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

Stabilizability of Markov jump linear systems modeling wireless networked control scenarios (extended version)

The communication channels used to convey information between the components of wireless networked control systems (WNCSs) are subject to packet losses due to time-varying fading and interference. The WNCSs with missing packets can be modeled as Markov jump linear systems with one time-step delayed mode observations. While the problem of the optimal linear quadratic regulation for such systems has been already solved, we derive the necessary and sufficient conditions for stabilizability. We also show, with an example considering a communication channel model based on WirelessHART (a on-the-market wireless communication standard specifically designed for process automation), that such conditions are essential to the analysis of WNCSs where packet losses are modeled with Bernoulli random variables representing the expected value of the real random process governing the channel.Comment: Extended version of the paper accepted for the presentation at the 58th IEEE Conference on Decision and Control (CDC 2019

Automatic Verification of Wireless Control in a Mining Ventilation System

International audienceWe address a wireless networked control problem for a mine ventilation system. Ventilation control is essential for the control of the operation of a mine for safety and energy optimization. The main control objective is to guarantee safety of the closed loop system. This test-case is simple enough to be computationally tractable, and yet it exposes the main difficulties encountered when using wireless networked systems for safety-critical applications. The focus of this paper is the formal verification of the operation of a closed loop control system for the so called secondary ventilation system that ensures air flow in the chambers of the mine where extraction takes place. The secondary ventilation system is modeled conservatively in the sense that if the formal verification process provides a positive answer then the system is guaranteed to work correctly while the converse is not necessarily true. For control, we use a simple threshold scheme. The overall closed-loop system is described by a hybrid model that takes into account the effects of time-delay, transmission errors and allows the precise formulation of the safety constraints. To ensure that the formal verification process is computationally tractable, we reason in the framework of temporal logics, and apply abstraction techniques and model checking tools that we developed previously

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 time-varying 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