Structural characterization of optimal event-based controllers for linear stochastic systems

Molin, Adam; Hirche, Sandra

doi:10.1109/cdc.2010.5717890

Cited by 43 publications

(32 citation statements)

References 12 publications

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“…In comparison with the conventional time-triggered communication, a notable advantage of the event triggering scheme is its capability of reducing redundant transmissions while preserving the guaranteed system performance. In recent years, increasing attention has been drawn on the event-triggered techniques for stochastic systems and many important results have been reported in the literature, see [5,7]. However, it should be pointed out that, many established results referring to eventtriggering schemes are in the framework of continuoustime systems and, when it comes to the discrete-time systems, the corresponding results have been scattered.…”

Section: Introductionmentioning

confidence: 98%

“…However, it should be pointed out that, many established results referring to eventtriggering schemes are in the framework of continuoustime systems and, when it comes to the discrete-time systems, the corresponding results have been scattered. The representative one [7] has addressed the problem of designing optimal event-triggered controllers under costly observations, in which the optimal event-trigger depends on the difference between the state estimates at controller and event-trigger. Although the importance of relative error-based event-triggering criterion has been widely recognized, the corresponding results for discretetime systems have been very few especially when the variance-constrained H ∞ control problem becomes a research focus.…”

Section: Introductionmentioning

confidence: 99%

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Variance-constrainedH∞control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

et al. 2016

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In this paper, a general event-triggered framework is set up to deal with the variance-constrained H∞ control problem for a class of discrete time-varying systems with randomly occurring saturations, stochastic nonlinearities and state-multiplicative noises. Based on the relative error with respect to the measurement signal, an event indicator variable is introduced and the corresponding event-triggered scheme is proposed in order to determine whether the measurement output is transmitted to the controller or not. The stochastic nonlinearities under consideration are characterized by statistical means which can cover several classes of well-studied nonlinearities. A set of unrelated random variables is exploited to govern the phenomena of randomly occurring saturations, stochastic nonlinearities and state-dependent noises. The purpose of the addressed multiobjective control problem is to design a set of time-varying output feedback controller such that, over a finite horizon, the closed-loop system achieves both the prescribed H∞ noise attenuation level and the state covariance constraints. A recursive matrix inequality approach is developed to derive the sufficient conditions for the existence of the desired finite-horizon controllers, and the analytical characterization of such controllers is also given. Simulation studies are conducted to demonstrate the effectiveness of the developed controller design scheme.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Variance-constrainedH∞control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

et al. 2016

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“…In most cases the observer reconstructs the plant state using solely event-based information in the sense that it only applies innovation steps exploiting received measurements at the event times, although some schemes also exploit the information present at synchronous (time-triggered) instants of time at which no events occur. The latter is, for instance, the case in [19], [20], [21]. In fact, [19] states literally "absence of an event is however information that can be used by the observer," see also [22].…”

mentioning

confidence: 99%

“…In fact, [19] states literally "absence of an event is however information that can be used by the observer," see also [22]. The observer-based schemes can still be categorized further based on the fact if the corresponding event-triggering conditions use information of the observer such as the estimated state, as, e.g., in [20], [23], [24] or not [21], [25]. The former schemes typically run the observer at the sensor side using essentially all measurements available, while at the controller side a predictor-like structure also produces a state estimate, which is based on only sporadically received information from the sensor system (including the observer) based on the event-triggering mechanisms.…”

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confidence: 99%

An introduction to event-triggered and self-triggered control

Heemels

Johansson

Tabuada

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

1,528

926

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Abstract-Recent developments in computer and communication technologies have led to a new type of large-scale resource-constrained wireless embedded control systems. It is desirable in these systems to limit the sensor and control computation and/or communication to instances when the system needs attention. However, classical sampled-data control is based on performing sensing and actuation periodically rather than when the system needs attention. This paper provides an introduction to event-and self-triggered control systems where sensing and actuation is performed when needed. Eventtriggered control is reactive and generates sensor sampling and control actuation when, for instance, the plant state deviates more than a certain threshold from a desired value. Selftriggered control, on the other hand, is proactive and computes the next sampling or actuation instance ahead of time. The basics of these control strategies are introduced together with a discussion on the differences between state feedback and output feedback for event-triggered control. It is also shown how event-and self-triggered control can be implemented using existing wireless communication technology. Some applications to wireless control in process industry are discussed as well.

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“…Similar to Lipsa and Martins [2011], Molin and Hirche [2009], let us rewrite the optimization problem by defining…”

Section: Preliminariesmentioning

confidence: 99%

An Iterative Algorithm for Optimal Event-Triggered Estimation*

Molin

Hirche

2012

IFAC Proceedings Volumes

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This paper investigates the optimal design of event-triggered estimation for firstorder linear stochastic systems. The problem is posed as a two-player team problem with a partially nested information pattern. The two players are given by an estimator and an eventtrigger. The event-trigger has full state information and decides whether the estimator shall obtain the current state information by transmitting it through a resource constrained channel. The objective is to find an optimal trade-off between the mean squared estimation error and the expected transmission rate. The proposed iterative algorithm alternates between optimizing one player while fixing the other player. It is shown that the solution of the algorithm converges to a linear predictor and a symmetric threshold policy, if the densities of the initial state and the noise variables are even and radially decreasing functions. The effectiveness of the approach is illustrated via numerical simulations. In case of a multimodal distribution of the noise variables a significant performance improvement can be achieved compared to a separate design that assumes a linear prediction and a symmetric threshold policy.

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Structural characterization of optimal event-based controllers for linear stochastic systems

Cited by 43 publications

References 12 publications

Variance-constrainedH∞control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

Variance-constrainedH∞control for a class of nonlinear stochastic discrete time-varying systems: The event-triggered design

An introduction to event-triggered and self-triggered control

An Iterative Algorithm for Optimal Event-Triggered Estimation*

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