Networks of interconnected dynamical systems may exhibit a so-called partial synchronization phenomenon, which refers to synchronous behaviors of some but not all of the systems. The patterns of partial synchronization are often characterized by partial synchronization manifolds, which are linear invariant subspace of the state space of the network dynamics. Here, we propose a Lyapunov-Krasovskii approach to analyze the stability of partial synchronization manifolds in delay-coupled networks. First, the synchronization error dynamics are isolated from the network dynamics in a systematic way. Second, we use a parameter-dependent Lyapunov-Krasovskii functional to assess the local stability of the manifold, by employing techniques originally developed for linear parameter-varying (LPV) time-delay systems. The stability conditions are formulated in the form of linear matrix inequalities (LMIs) which can be solved by several available tools.@en

In this paper, a method for pattern analysis in networks of diffusively coupled nonlinear systems of Lur'e form is presented. We consider a class of nonlinear systems which are globally asymptotically stable in isolation. Interconnecting such systems into a network via diffusive coupling can result in persistent oscillatory behavior, which may lead to pattern formation in the coupled systems. Some of these patterns may coexist and can even all be locally stable, i.e. the network dynamics can be multistable. Multistability makes the application of common analysis methods, such as the direct Lyapunov method, highly involved. We develop a numerically efficient method in order to analyze the oscillatory behavior occurring in such networks. We focus on networks of Lur'e systems in which the oscillations appear via a Hopf bifurcation with the (diffusively) coupling strength as a bifurcation parameter and therefore display sinusoidal-like behavior in the neighborhood of the bifurcation point. Using the describing function method, we replace nonlinearities with their linear approximations. Then we analyze the system of linear equations by means of the multivariable harmonic balance method. We show that the multivariable harmonic balance method is able to accurately predict patterns that appear in such a network, even if multiple patterns coexist.@en

This paper proposes a cooperative intersection control strategy, which aims to decrease the number of accidents and to increase the traffic flow at intersections. Existing high-level automation methodologies mainly focus on the determination of a safe crossing sequence of the involved vehicles, typically ignoring realistic vehicle dynamics aspects. The solution proposed in this paper, referred to as cooperative intersection control (CIC), takes into account the dynamics of the vehicles and is based on the novel concept of virtual platooning. Virtual platooning allows to form platoons of vehicles that are in different lanes of the intersection and have different directional intentions. Herewith, both safe passage of the vehicles through the intersection and a high intersection throughput (due to close "virtual" vehicle following) can be achieved. The performance of the proposed strategy is assessed, and a comparison between the CIC and an intersection controlled with traffic lights is presented.@en

This work addresses the problem of pattern analysis in networks consisting of delay-coupled identical Lur'e systems. We study a class of nonlinear systems, which, being isolated, are globally asymptotically stable. Assembling such systems into a network via time-delayed coupling may result in the change of network equilibrium stability under parameter variation in the coupling. In this work, we focus on cases where a Hopf bifurcation causes the change of stability of the network equilibrium and leads to the occurrence of oscillatory modes (patterns). Moreover, some of these patterns can co-exist for the same set of coupling parameters, which makes the analysis by means of common methods, such as the Lyapunov-Krasovskii method or the analysis of Poincaré maps, cumbersome. A numerically efficient algorithm, aiming at the computation of the oscillatory patterns occurring in such networks, is presented. Moreover, we show that our approach is able to deal with co-existing patterns, and both stable and unstable regimes can be simultaneously computed, which gives deep insight into the network dynamics. In order to illustrate the efficiency of the method, we present two examples in which the instability of the network equilibria is caused by a subcritical and a supercritical Hopf bifurcation. In addition, a bifurcation analysis of the subcritical case is performed in order to further explain the occurrence of the detected coexisting modes. @en

This chapter presents results on the design and experimental implementation and testing of robust controllers for the high-speed milling process for the purpose of avoiding chatter vibrations. Chatter vibrations are intimately related to the delay nature of the cutting process inherent to milling and should be avoided to ensure a high product quality. A design approach based on μμ -synthesis is used to synthesize a controller that avoids chatter vibrations in the presence of model uncertainties and while respecting key performance specifications. The experimental validation of this controller on a benchmark setup, involving a spindle system including an active magnetic bearing, shows that chatter can be robustly avoided while significantly increasing the material removal rate, i.e., the productivity.@en