Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. When the local cost functions are convex and the global cost function is strictly convex, we establish asymptotic convergence under connected graph topologies. We also characterize the algorithm's correctness under time-varying interaction topologies and study its privacy preservation properties. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication. Building on this result, we design a provably-correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results.Comment: 12 page

Multiple Loop Self-Triggered Model Predictive Control for Network Scheduling and Control

We present an algorithm for controlling and scheduling multiple linear time-invariant processes on a shared bandwidth limited communication network using adaptive sampling intervals. The controller is centralized and computes at every sampling instant not only the new control command for a process, but also decides the time interval to wait until taking the next sample. The approach relies on model predictive control ideas, where the cost function penalizes the state and control effort as well as the time interval until the next sample is taken. The latter is introduced in order to generate an adaptive sampling scheme for the overall system such that the sampling time increases as the norm of the system state goes to zero. The paper presents a method for synthesizing such a predictive controller and gives explicit sufficient conditions for when it is stabilizing. Further explicit conditions are given which guarantee conflict free transmissions on the network. It is shown that the optimization problem may be solved off-line and that the controller can be implemented as a lookup table of state feedback gains. Simulation studies which compare the proposed algorithm to periodic sampling illustrate potential performance gains.Comment: Accepted for publication in IEEE Transactions on Control Systems Technolog

Resource-aware IoT Control: Saving Communication through Predictive Triggering

The Internet of Things (IoT) interconnects multiple physical devices in large-scale networks. When the 'things' coordinate decisions and act collectively on shared information, feedback is introduced between them. Multiple feedback loops are thus closed over a shared, general-purpose network. Traditional feedback control is unsuitable for design of IoT control because it relies on high-rate periodic communication and is ignorant of the shared network resource. Therefore, recent event-based estimation methods are applied herein for resource-aware IoT control allowing agents to decide online whether communication with other agents is needed, or not. While this can reduce network traffic significantly, a severe limitation of typical event-based approaches is the need for instantaneous triggering decisions that leave no time to reallocate freed resources (e.g., communication slots), which hence remain unused. To address this problem, novel predictive and self triggering protocols are proposed herein. From a unified Bayesian decision framework, two schemes are developed: self triggers that predict, at the current triggering instant, the next one; and predictive triggers that check at every time step, whether communication will be needed at a given prediction horizon. The suitability of these triggers for feedback control is demonstrated in hardware experiments on a cart-pole, and scalability is discussed with a multi-vehicle simulation.Comment: 16 pages, 15 figures, accepted article to appear in IEEE Internet of Things Journal. arXiv admin note: text overlap with arXiv:1609.0753