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This document is an editorial for a special issue of the International Journal of Robust & Nonlinear Control on the topic of time-delay systems. It provides a historical overview of functional differential equations and highlights the contributions of Nikolay Nikolayevich Krasovskii and Aristide Halanay to the field. The special issue includes 21 research papers covering stability, robustness, observer theory, predictors, and delay-based approaches to partial differential equation models. Each paper is briefly described, covering topics such as stabilization of uncertain systems, sampled-data control for nonlinear systems, observer theory for differential delay systems, sensor fault estimation, and control approaches for vehicular platoons. The summaries aim to provide library patrons with a quick understanding of the papers' contents and their relevance to their research interests. [Extracted from the article]

The event-driven model-free control is proposed in this article, which deals with the 'trade-off' between computational cost and system performance. Model-free controllers demand low computational resources and have high robustness, which is especially suitable for embedded systems with complex dynamics and/or affected by disturbances. The proposed method is implemented in two distinct nonlinear Multiple Input, Multiple Output (MIMO) motion models: a quadrotor model hovering in different weather circumstances and a vehicular friction control model operating in variable road surface conditions. Under the time- and event-driven schemes, the model-free control is compared with standard control strategies in various realistic scenarios. [ABSTRACT FROM AUTHOR]

In this paper, a sensor fault-tolerant control scheme using robust model predictive control (MPC) and set-theoretic fault detection and isolation (FDI) is proposed. The robust MPC controller is used to control the plant in the presence of process disturbances and measurement noises while implementing a mechanism to tolerate faults. In the proposed scheme, fault detection (FD) is passive based on interval observers, while fault isolation (FI) is active by means of MPC and set manipulations. The basic idea is that for a healthy or faulty mode, one can construct the corresponding output set. The size and location of the output set can be manipulated by adjusting the size and center of the set of plant inputs. Furthermore, the inputs can be adjusted on-line by changing the input-constraint set of the MPC controller. In this way, one can design an input set able to separate all output sets corresponding to all considered healthy and faulty modes from each other. Consequently, all the considered healthy and faulty modes can be isolated after detecting a mode changing while preserving feasibility of MPC controller. As a case study, an electric circuit is used to illustrate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Center of Intelligent Control and Telescience, Graduate School at Shenzhen Tsinghua University, University Town, Nanshan, 518055 Shenzhen, PR China In this paper, a fault-tolerant control (FTC) scheme is proposed for actuator faults, which is built upon tube-based model predictive control (MPC) as well as set-based fault detection and isolation (FDI). In the class of MPC techniques, tubebased MPC can effectively deal with system constraints and uncertainties with relatively low computational complexity compared with other robust MPC techniques such as min-max MPC. Set-based FDI, generally considering the worst case of uncertainties, can robustly detect and isolate actuator faults. In the proposed FTC scheme, fault detection (FD) is passive by using invariant sets, while fault isolation (FI) is active by means of MPC and tubes. The active FI method proposed in this paper is implemented by making use of the constraint-handling ability of MPC to manipulate the bounds of inputs. After the system has been detected to become faulty, the input-constraint set of the MPC controller is adjusted to actively excite the system for achieving FI guarantees on-line, where an active FI-oriented input set is designed off-line. In this way, the system can be excited in order to obtain more extra system-operating information for FI than passive FI approaches. Overall, the objective of this paper is to propose an actuator MPC scheme with as little as possible of FI conservatism and computational complexity by combining tube-based MPC and set theory within the framework of MPC, respectively. Finally, a case study is used to show the effectiveness of the proposed FTC scheme. [ABSTRACT FROM AUTHOR]

SUMMARY Interval observers are constructed for discrete-time systems. First, time-invariant interval observers are proposed for a family of nonlinear systems. Second, it is shown that, for any time-invariant exponentially stable discrete-time linear system with additive disturbances, time-varying exponentially stable discrete-time interval observers can be constructed. The latter result relies on the design of time-varying changes of coordinates, which transform a linear system into a nonnegative one. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: For time-varying forward-complete nonlinear systems with delay in the input, a new reduction model approach is proposed. It presents three advantages. First, the corresponding control laws do not include distributed terms. Second, it yields closed-loop systems with positive solutions that can be easily derived. Finally, the stabilized systems possess some robustness properties that can be estimated. [Copyright &y& Elsevier]

