Event-triggered control for rational and Lur’e type nonlinear systems

In the present work, the design of event-triggered controllers for two classes of nonlinear systems is addressed: rational systems and Lur’e type systems. Lyapunov theory techniques are used in both cases to derive asymptotic stability conditions in the form of linear matrix inequalities that are then used in convex optimization problems as means of computing the control system parameters aiming at a reduction of the number of events generated. In the context of rational systems, state-feedback control is considered and differentialalgebraic representations are used as means to obtain tractable stability conditions. An event-triggering strategy which uses weighting matrices to strive for less events is proposed and then it is proven that this strategy does not lead to Zeno behavior. In the case of Lur’e systems, observer-based state-feedback is addressed with event generators that have access only to the system output and observed state, but it imposes the need of a dwell-time, i.e. a time interval after each event where the trigger condition is not evaluated, to cope with Zeno behavior. Two distinct approaches, exact time-discretization and looped-functional techniques, are considered to ensure asymptotic stability in the presence of the dwell-time. For both system classes, emulation design and co-design are addressed. In the emulation design context, the control law (and the observer gains, when appropriate) are given and the task is to compute the event generator parameters. In the co-design context, the event generator and the control law or the observer can be simultaneously designed. Numerical examples are presented to illustrate the application of the proposed methods.Neste trabalho é abordado o projeto de controladores baseados em eventos para duas classes de sistemas não lineares: sistemas racionais e sistemas tipo Lur’e. Técnicas da teoria de Lyapunov são usadas em ambos os casos para derivar condições de estabilidade assintótica na forma de inequações matriciais lineares. Tais condições são então utilizadas em problemas de otimização convexa como meio de calcular os parâmetros do sistema de controle, visando uma redução no número de eventos gerados. No contexto de sistemas racionais, realimentação de estados é considerada e representações algébrico-diferenciais são usadas como meio de obter condições de estabilidade tratáveis computacionalmente. Uma estratégia de disparo de eventos que usa uma medida de erro ponderado através de matrizes definidas positivas é proposta e é demonstrado que tal estratégia não gera comportamento de Zenão. No caso de sistemas tipo Lur’e, considera-se o caso de controladores com restrições de informações, a saber, com acesso apenas às saídas do sistema. Um observador de estados é então utilizado para recuperar a informação faltante. Neste contexto, é necessária a introdução de um tempo de espera (dwell time, em inglês) para garantir a inexistência de comportamento de Zenão. Todavia, a introdução do tempo de espera apresenta um desafio adicional na garantia de estabilidade que é tratado neste trabalho considerando duas técnicas possíveis: a discretização exata do sistema e o uso de looped-functionals (funcionais em laço, em uma tradução livre). Para ambas classes de sistemas, são tratados os problemas de projeto por emulação e co-design (projeto simultâneo, em uma tradução livre). No projeto por emulação, a lei de controle (e os ganhos do observador, quando apropriado) são dados a priori e a tarefa é projetar os parâmetros do gerador de eventos. No caso do co-design, o gerador de eventos e a lei de controle ou o observador são projetados simultaneamente. Exemplos numéricos são usados para ilustrar a aplicação dos métodos propostos

Manufacturing systems considered as time domain control systems : receding horizon control and observers

This thesis considers manufacturing systems and model-based controller design, as well as their combinations. The objective of a manufacturing system is to create products from a selected group of raw materials and semifinished goods. In the field of manufacturing systems control is an important issue appearing at various operation levels. At the level of fabrication, for example, control is necessary in order to assure properly working production processes such that products are being fabricated in the desired way. At a higher level in the hierarchy of manufacturing system control, the product streams through the system are controlled in order to satisfy, for example, customer demands in an optimal way. Here, the definition of optimal can be interpreted in various ways, such as "with the least possible costs in terms of money" or "in the shortest possible time". In this research, the attention is focussed on this higher hierarchy level of manufacturing system control. In the literature, many heuristic methods have been developed for the control of a manufacturing system. Nowadays, some heuristicmethods are still being used in combination with operator experience for management of resources and planning of production. However, as the complexity of the manufacturing systems increases rapidly, the (simple) heuristic methods and operator experience will at some point become incapable of finding an optimal control strategy. In this dissertation the potential of consideringmanufacturing system control from a control systems point of view is investigated. The ultimate goal of the research is to eventually obtain a more constructive way to address controller design for manufacturing systems. One control strategy from control systems theory, on which is in particularly focused in this research, is a model-based receding horizon control strategy, known in literature as Model Predictive Control (MPC). Since in manufacturing systems a lot of physical system constraints are involved, like for example finite machine process capacities, finite product storage capacities, finite product arrival rates, etc., the capability for a manufacturing control strategy to handle those constraints is a necessity. One of the key features of model predictive control is the capability of handling constraints in the controller design. This is one of the major motivations to investigate the model predictive control principle as a control strategy for manufacturing systems. Other issues that are important and that the model predictive control design methodology can handle is to enforce optimality, to introduce feedback, and the capability of allowing for mixed continuous and discrete model structures. The later are typically encountered when models of manufacturing systems are derived. The main results that are obtained in this dissertation and that are relevant in the context of manufacturing systems control, but are certainly also relevant beyond this field are: • One has developed an robust computationally friendly nonlinear model predictive control algorithm that can handle model structures with mixed continuous and discrete dynamics. The algorithm can be designed for additive disturbance rejection purposes; • Robustness (with respect to measurement noise) results that are in particulary of interest in the field of nonlinear model predictive control are obtained; • An asymptotically stabilizing output based nonlinear model predictive control scheme for a class of nonlinear discrete-time systems is developed. Results that are relevant in the context of manufacturing systems control are: • It is illustrated howthe aforementioned developed robust computationally friendly nonlinear model predictive control algorithm can be employed to solve a large scale manufacturing control problem in an efficient decentralized manner; • The relation between the so-called event domain modeling approaches for a class of discrete-eventmanufacturing systems to time domainmodels is derived. This results enables one to solve seemingly untractable time domain formulated optimal control problems for a class of manufacturing systems in a tractable manner; • An observer theory for a class of discrete-event manufacturing systems is developed