Simultaneous control of linear systems by state feedback

Saadatjoo, Fatemeh; Derhami, Vali; Karbassi, S. M.

doi:10.1016/j.camwa.2009.01.039

Cited by 10 publications

(8 citation statements)

References 15 publications

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“…From LaSalle's invariance principle, the closed-loop system (13) is asymptotically stable atX 0 when ω = 0. Thus R1 and R2 hold under the controller (11). This completes the proof.…”

Section: Robust Controller Designsupporting

confidence: 54%

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A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems

Cao

Hou

Zhao

2016

Asian Journal of Control

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This paper investigates the robust simultaneous stabilization (RSS) and robust adaptive simultaneous stabilization (RASS) problem for a set of port‐controlled Hamiltonian (PCH) systems. Some results for designing a family of robust simultaneous controllers with tuning parameters for such systems are proposed. Firstly, using the dissipative Hamiltonian structural properties, these systems are combined to generate an augmented PCH system, and two simultaneous stabilization controllers with parameters are designed for the systems: one is a robust controller and the other is adaptive. Secondly, an algorithm for solving the tuning parameters’ ranges of controller is proposed with symbolic computation. Finally, a numerical example is studied by applying the method obtained in this paper to a set of PCH systems with external disturbance. The effectiveness of the proposed control method is verified by simulations. Compared with conventional simultaneous stabilization control, the controller obtained in this paper not only has strong robustness for a set of systems, but also can optimize the robustness for the systems by adjusting the parameters’ values.

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“…From LaSalle's invariance principle, the closed-loop system (13) is asymptotically stable atX 0 when ω = 0. Thus R1 and R2 hold under the controller (11). This completes the proof.…”

Section: Robust Controller Designsupporting

confidence: 54%

“…We will introduce how to obtain the tuning parameters' ranges of controller (11). The ranges of tuning parameters in controller (25) can be obtained through same method.…”

Section: Solving the Tuning Parameters' Ranges Algorithmmentioning

confidence: 99%

A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems

Cao

Hou

Zhao

2016

Asian Journal of Control

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“…The simultaneous state-feedback control system can be represented as (see [9], [10], [11], [12], [13], and [14] for a small account)…”

Section: A Application To the Simultaneous State-feedback Problemmentioning

confidence: 99%

Stationary policies for the second moment stability in a class of stochastic systems

Vargas

Val

2011

IEEE Conference on Decision and Control and European Control Conference

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This paper presents a study on the uniform second moment stability for a class of stochastic control system. The main result states that the existence of the long-run average cost under a stationary policy is equivalent to the uniform second moment stability of the corresponding stochastic control system. To illustrate the result, a numerical example is developed to verify the uniform second moment stability of a simultaneous state-feedback control system.Index Terms-average cost problems, second moment stability, stochastic control, Markov processes.

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“…The simultaneous state-feedback control problem has been studied by many investigators, seeking the characterization of the optimal solution, see for instance [11][12][13][14][15][16]. Although yet open in the literature, our paper revisits this important control problem with a contribution towards the characterization of the optimal solution for this problem.…”

Section: Application To the Simultaneous State-feedback Controlmentioning

confidence: 99%

Stationary policies for lower bounds on the minimum average cost of discrete-time nonlinear control systems

Vargas

Ishihara

Val

2013

Int. J. Robust. Nonlinear Control

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SUMMARYThe paper deals with the control problem of discrete‐time nonlinear systems. The main contribution of this note is to present conditions that assure the existence of stationary policies that generate lower bounds for the minimal long‐run average cost. These lower bounds coincide with the optimal solution when a mild convergence assumption holds. To illustrate the results, the paper presents an application for the simultaneous state‐feedback control problem, and the derived strategy is used to design a real‐time simultaneous control for two direct current motor devices. The dynamics of these two devices are written in terms of a nonlinear algebraic matrix recurrence, which in turn represents a particular case for our general nonlinear approach. The optimal gain for the corresponding simultaneous state‐feedback problem is obtained, and such a gain was implemented in a laboratory testbed to control simultaneously the two direct current motors. Copyright © 2013 John Wiley & Sons, Ltd.

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Simultaneous control of linear systems by state feedback

Cited by 10 publications

References 15 publications

A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems

A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems

Stationary policies for the second moment stability in a class of stochastic systems

Stationary policies for lower bounds on the minimum average cost of discrete-time nonlinear control systems

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