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

Energy optimal coordination of fully autonomous vehicles in urban intersections

This paper provides a solution to conflict resolutions between Autonomous Vehicles (AV) crossing an urban intersection. The conflict resolution problem is formulated as an optimal control problem, where the objective is to minimize the energy consumption of all the vehicles, while avoiding collisions. Since the problem has a combinatorial nature, it is tackled though a sequential mixed-integer quadratically constrained programming approach. Simulation results show that since the AVs do not need to follow specific driving rules, the intersection crossing order is chosen to optimize the overall energy consumption. The research outcome underlines the benefits of moving towards fully autonomous systems which will allow for higher traffic throughput. Furthermore, the proposed formulation is the starting point for future explorations towards real-time implementation

A model predictive control approach for stochastic networked control systems

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An approach to observer-based decentralized control under periodic protocols

This paper provides an approach to analyze and design decentralized observer-based controllers for large-scale linear plants subject to network communication constraints and varying sampling intervals. Due to communication constraints, it is impossible to transmit all input and output data simultaneously over the communication network that connects sensors, actuators and controllers. A protocol orchestrates whatdata is sent over the network at each transmission instant. To handle these communication constraints, it is fruitful to adopt a switched observer structure that switches based on the transmitted information. By taking a discrete-time switched linear system perspective, we are able to derive a general model that captures all these aspects and provides insight into how they influence each other. Focusing on the class of so-called periodic protocols (of which the well-known Round Robin protocol is a special case), we provide a method to assess robust stability using a polytopic overapproximation and LMI-based stability conditions. Although the design problem is in generalnon-convex, we provide a procedure to find stabilizing control laws by simplifying the control problem. The design of the controller exploits the periodicity of protocols and ignores the global coupling between subsystems of the plant and variation of the sampling intervals. To assess the robust stability of the resulting closed-loop system including the ignored effects, an a posteriori analysis is conducted based on the derived LMIs. Click here to download the pape

Output-based event-triggered control with guaranteed cal L∞ -gain and improved and decentralised event-triggering

Most event-triggered controllers available nowadays are based on static state-feedback controllers. As in many control applications full state measurements are not available for feedback, it is the objective of this paper to propose eventtriggered dynamical output-based controllers. The fact that the controller is based on output feedback instead of state feedback does not allow for straightforward extensions of existing eventtriggering mechanisms if a minimum time between two subsequent events has to be guaranteed. Furthermore, since sensor and actuator nodes can be physically distributed, centralised eventtriggering mechanisms are often prohibitive and, therefore, we will propose a decentralised event-triggering mechanism. This event-triggering mechanism invokes transmission of the outputs in a node when the difference between the current values of the outputs in the node and their previously transmitted values becomes large compared to the current values and an additional threshold. For such event-triggering mechanisms, we will study closed-loop stability and L1-performance and provide bounds on the minimum time between two subsequent events generated by each node, the so-called inter-event time of a node. This enables us to make tradeoffs between closed-loop performance on the one hand and communication load on the other hand, or even between the communication load of individual nodes. In addition, we will model the event-triggered control system using an impulsive model, which truly describes the behaviour of the event-triggered control system. As a result, we will be able to guarantee stability and performance for event-triggered controllers with larger minimum inter-event times than the existing results in the literature. We illustrate the developed theory using three numerical examples

Joint state and parameter estimation for discrete-time polytopic linear parameter-varying systems

Linear parameter-varying systems are very suitable for modelling nonlinear systems, since well-established methods from the linear-systems domain can be applied. Knowledge about the scheduling parameter is an important condition in this modelling framework. In case this parameter is not known, joint state and parameter-estimation methods can be employed, e.g., using interacting multiple-model estimation methods, or using an extended Kalman filter. However, these methods cannot be directly used in case the parameters lie in a polytopic set. Furthermore, these existing methods require tuning in order to have convergence and stability. In this paper, we propose to solve the joint-estimation problem in a two-step, Dual Estimation approach, where we first solve the parameter-estimation problem by solving a constrained optimisation problem in a recursive manner and secondly, employ a robust polytopic observer design for state estimation. Simulations show that our novel method outperforms the existing joint-estimation methods and is a promising first step for further research

Output-based event-triggered control with guaranteed L∞-gain and improved event-triggering

Most event-triggered controllers available nowadays are based on static state-feedback controllers. As in many control applications the full state is not available for feedback, it is the objective of this paper to propose event-triggered dynamical output-based controllers. The fact that the controller is based on output feedback instead of state feedback does not allow for straightforward extensions of existing event-triggering mechanisms if a minimum time between two subsequent events, the so-called ‘minimum inter-event time’, has to be guaranteed. Therefore, we will propose an event-triggering mechanism that invokes execution of the control task when the difference between the measured output or the control input of the plant or controller, respectively, and its previously sampled value becomes ‘large’ compared to its current value and an additional threshold. For such event-triggering mechanisms, we will study closed-loop stability and L1-performance and provide bounds on the minimum inter-event time. In addition, we will model the event-triggered control system using impulsive systems, which truly describe the behaviour of the event-triggered control system. As a result, we can guarantee stability and performance for improved event-triggered controllers with larger minimum inter-event times than existing results in literature