On general systems with network-enhanced complexities

In recent years, the study of networked control systems (NCSs) has gradually become an active research area due to the advantages of using networked media in many aspects such as the ease of maintenance and installation, the large flexibility and the low cost. It is well known that the devices in networks are mutually connected via communication cables that are of limited capacity. Therefore, some network-induced phenomena have inevitably emerged in the areas of signal processing and control engineering. These phenomena include, but are not limited to, network-induced communication delays, missing data, signal quantization, saturations, and channel fading. It is of great importance to understand how these phenomena influence the closed-loop stability and performance properties

Event-triggered robust distributed state estimation for sensor networks with state-dependent noises

This paper is concerned with the event-triggered distributed state estimation problem for a class of uncertain stochastic systems with state-dependent noises and randomly occurring uncertainties over sensor networks. An event-triggered communication scheme is proposed in order to determine whether the measurements on each sensor should be transmitted to the estimators or not. The norm-bounded uncertainty enters into the system in a random way. Through available output measurements from not only the individual sensor but also its neighbouring sensors, a sufficient condition is established for the desired distributed estimator to ensure that the estimation error dynamics are exponentially mean-square stable. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities, and then the explicit expression is given for the distributed estimator gains. Finally, a simulation example is provided to show the effectiveness of the proposed event-triggered distributed state estimation scheme.This work was supported in part by the Deanship of Scientific Research (DSR) at King Abdulaziz University of Saudi Arabia under Grant 16-135-35-HiCi, the National Natural Science Foundation of China under Grants 61374127 and 61329301, the Scientific and Technology Research Foundation of Heilongjiang Education Department of China under Grant 12541061 and 12511014, and the Alexander von Humboldt Foundation of Germany

Networked and event-triggered control systems

In this thesis, control algorithms are studied that are tailored for platforms with limited computation and communication resources. The interest in such control algorithms is motivated by the fact that nowadays control algorithms are implemented on small and inexpensive embedded microprocessors and that the sensors, actuators and controllers are connected through multipurpose communication networks. To handle the fact that computation power is no longer abundant and that communication networks do not have in finite bandwidth, the control algorithms need to be either robust for the deficiencies induced by these constraints, or they need to optimally utilise the available computation and communication resources. In this thesis, methodologies for the design and analysis of control algorithms with such properties are developed. Networked Control Systems: In the first part of the thesis, so-called networked control systems (NCSs) are studied. The control algorithms studied in this part of the thesis can be seen as conventional sampled-data controllers that need to be robust against the artefacts introduced by using a finite bandwidth communication channel. The network-induced phenomena that are considered in this thesis are time-varying transmission intervals, time-varying delays, packet dropouts and communication constraints. The latter phenomenon causes that not all sensor and actuator data can be transmitted simultaneously and, therefore, a scheduling protocol is needed to orchestrate when to transmit what data over the network. To analyse the stability of the NCSs, a discrete-time modelling framework is presented and, in particular, two cases are considered: in the first case, the transmission intervals and delays are assumed to be upper and lower bounded, and in the second case, they are described by a random process, satisfying a continuous joint probability distribution. Both cases are relevant. The former case requires a less detailed description of the network behaviour than the latter case, while the latter results in a less conservative stability analysis than the former. This allows to make a tradeoff between modelling accuracy (of network-induced effects) and conservatism in the stability analysis. In both cases, linear plants and controllers are considered and the NCS is modelled as a discrete-time switched linear parameter-varying system. To assess the stability of this system, novel polytopic overapproximations are developed, which allows the stability of the NCS to be studied using a finite number of linear matrix inequalities. It will be shown that this approach reduces conservatism significantly with respect to existing results in the literature and allows for studying larger classes of controllers, including discrete-time dynamical output-based controllers. Hence, the main contribution of this part of the thesis is the development of a new and general framework to analyse the stability of NCSs subject to four network-induced phenomena in a hardly conservative manner. Event-Triggered Control Systems: In the second part of the thesis, socalled event-triggered control (ETC) systems are studied. ETC is a control strategy in which the control task is executed after the occurrence of an external event, rather than the elapse of a certain period of time as in conventional periodic control. In this way, ETC can be designed to only provide control updates when needed and, thereby, to optimally utilise the available computation and communication resources. This part of the thesis consists of three main contributions in this appealing area of research. The first contribution is the extension of the existing results on ETC towards dynamical output-based feedback controllers, instead of state-feedback control, as is common in the majority of the literature on ETC. Furthermore, extensions towards decentralised event triggering are presented. These extensions are important for practical implementations of ETC, as in many control applications the full state is hardly ever available for feedback, and sensors and actuators are often physically distributed, which prohibits the use of centralised event-triggering conditions. To study the stability and the L1-performance of this ETC system, a modelling framework based on impulsive systems is developed. Furthermore, for the novel output-based decentralised event-triggering conditions that are proposed, it is shown how nonzero lower bounds on the minimum inter-event times can be guaranteed and how they can be computed. The second contribution is the proposition of the new class of periodic event-triggered control (PETC) algorithms, where the objective is to combine the benefits that, on the one hand, periodic control and, on the other hand, ETC offer. In PETC, the event-triggering condition is monitored periodically and at each sampling instant it is decided whether or not to transmit the data and to use computation resources for the control task. Such an event-triggering condition has several benefits, including the inherent existence of a minimum inter-event time, which can be tuned directly. Furthermore, the fact that the event-triggering condition is only verified at the periodic sampling times, instead of continuously, makes it possible to implement this strategy in standard time-sliced embedded software architectures. To analyse the stability and the L2-performance for these PETC systems, methodologies based on piecewiselinear systems models and impulsive system models will be provided, leading to an effective analysis framework for PETC. Finally, a novel approach to solving the codesign problem of both the feedback control algorithm and the event-triggering condition is presented. In particular, a novel way to solve the minimum attention and anytime attention control problems is proposed. In minimum attention control, the `attention' that a control task requires is minimised, and in anytime attention control, the performance under the `attention' given by a scheduler is maximised. In this context, `attention' is interpreted as the inverse of the time elapsed between two consecutive executions of a control task. The two control problems are solved by formulating them as linear programs, which can be solved efficiently in an online fashion. This offers a new and elegant way to solve both the minimum attention control problem and the anytime attention control problem in one unifying framework. The contributions presented in this thesis can form a basis for future research explorations that can eventually lead to a mature system theory for both NCSs and ETC systems, which are indispensable for the deployment of NCSs and ETC systems in a large variety of practical control applications

Sequence-based Anytime Control

We present two related anytime algorithms for control of nonlinear systems when the processing resources available are time-varying. The basic idea is to calculate tentative control input sequences for as many time steps into the future as allowed by the available processing resources at every time step. This serves to compensate for the time steps when the processor is not available to perform any control calculations. Using a stochastic Lyapunov function based approach, we analyze the stability of the resulting closed loop system for the cases when the processor availability can be modeled as an independent and identically distributed sequence and via an underlying Markov chain. Numerical simulations indicate that the increase in performance due to the proposed algorithms can be significant.Comment: 14 page