531 research outputs found
Co-design of output feedback laws and event-triggering conditions for linear systems
We present a procedure to simultaneously design the output feedback law and
the event-triggering condition to stabilize linear systems. The closed-loop
system is shown to satisfy a global asymptotic stability property and the
existence of a strictly positive minimum amount of time between two
transmissions is guaranteed. The event-triggered controller is obtained by
solving linear matrix inequalities (LMIs). We then exploit the flexibility of
the method to maximize the guaranteed minimum amount of time between two
transmissions. Finally, we provide a (heuristic) method to reduce the amount of
transmissions, which is supported by numerical simulations
Lyapunov Design for Event-Triggered Exponential Stabilization
Control Lyapunov Functions (CLF) method gives a constructive tool for
stabilization of nonlinear systems. To find a CLF, many methods have been
proposed in the literature, e.g. backstepping for cascaded systems and sum of
squares (SOS) programming for polynomial systems. Dealing with continuous-time
systems, the CLF-based controller is also continuous-time, whereas practical
implementation on a digital platform requires sampled-time control. In this
paper, we show that if the continuous-time controller provides exponential
stabilization, then an exponentially stabilizing event-triggered control
strategy exists with the convergence rate arbitrarily close to the rate of the
continuous-time system.Comment: accepted by ACM HSCC 2018 conferenc
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 à s saÃdas 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 possÃveis: 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
Event-triggered gain scheduling of reaction-diffusion PDEs
This paper deals with the problem of boundary stabilization of 1D
reaction-diffusion PDEs with a time- and space- varying reaction coefficient.
The boundary control design relies on the backstepping approach. The gains of
the boundary control are scheduled under two suitable event-triggered
mechanisms. More precisely, gains are computed/updated on events according to
two state-dependent event-triggering conditions: static-based and dynamic-based
conditions, under which, the Zeno behavior is avoided and well-posedness as
well as exponential stability of the closed-loop system are guaranteed.
Numerical simulations are presented to illustrate the results.Comment: 20 pages, 5 figures, submitted to SICO
Event-triggered boundary control of constant-parameter reaction-diffusion PDEs: a small-gain approach
This paper deals with an event-triggered boundary control of
constant-parameters reaction-diffusion PDE systems. The approach relies on the
emulation of backstepping control along with a suitable triggering condition
which establishes the time instants at which the control value needs to be
sampled/updated. In this paper, it is shown that under the proposed
event-triggered boundary control, there exists a minimal dwell-time
(independent of the initial condition) between two triggering times and
furthermore the well-posedness and global exponential stability are guaranteed.
The analysis follows small-gain arguments and builds on recent papers on
sampled-data control for this kind of PDE. A simulation example is presented to
validate the theoretical results.Comment: 10 pages, to be submitted to Automatic
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