and what is the appropriate control law. We approach the problem from an optimality point of view with the scheduling and control policies being the optimization variables. We derive an efficient and tractable decomposition, which allows a distributed solution for control and scheduling decisions coordinated by a price-based mechanism. It turns out that an event-triggered control scheme is optimal and that certainty equivalence holds. In fact, our scheme exploits the adaptation ability of event-triggered control in terms of communication traffic elasticity. Furthermore, we provide stability results linking the resource constraints with the system dynamics.