Networks of coupled systems may exhibit a form of incomplete synchronization called partial synchronization or cluster synchronization, which refers to the situation where only some, but not all, systems exhibit synchronous behavior. Moreover, due to perturbations or uncertainties in the network, exact partial synchronization in the sense that the states of the systems within each cluster become identical, cannot be achieved. Instead, an approximate synchronization may be observed, where the states of the systems within each cluster converge up to some bound, and this bound tends to zero if (the size of) the perturbations tends to zero. In order to derive sufficient conditions for this robustified notion of synchronization, which we refer to as practical partial synchronization, first, we separate the synchronization error dynamics from the network dynamics and interpret them in terms of a nonautonomous system of delay differential equations with a bounded additive perturbation. Second, by assessing the practical stability of this error system, conditions for practical partial synchronization are derived and formulated in terms of linear matrix inequalities. In addition, an explicit relation between the size of perturbation and the bound of the synchronization error is provided.

Sensitivity analysis for hybrid systems with state-triggered jumps is experiencing renewed attention for the control of robots with intermittent contacts. The basic assumption that enables this type of analysis is that jumps are triggered when the state reaches, transversally, a sufficiently smooth switching surface. In many scenarios of practical relevance, however, this switching surface is just piecewise smooth and, moreover, a perturbation of the initial conditions or the input leads to a different number of jumps than the nominal trajectory's. This work extends the sensitivity analysis in this context, under the assumptions that (i) at least locally, the intermediate perturbation-dependent jumps lead the system to reach always the nominal post-impact mode and (ii) once a switching and corresponding intermediate jump has occurred, its corresponding constraint remains active until reaching the nominal post-impact mode. Numerical simulations complement and validate the theoretical findings.

We give an introduction to the analysis of the dynamics of deterministic nonlinear systems from a systems and control point of view. In particular, we discuss the stabilizing or destabilizing effect of feedback interconnections in nonlinear dynamical systems. With the help of this machinery we explain two types of complex collective dynamics in networks of nonlinear systems.

High-speed visual servo systems are used in an increasing number of applications. Yet modeling and optimizing these systems remains a research challenge, largely because these systems consist of tightly-coupled design parameters across multiple domains, including image sensors, vision algorithms, processing systems, mechanical systems, control systems, among others. To overcome such a challenge, this work applies an axiomatic design method to the design of high-speed visual servo systems, such that cross-domain couplings are explicitly modeled and subsequently eliminated when possible. More importantly, methods are proposed to model the sample rate, measurement error, and delay of visual feedback based on design parameters across multiple domains. Lastly, methods to construct a holistic model and to perform cross-domain optimization are proposed. The proposed methods are applied to a representative case study that demonstrates the necessity of cross-domain modeling and optimization, as well as the effectiveness of the proposed methods.

This paper considers the design of a nonlinear observer-based output-feedback controller for oil-field drill-string systems aiming to eliminate (torsional) stick-slip oscillations. Such vibrations decrease the performance and reliability of drilling systems and can ultimately lead to system failure. Current industrial controllers regularly fail to eliminate stick-slip vibrations under increasingly challenging operating conditions caused by the tendency towards drilling deeper and inclined wells, where multiple vibrational modes play a role in the occurrence of stick-slip vibrations. As a basis for controller synthesis, a multi-modal model of the torsional drill-string dynamics for a real rig is employed, and a bit-rock interaction model with severe velocity-weakening effect is used. The proposed model-based controller design methodology consists of a state-feedback controller and a (nonlinear) observer. Conditions, guaranteeing asymptotic stability of the desired equilibrium, corresponding to nominal drilling operation, are presented. The proposed control strategy has a significant advantage over existing vibration control systems as it can effectively cope with multiple modes of torsional vibration. Case study results using the proposed control strategy show that stick-slip oscillations can indeed be eliminated in realistic drilling scenarios in which industrial controllers fail to do so. Moreover, key robustness aspects of the control system involving the robustness against uncertainties in the bit-rock interaction and changing operational conditions are evidenced.

Stick-slip vibrations decrease the performance, reliability, and fail safety of drilling systems. The aim of this paper is to design a robust output-feedback control approach to eliminate torsional stick-slip vibrations in drilling systems. Current industrial controllers regularly fail to eliminate stick-slip vibrations, especially when multiple torsional flexibility modes play a role in the onset of stick-slip vibrations. As a basis for controller synthesis, a multimodal model of the torsional dynamics for a real drill-string system is employed. The proposed controller design strategy is based on skewed-μ DK iteration and aims at optimizing the robustness with respect to uncertainty in the nonlinear bit-rock interaction. Moreover, a closed-loop stability analysis for the nonlinear drill-string model is provided. This controller design strategy offers several benefits compared with existing controllers. First, only surface measurements are employed, therewith avoiding the need for down-hole measurements. Second, multimodal drill-string dynamics are effectively dealt with in ways inaccessible to state-of-practice controllers. Third, robustness with respect to uncertainties in the bit-rock interaction is explicitly provided and closed-loop performance specifications are included in the controller design. Case study results confirm that stick-slip vibrations are indeed eliminated in realistic drilling scenarios using the designed controller in which state-of-practice controllers fail to achieve this.

This work explores the stabilization of desired dynamic motion tasks involving hard impacts at non-negligible speed for humanoid robots. To this end, a so-called reference spreading hybrid control law is designed showing promising results in simulation. The simulations are performed employing a dynamical model of an existing humanoid robot and impacts are assumed to be inelastic. The desired motion task consists of having the robot balancing on one foot while repeatedly making and breaking contact with a wall by means of one hand. The simulation results illustrate that the considered controller is suited to control humanoid robot motions with impacts.

In this paper, a distributed consensus control approach for vehicular platooning systems is proposed. In formalizing the underlying consensus problem, a realistic vehicle dynamics model is considered and a velocity-dependent spacing policy between two consecutive vehicles is realized. As a particular case, the approach allows to consider bidirectional vehicle interaction, which improves the cohesion between vehicles in the platoon. Exponential stability of the platoon dynamics is evaluated, also in the challenging scenario in which a limitation on the velocity of one of the vehicles in the platoon is introduced. The theoretical results are experimentally validated using a three-vehicle platoon consisting of (longitudinally) automated vehicles equipped with wireless intervehicle communication and radar-based sensing.

In this paper, a novel distributed consensus control approach for vehicular platooning systems is proposed. In formalizing the underlying consensus problem, a realistic vehicle dynamics model is considered and a velocity-dependent spacing-policy between two consecutive vehicles is realized. For a generic communication topology, conditions for asymptotic platoon stability are proposed. As a particular case, these results allow to consider bi-directional vehicle interaction, which improves the coherence between the vehicles in the platoon. The theoretical results are experimentally validated using a three-vehicle platoon consisting of (longitudinally) automated vehicles equipped with wireless inter-vehicle communication and radar-based sensing.

Active trailer steering control can improve the manoeuvrability of (long) truck-trailer combinations during cornering. To assess the effectiveness of trailer steering control, we formulate the problem of reducing the so-called swept-path width during cornering, and that of eliminating unsafe tail swing of the trailer, as a tracking control problem. We present a kinematic tractor-trailer model including off-axle hitching, on the basis of which nonlinear control strategies solving this tracking problem are developed. The effectiveness of the proposed approach is evidenced by means of a benchmark simulation study.