Feedback stabilization of dynamical systems with switched delays

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast this problem as a subclass of classical switching systems, which is a non-trivial generalization of classical LTI systems with timevarying delays. We consider both cases where delay-dependent and delay independent controllers are used, and show that both can be modeled as switching systems with unconstrained switchings. We provide NP-hardness results for the stability verification problem, and propose a general methodology for approximate stability analysis with arbitrary precision. We finally give evidence that non-trivial design problems arise for which new algorithmic methods are needed

Fault detection and isolation of malicious nodes in MIMO Multi-hop Control Networks

A MIMO Multi-hop Control Network (MCN) consists of a MIMO LTI system where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. We provide necessary and sufficient conditions on the plant dynamics and on the communication protocol configuration such that the Fault Detection and Isolation (FDI) problem of failures and malicious attacks to communication nodes can be solved.Comment: 6 page

Optimal co-design of control, scheduling and routing in multi-hop control networks

A Multi-hop Control Network consists of a plant where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. Given a SISO LTI plant, we will address the problem of co-designing a digital controller and the network parameters (scheduling and routing) in order to guarantee stability and maximize a performance metric on the transient response to a step input, with constraints on the control effort, on the output overshoot and on the bandwidth of the communication channel. We show that the above optimization problem is a polynomial optimization problem, which is generally NP-hard. We provide sufficient conditions on the network topology, scheduling and routing such that it is computationally feasible, namely such that it reduces to a convex optimization problem.Comment: 51st IEEE Conference on Decision and Control, 2012. Accepted for publication as regular pape

Feedback Control Goes Wireless: Guaranteed Stability over Low-power Multi-hop Networks

Closing feedback loops fast and over long distances is key to emerging applications; for example, robot motion control and swarm coordination require update intervals of tens of milliseconds. Low-power wireless technology is preferred for its low cost, small form factor, and flexibility, especially if the devices support multi-hop communication. So far, however, feedback control over wireless multi-hop networks has only been shown for update intervals on the order of seconds. This paper presents a wireless embedded system that tames imperfections impairing control performance (e.g., jitter and message loss), and a control design that exploits the essential properties of this system to provably guarantee closed-loop stability for physical processes with linear time-invariant dynamics. Using experiments on a cyber-physical testbed with 20 wireless nodes and multiple cart-pole systems, we are the first to demonstrate and evaluate feedback control and coordination over wireless multi-hop networks for update intervals of 20 to 50 milliseconds.Comment: Accepted final version to appear in: 10th ACM/IEEE International Conference on Cyber-Physical Systems (with CPS-IoT Week 2019) (ICCPS '19), April 16--18, 2019, Montreal, QC, Canad

Linear quadratic regulation of polytopic time-inhomogeneous Markov jump linear systems (extended version)

In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying. We take into account this aspect by considering Markov jump linear systems where the underlying Markov chain is polytopic and time-inhomogeneous, i.e. its transition probability matrix is varying over time, with variations that are arbitrary within a polytopic set of stochastic matrices. We address and solve for this class of systems the infinite-horizon optimal control problem. In particular, we show that the optimal controller can be obtained from a set of coupled algebraic Riccati equations, and that for mean square stabilizable systems the optimal finite-horizon cost corresponding to the solution to a parsimonious set of coupled difference Riccati equations converges exponentially fast to the optimal infinite-horizon cost related to the set of coupled algebraic Riccati equations. All the presented concepts are illustrated on a numerical example showing the efficiency of the provided solution.Comment: Extended version of the paper accepted for the presentation at the European Control Conference (ECC 2019

Cooperative learning in multi-agent systems from intermittent measurements

Motivated by the problem of tracking a direction in a decentralized way, we consider the general problem of cooperative learning in multi-agent systems with time-varying connectivity and intermittent measurements. We propose a distributed learning protocol capable of learning an unknown vector $\mu$ from noisy measurements made independently by autonomous nodes. Our protocol is completely distributed and able to cope with the time-varying, unpredictable, and noisy nature of inter-agent communication, and intermittent noisy measurements of $\mu$. Our main result bounds the learning speed of our protocol in terms of the size and combinatorial features of the (time-varying) networks connecting the nodes