Recent developments in computer and communication technologies are leading to an increasingly networked and wireless world. This raises new challenging questions in the context of networked control systems, especially when the computation, communication and energy resources of the system are limited. To efficiently use the available resources it is desirable to limit the control actions to instances when the system really needs attention. Unfortunately, the classical time-triggered control paradigm is based on performing sensing and actuation actions periodically in time (irrespective of the state of the system) rather than when the system needs attention. Therefore, it is of interest to consider event-triggered control as an alternative paradigm as it is more natural to trigger control actions based on the system state, output, or other available information. Event-triggered control can thus be seen as the introduction of feedback in the sensing, communication, and actuation processes. To facilitate an easy implementation of event-triggered control, we propose to combine the principles and particularly the benefits of event-triggered control and classical periodic time-triggered control. The idea is to periodically evaluate the triggering condition and to decide, at every sampling instant, whether the feedback loop needs to be closed. This leads to the so-called periodic event-triggered control (PETC) systems. In this chapter, we discuss PETC strategies, their benefits and two analysis and design frameworks for linear and nonlinear plants, respectively.

In event-triggered control, the control task consisting of sampling the plant’s output and updating the control input is executed whenever a certain event function exceeds a given threshold. The event function typically needs to be monitored continuously, which is difficult to realize in digital implementations. This has led to the development of periodic event-triggered control (PETC), in which the event function is only evaluated periodically. In this paper, we consider general nonlinear continuous event-triggered control (CETC) systems, and present a method to transform the CETC system into a PETC system. In particular, we provide an explicit sampling period at which the event function is evaluated and we present a constructive procedure to redesign the triggering condition. The latter is obtained by upper-bounding the evolution of the event function of the CETC system between two successive sampling instants by a linear time-invariant system and then by using convex overapproximation techniques. Using this approach, we are able to preserve the control performance guarantees (e.g., asymptotic stability with a certain decay rate) of the original CETC system.

Automated vehicles are required to operate on highways and in complex urban scenarios. To safely handle these complex environmental influences, sophisticated automated driving functions demand a high availability of all involved components in combination with increased computational power. Particular multi-core platforms are deployed to cope with these demands. To achieve higher system availability for SAE level 3 and higher, fail operational concepts from system level down to Microcontroller Unit (MCU) level are needed. These concepts include hardware as well as software requirements and are discussed in this paper. For an increased computing performance, the idea and further the model of a parallel computation method for driving functions and their control algorithms is introduced. For that a stabilizing controller is implemented on different cores of the multi-core processor. Finally, this resulting closed-loop system is modeled as a hybrid system which will serve as an input for further stability analysis.

We address the problem of attack detection and isolation for a class of discrete-time nonlinear systems under (potentially unbounded) sensor attacks and measurement noise. We consider the case when a subset of sensors is subject to additive false data injection attacks. Using a bank of observers, each observer leading to an Input-to-State Stable (ISS) estimation error, we propose two algorithms for detecting and isolating sensor attacks. These algorithms make use of the ISS property of the observers to check whether the trajectories of observers are "consistent" with the attack-free trajectories of the system. Simulations results are presented to illustrate the performance of the proposed algorithms.

We consider a multi-agent system in which agents arrive and depart from a network randomly as a Bernoulli process. Each agent that is active in the network must decide between two actions represented by 0 or 1. Each active agent then observes the action of a random neighbour and updates its preference towards a certain action. New agents that arrive into the network are activated with a random preference and action. This means that the notion of consensus in the standard sense can no longer be applied and instead, we provide conditions under which majority action preservation occurs when the number of agents is arbitrarily large. This property will imply that a large fraction of the active agent population will retain their action almost surely.

We address the problem of robust state estimation and attack isolation for a class of discrete-time nonlinear systems with positive-slope nonlinearities under (potentially unbounded) sensor attacks and measurement noise. We consider the case when a subset of sensors is subject to additive false data injection attacks. Using a bank of circle-criterion observers, each observer leading to an Input-to-State Stable (ISS) estimation error, we propose a estimator that provides robust estimates of the system state in spite of sensor attacks and measurement noise; and an algorithm for detecting and isolating sensor attacks. Our results make use of the ISS property of the observers to check whether the trajectories of observers are consistent with the attack-free trajectories of the system. Simulations results are presented to illustrate the performance of the results.

We investigate how changes in network structure can lead to pathological oscillations similar to those observed in epileptic brain. Specifically, we conduct a bifurcation analysis of a network of two Jansen-Rit neural mass models, representing two cortical regions, to investigate different aspects of its behavior with respect to changes in the input and interconnection gains. The bifurcation diagrams, along with simulated EEG time series, exhibit diverse behaviors when varying the input, coupling strength, and network structure. We show that this simple network of neural mass models can generate various oscillatory activities, including delta wave activity, which has not been previously reported through analysis of a single Jansen-Rit neural mass model. Our analysis shows that spike-wave discharges can occur in a cortical region as a result of input changes in the other region, which may have important implications for epilepsy treatment. The bifurcation analysis is related to clinical data in two case studies.

Abstract This paper studies a distributed multi-agent control problem in which the agents have single-integrator dynamics. A distributed control law is proposed to drive the agents to attain a desired formation shape and acquire an identical velocity. Using singular perturbation theory and stability results for nonlinear cascade systems, it is shown that agents can achieve the desired formation shape and velocity at different time scales. Moreover, it is shown that there exists an upper bound for a time-scale parameter (perturbation parameter) in the control law such that for time-scale parameters less than this bound, the initial conditions of the shape control error system will remain in a stability basin of the equilibrium. Simulation results are provided to validate the proposed algorithm.

We study networked control systems (NCSs) where the controller is given by a state-feedback law and the plant is modeled by a dynamical system evolving on two time-scales, representing a characterization by some slow and fast dynamics. When using the stability analysis frameworks for NCSs from the literature, this time-scale separation is ignored and, as a result, the slow dynamics are in general updated at the same rate as the fast dynamics, leading to many redundant transmissions of the slow dynamics. Therefore, we assume in this paper that the slow dynamics and fast dynamics can be transmitted separately over the network, allowing us to use techniques inspired by singular perturbation methods in the stability analysis. That is, we show by means of a Lyapunov-based proof how to obtain conditions on the transmission rates (expressed in maximal allowable transmission intervals (MATIs)) for the slow and fast dynamics separately such that stability of the NCS is guaranteed, based only on approximated models of the slow and the fast dynamics.