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

System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

Delay-independent decentralised output feedback control for large-scale systems with nonlinear interconnections

In this paper, a stabilisation problem for a class of large-scale systems with nonlinear interconnections is considered. All the uncertainties are nonlinear and are subject to the effects of time delay. A decentralised static output feedback variable structure control is synthesised and the stability of the corresponding closed-loop system is analysed based on the Lyapunov Razumikhin approach. A set of conditions is developed to guarantee that the large-scale interconnected system is stabilised uniformly asymptotically. Further study shows that the conservatism can be reduced by employing additive controllers if the known interconnections are separated into matched and mismatched parts. It is not required that the subsystems are square. The designed controller is independent of time delay and thus it does not require memory. Simulation results show the effectiveness of the proposed approach

Delay-Based Controller Design for Continuous-Time and Hybrid Applications

Motivated by the availability of different types of delays in embedded systems and biological circuits, the objective of this work is to study the benefits that delay can provide in simplifying the implementation of controllers for continuous-time systems. Given a continuous-time linear time-invariant (LTI) controller, we propose three methods to approximate this controller arbitrarily precisely by a simple controller composed of delay blocks, a few integrators and possibly a unity feedback. Different problems associated with the approximation procedures, such as finding the optimal number of delay blocks or studying the robustness of the designed controller with respect to delay values, are then investigated. We also study the design of an LTI continuous-time controller satisfying given control objectives whose delay-based implementation needs the least number of delay blocks. A direct application of this work is in the sampled-data control of a real-time embedded system, where the sampling frequency is relatively high and/or the output of the system is sampled irregularly. Based on our results on delay-based controller design, we propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. Unlike a typical sampled-data controller, the hybrid controller introduced here -— consisting of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback -— is robust to sampling jitter and can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation

A unified smith predictor approach for power system damping control design using remote signals

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