This article focuses on the stabilisation problem of fluid-flow delay models of transmission control protocol/active queue management (TCP/AQM) networks by using a proportional-integral (PI) controller as AQM strategy. More precisely, the complete set of PI controllers that exponentially stabilises the corresponding linear time-delay system is derived. Using the particular geometric properties of this set of the controller parameters, the issues of robustness to uncertainty in the network parameters and to perturbation in the controller coefficients are addressed. Then, a methodology to compute a non-fragile PI AQM controller is provided. Finally, exponential estimates for the closed-loop system solutions, allowing to evaluate the performance of the corresponding PI-controlled closed-loop system, are proposed by using a Lyapunov-Krasovskii functional approach. An illustrative example completes the presentation. [ABSTRACT FROM AUTHOR]

In this paper, we present a geometric method for describing the effects of the ‘delay-induced uncertainty’ on the stability of a standard Smith predictor control scheme. The method consists of deriving the ‘stability crossing curves’ in the parameter space defined by the ‘nominal delay’ and ‘delay uncertainty’, respectively. More precisely, we start by computing the ‘crossing set’, which consists of all frequencies corresponding to all points on the stability crossing curve, and next we give their ‘complete classification’, including also the explicit characterization of the ‘directions’ in which the zeros cross the imaginary axis. This approach complements existing algebraic stability tests, and it allows some new insights in the stability analysis of such control schemes. Several illustrative examples are also included. [ABSTRACT FROM PUBLISHER]

We address the output feedback stabilization problem of linear finite-dimensional SISO systems. Limitations of static time-invariant output feedback on stabilizability are well known. We investigate and compare the possibilities of two recently proposed simple modifications/generalizations of static time-invariant output feedback to remove such limitations. The first approach consists of introducing a time-delay in the control law, which can be treated as an additional control parameter. The second approach consists of making the gain time-varying. We show that both approaches are complementary. Existing theoretical results are brought together in a unifying framework. Numerical procedures for the construction of the controllers are provided. Robustness w.r.t. both parametric and delay uncertainty are dealt with. As an illustration the stabilizability of all second-order systems is completely determined. [ABSTRACT FROM PUBLISHER]

This paper focuses on the robustness analysis of a simple (second-order) control algorithm for data transfer in high-speed networks. The model under consideration (derived using a fluid approximation technique) can be found in Izmailov (SIAM J. Contr. Optimiz. 34 (1996) 1767). The novelty of the approach lies in characterizing the stability of the scheme in the delay-parameter space (where the delays correspond to the control-time interval, and to the round-trip time, respectively). Thus, we shall compute some delay-insensitive measures for the algorithm which give upper and lower bounds for the uncertainty in the knowledge of the round-trip times. [Copyright &y& Elsevier]

Abstract: For a family of nonlinear discrete-time systems with input, output and uncertain terms, a new interval observer is designed. Its main feature is that it is composed of two copies of classical observers. This interval observer applies in the presence of unknown bounded nonlinear terms and additive disturbances and is used to achieve asymptotic stability through an appropriate choice of dynamic output feedback. An illustrative example completes the presentation. [Copyright &y& Elsevier]

Abstract: Congestion control is a fundamental building block in packet switching networks such as the Internet due to the fact that communication resources are shared. It has been shown that the plant dynamics is essentially made up of an integrator plus time delay and that a proportional controller plus a Smith predictor defines a simple and effective controller. It has also been shown that the TCP congestion control can be modelled using a Smith predictor plus a proportional controller. Due to the importance of this control structure in the field of data network congestion control, we analyse the robust stability of the closed-loop system in the face of delay uncertainties that are present in data networks due to queuing. In particular, by applying a geometric approach, we derive a bound on the proportional controller gain which is necessary and sufficient to guarantee the closed-loop stability for a given bound on the delay uncertainty. [Copyright &y& Elsevier]