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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]

This paper proposes a constructive solution to the output regulation — output tracking problem for a general class of interconnected systems. The class of systems under consideration consists of a linear 2 × 2 hyperbolic Partial Differential Equations (PDE) system coupled at both ends with Ordinary Differential Equations (ODEs). The proximal ODE system, which represents actuator dynamics, is actuated. Colocated measurements are available. The distal ODE system represents the load dynamics. The control objective is to ensure, in the presence of a disturbance signal (regulation problem), that a virtual output exponentially converges to zero. By doing so, we can ensure that a state component of the distal ODE state robustly converges towards a known reference trajectory (output tracking problem) even in the presence of a disturbance with a known structure. The proposed approach combines the backstepping methodology and frequency analysis techniques. We first map the original system to a simpler target system using an invertible integral change of coordinates. From there, we design an adequate full-state feedback controller in the frequency domain. Following a similar approach, we propose a state observer that estimates the state and reconstructs the disturbance from the available measurement. Combining the full-state feedback controller with the state estimation results in a dynamic output-feedback control law. Finally, existing filtering techniques guarantee the closed-loop system robustness properties. [ABSTRACT FROM AUTHOR]

The paper develops an adaptive constrained tracking control technique for a class of 2 × 2 hyperbolic partial differential equation (PDE) systems with boundary actuator dynamics, which are described by a set of ordinary differential equations (ODEs) in the presence of unknown parametric nonlinearities. Since the control input only appears in the uncertain ODE subsystem rather than directly on the boundary of PDE subsystem, the control task becomes quite difficult and the existing direct boundary control approaches are ineffective. Moreover, in this paper, a more challenging problem is considered such that the controlled output and the states of ODE actuators are constrained. To this end, by utilizing finite and infinite dimensional backstepping techniques, barrier Lyapunov functions (BLFs) and adaptive methods, a novel adaptive tracking control approach is proposed. It is the first time that such a constrained tracking control problem is addressed for the PDE-ODE coupled systems considered in this paper. On the basis of the presented method, the rigorous theoretical proof is provided to show that the PDE controlled output and all the states of the ODE actuator stay within the predefined compact sets. Finally, the results are illustrated via a comparative numerical simulation. [Display omitted] • For a linear 2 × 2 hyperbolic PDE systems, the high-order unknown nonlinear actuator dynamics described by a set of ODEs are considered in the boundary point of the PDE. A tracking controller with adaptive dynamic compensation mechanism is developed such that the tracking control problem is addressed for the PDE-ODE coupled system considered in this paper. • For practical requirements for state constraints such as safe operations, physical limitations and so on, the Barrier Lyapunov function is employed to constrain the spatially distributed output of infinite-dimensional system and all the actuator states. [ABSTRACT FROM AUTHOR]