Anton Selivanov

Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators.

We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime. We propose goal functions based on both the difference of the oscillators and a generalized order parameter and demonstrate that the speed-gradient method allows one to find appropriate coupling phases with which different states of synchronization, e.g., in-phase oscillation, splay, or various cluster states, can be selected.

Event-Triggered

Event-triggered approach to networked control systems is used to reduce the workload of the communication network. For the static output-feedback continuous event-trigger may generate an infinite number of sampling instants in finite time (Zeno phenomenon) what makes it inapplicable to the real-world systems. Periodic event-trigger avoids this behavior but does not use all the available information. In the present paper we aim to exploit the advantage of the continuous-time measurements and guarantee a positive lower bound on the inter-event times by introducing a switching approach for finding a waiting time in the event-triggered mechanism. Namely, our idea is to present the closed-loop system as a switching between the system under periodic sampling and the one under continuous event-trigger and take the maximum sampling preserving the stability as the waiting time. We extend this idea to the L2-gain and ISS analysis of perturbed networked control systems with network-induced delays. By examples we demonstrate that the switching approach to event-triggered control can essentially reduce the amount of measurements to be sent through a communication network compared to the existing methods.

H_{\infty}

This paper is aimed at application of the passification based adaptive control to decentralized synchronization of dynamical networks. We consider Lurie type systems with hyper-minimum-phase linear parts and two types of nonlinearities: Lipschitz and matched. The network is assumed to have both instant and delayed time-varying interconnections. Agent model may also include delays. Based on the speed-gradient method decentralized adaptive controllers are derived, i.e. each controller measures only the output of the node it controls. Synchronization conditions for disturbance free networks and ultimate boundedness conditions for networks with disturbances are formulated. The proofs are based on Passification lemma in combination with Lyapunov–Krasovskii functionals technique. Numerical examples for the networks of 4 and 100 interconnected Chua systems are presented to demonstrate the efficiency of the proposed approach.

Control: A Switching Approach

We introduce distributed event-triggered networked control of parabolic systems governed by semilinear diffusion PDEs. Sampled in time spatially distributed (either point or averaged) measurements are transmitted through a communication network to the controller only if a triggering condition is violated. We take into account quantization of the transmitted measurements and network-induced delays that are allowed to be larger than sampling intervals. We show that decentralized event-triggering mechanism can significantly reduce amount of transmitted measurements while preserving the system performance.

Passification-based decentralized adaptive synchronization of dynamical networks with time-varying delays

We suggest an adaptive control scheme for the control of in-phase and cluster synchronization in delay-coupled networks. Based on the speed-gradient method, our scheme adapts the topology of a network such that the target state is realized. It is robust towards different initial conditions as well as changes in the coupling parameters. The emerging topology is characterized by a delicate interplay of excitatory and inhibitory links leading to the stabilization of the desired cluster state. As a crucial parameter determining this interplay we identify the delay time. Furthermore, we show how to construct networks such that they exhibit not only a given cluster state but also with a given oscillation frequency. We apply our method to coupled Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in an expansion of systems close to a Hopf bifurcation. The successful and robust control of this generic model opens up possible applications in a wide range of systems in physics, chemistry, technology, and life science.

Distributed event-triggered control of diffusion semilinear PDEs

We consider output-feedback predictor-based stabilization of networked control systems with large unknown time-varying communication delays. For systems with two networks (sensors-to-controller and controller-to-actuators), we design a sampled-data observer that gives an estimate of the system state. This estimate is used in a predictor that partially compensates unknown network delays. We emphasize the purely sampled-data nature of the measurement delays in the observer dynamics. This allows an efficient analysis via the Wirtinger inequality, which is extended here to obtain exponential stability. To reduce the number of sent control signals, we incorporate the event-triggering mechanism. For systems with only a controller-to-actuators network, we take advantage of continuously available measurements by using a continuous-time predictor and employing a recently proposed switching approach to event-triggered control. For systems with only a sensors-to-controller network, we construct a continuous observer that better estimates the system state and increases the maximum output sampling, therefore, reducing the number of required measurements. A numerical example illustrates that the predictor-based control allows one to significantly increase the network-induced delays, whereas the event-triggering mechanism significantly reduces the network workload.

Controlling cluster synchronization by adapting the topology.

We consider state-feedback predictor-based control of networked control systems with large time-varying communication delays. We show that even a small controller-to-actuators delay uncertainty may lead to a non-small residual error in a networked control system and reveal how to analyze such systems. Then we design an event-triggered predictor-based controller with sampled measurements and demonstrate that, depending on the delay uncertainty, one should choose various predictor models to reduce the error due to triggering. For the systems with a network only from a controller to actuators, we take advantage of the continuously available measurements by using a continuous-time predictor and employing a recently proposed switching approach to event-triggered control. By an example of an inverted pendulum on a cart we demonstrate that the proposed approach is extremely efficient when the uncertain time-varying network-induced delays are too large for the system to be stabilizable without a predictor.

Observer-based input-to-state stabilization of networked control systems with large uncertain delays

An adaptive master-slave output feedback synchronization problem is studied firstly for a network of interconnected nonlinear dynamical systems with bounded disturbance and then for a network of systems with delayed couplings. The proposed structure of decentralized controller and adaptation algorithms in both cases is based on speed-gradient and passification methods. Synchronization conditions for systems with disturbances and for systems with delayed couplings are established. An example of synchronization of the network of Chua systems with bounded disturbances is given. The problem of convergence with prespecified accuracy is examined for the networks of dynamical systems with disturbances. 1

Predictor-based networked control under uncertain transmission delays

We consider a linear uncertain system with an unknown bounded disturbance under a passification-based adaptive controller with quantized measurements. First, we derive conditions ensuring ultimate boundedness of the system. Then we develop a switching procedure for an adaptive controller with a dynamic quantizer that ensures convergence to a smaller set. The size of the limit set is defined by the disturbance bound. Finally, we demonstrate applicability of the proposed controller to polytopic-type uncertain systems and its efficiency by the example of a yaw angle control of a flying vehicle.

Decentralized adaptive controller for synchronization of dynamical networks with delays and bounded disturbances

For a class of uncertain systems we analyze passification-based adaptive controller in the presence of small, unavoidable input and output time-varying delays as may be present in controller implementation. We derive upper bounds for time delays such that in some domain of initial conditions the states of the closed-loop system tend to zero, whereas an adaptive controller gain tends to a constant value. The results are semi-global, that is the domain of initial conditions is bounded but can be made arbitrary large by tuning an appropriate controller parameter. For the first time, we apply an adaptive controller to linear uncertain networked control systems, where sensors, controllers, and actuators exchange their information through communication networks. The efficiency of the results is demonstrated by the example of adaptive network-based control of an aircraft.