The Optimal Sampling Pattern for Linear Control Systems

Bini, Enrico; Buttazzo, Giuseppe

doi:10.1109/tac.2013.2279913

Cited by 37 publications

(66 citation statements)

References 13 publications

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“…La garantía de rendimiento se da en términos de densidad de muestreo, definida como el número de muestras a lo largo de un intervalo de tiempo (véase (Bini, 2014)). Las muestras se disparan de acuerdo con la derivativa de la entrada de control LQR de tiempo continuo y tienen como límite superior un valor máximo dado.…”

Section: Control Auto-disparado Inspirado En Muestreo óPtimo (Osist)unclassified

“…El problema de la regla para muestreo óptimo ha sido recientemente abordado en (Rabi, 2008), (Velasco, 2011), (Meng, 2012), (Molin, 2013), (Bini, 2014), (Gommans, 2014) y (Velasco, 2015), cuya contribución ofrece formulaciones factibles en diferentes entornos, a la vez que identifica posibles limitaciones en términos de optimalidad, tratabilidad computacional y/o aplicación práctica. Sin embargo, dentro de la literatura existente, no se encuentra un marco comparativo o una metodología para evaluar sus propiedades.…”

Section: Introductionunclassified

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Rendimiento de Enfoques de Control Auto-Disparado

et al. 2017

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El control auto-disparado produce secuencias de muestreo no periódico que varían dependiendo de factores de diseño relacionados con la estabilidad y el rendimiento del sistema a ser controlado. Dentro de este marco, recientemente han sido desarrollados dos enfoques dirigidos a minimizar un costo cuadrático, considerando un rendimiento óptimo y persiguiendo el mismo objetivo de control; cada una de ellos sigue una regla de muestreo diferente. Un enfoque se basa en mantener el valor de control actual tanto tiempo como sea posible, mientras que un umbral de rendimiento óptimo no se traspase. El otro enfoque se basa en la generación de una señal de control a trozos que se aproxima a una señal de control óptima continua, sujeta a determinadas limitaciones. Este artículo presenta un estudio comparativo entre los dos enfoques, proporcionando una percepción útil para la realización de futuras investigaciones. Como métricas de interés, el rendimiento de control y la utilización de recursos fueron considerados, y para evaluarlos, se hizo uso del intervalo de muestreo promedio y del costo normalizado. Se demostró que el diferente espacio de búsqueda de cada enfoque plantea un desafío para diseñar un marco de comparación equitativo, y que ambos enfoques superan al muestreo periódico.

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Section: Control Auto-disparado Inspirado En Muestreo óPtimo (Osist)unclassified

Section: Introductionunclassified

Rendimiento de Enfoques de Control Auto-Disparado

et al. 2017

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“…Based on the optimal control theory [6][7][8][9], from (4)- (10), one can easily find that the optimal control input sequence u k (k = 0, 1, . .…”

Section: (X T (T)qx(t) + U T (T)ru(t)) Dtmentioning

confidence: 99%

“…We assume h min ≤ h k ≤ h max , where h max and h min are the maximum and minimum values of the sampling period, respectively. For given sampling periods, the optimal control input u k that minimises the cost function (2) for system (1) can be analytically determined through solving the discrete-time LQR problem (see [6][7][8]…”

Section: Introductionmentioning

confidence: 99%

Sampling and control strategy: networked control systems subject to packet disordering

Huang

2016

IET Control Theory & Applications

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This study proposes a novel sampling and control strategy to find a suboptimal sampling period sequence and control input sequence, such that a quadratic cost function of state and control input of a networked control system (NCS) with packet disordering is minimised. First, a discrete-time system model of the NCS with packet disordering, transmission delay and packet loss in terms of displacement values of packets is put forward. Second, a linear quadratic regulation (LQR) problem of the NCS is formulated, showing that the optimal controller depends on sampling period and quality of services (QoS) of networks. Interactive effects between sampling period and QoS of networks pose a challenge in solving the LQR problem of the NCS. To overcome this difficulty, different from traditional transmission-delay-based or packet-loss-based sampling scheme, a novel packet-disordering-based sampling period selection scheme is proposed. Furthermore, an algorithm is presented to find a suboptimal solution to the LQR problem in this study. Finally, simulation results demonstrate the effectiveness of the proposed approach. IntroductionFacing the increasing demand of control networks in industrial processes, commercial systems and traffic systems, a rapidly increasing focus on networked control systems (NCSs) has been witnessed [1][2][3]. NCSs have been hotspots of research in the past decades. The introduction of control networks can improve the efficiency, flexibility and reliability of these applications, reducing installation, maintenance, reconfiguration and costs. However, some unexpected phenomena potentially occur in network channels including transmission delay, packet loss and packet disordering and so on [4,5]. Therefore, different from traditional control systems, optimal control problems of NCSs require not only control system design, but also network system design. In this paper, we investigate the effects of sampling rate and packet disordering on solution of linear quadratic regulation (LQR) problem. We first formulate the LQR problem for the following continuous linear systemẋwhere x ∈ R n and u ∈ R m , respectively, are state and control input of the plant, and A ∈ R n×n and B ∈ R n×m are matrices with appropriate dimensions. The term t 0 is the initial time instant and x 0 is the initial state. Consider the following quadratic performance index for system (1)where Q ∈ R n×n and R ∈ R m×m are positive semi-definite matrix and positive definite matrix, respectively, and the term t f is the terminal time instant.The control input is assumed to be piecewise constantwhere u k = u(t k ), t k is the kth sampling time instant with 0 ≤ t 0 < t 1 < · · · < t k < · · · ≤ t f , and h k = t k+1 − t k is called sampling period. We assume h min ≤ h k ≤ h max , where h max and h min are the maximum and minimum values of the sampling period, respectively. For given sampling periods, the optimal control input u k that minimises the cost function (2) for system (1) can be analytically determined through solving the disc...

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“…The reason is that, regarding minimal bandwidth consumption, a uniform sampling is not always the best choice (see e.g. [10] and Remark 1 below).…”

Section: Admissible Controlsmentioning

confidence: 99%

Min–max piecewise constant optimal control for multi-model linear systems

Miranda

Castaños

Poznyak

2015

IMA J Math Control Info

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The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set (i.e., there exist only finitely many possible models for the plant). Uncertainty is dealt with using a min-max approach (i.e., we seek the best control for the worst possible plant). The optimal control is derived using a multi-model version of Lagrange's multipliers method, which specifies the control in terms of a discrete-time Riccati equation and an optimization problem over a simplex. A numerical algorithm for computing the optimal control is proposed and tested by simulation.

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The Optimal Sampling Pattern for Linear Control Systems

Cited by 37 publications

References 13 publications

Rendimiento de Enfoques de Control Auto-Disparado

Rendimiento de Enfoques de Control Auto-Disparado

Sampling and control strategy: networked control systems subject to packet disordering

Min–max piecewise constant optimal control for multi-model linear systems

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