Equivalant Condition of Actuator Comparability for LQ Problem

Kuwahara, Masanori

doi:10.9746/sicetr1965.21.659

Cited by 2 publications

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“…We have reported a number of results on actuator selection problems [4][5][6][7][8], which may be regarded as the dual of the problem considered here [3]. The control problem involving actuator selection is the problem of complex combinatorial nature, and no optimal solution has yet been found.…”

Section: Introductionmentioning

confidence: 99%

“…The problem was first addressed by Vanbeveren and Gevers, who found conditions for the exclusion of unwanted actuator sets [3] but did not consider the optimality of selection. We earlier introduced the concept of comparability of actuators and obtained results on the uniqueness of solutions [4,5]. And we used this concept to derive equivalent conditions for comparability of actuators so as to find a general solution.…”

Section: Introductionmentioning

confidence: 99%

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A study for sensor selection LQ problem

Kuwahara

Kawaji

2009

Elect Comm in Japan

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SUMMARYAlthough linear control theory is considered to be almost fully systematized, unsolved control problems still occur under certain realistic conditions. As an example, this paper discusses the sensor selection LQ problem. Recent technology has made it possible to arrange a process of large numbers of inexpensive sensors. In such cases we can expect to achieve more effective real-time control by appropriately switching between sensors. This is an essential control problem but has not been discussed in the literature because of the combinatorial nature of the solution. In this paper we introduce the concept of "comparability of sensors" and present results on the uniqueness of the optimal solution. We then extend the problem to include the use of an observer and derive a sufficient condition for the existence of the unique solution.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A study for sensor selection LQ problem

Kuwahara

Kawaji

2009

Elect Comm in Japan

Self Cite

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A Study for Sensor Selection LQ Problem

Kuwahara

Kawaji

2007

IEEJ Trans.EIS

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Keywords: sensor selection LQ problem, uniqueness of solution, comparability of sensor Although it is recognized that linear control theory has been established mostly, but depending on realistic conditions there remain unsolved control problems. As an example we will discuss the sensor selection LQ problem in this paper. Recent sensor technology makes a process to arrange many low-priced sensors possible. In such case we can expect more effective real-time control by changing sensors properly. This problem will be an essential control problem, but it has not been discussed in the literature. This is because of the combinatorial property of the problem solution. In this paper, we first propose the concept of "the comparability of sensors" and yield a result for the uniqueness of optimal solution. Next, we extend the problem in the case of use of observer and yield a sufficient condition for existence of the unique solution.Let's consider the LQ problem with linear dynamic systemsand control performance indexwhere, x k ∈R n , u k ∈R m , y k ∈R l are the state vector, the input vector, the output vector respectively. The sensor matrixThen LQ problem with sensor selection is to determine optimal sensor sequence {C * k } and optimal input sequence {u * k } so as to minimize the control performance eq.(3) for the system in (1),(2). This problem is difficult to be solved because of the combinatory property. So, in this paper we discuss with the uniqueness of the solution and the comparability of sensor.By substituting (2) into (3), the control performance is rewritten asFollowing the solution of the usual LQ problem in the case of fixed sensor sequence {C k }, we assume the algorithm of the solution for this problem as follows.

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Equivalant Condition of Actuator Comparability for LQ Problem

Cited by 2 publications

References 5 publications

A study for sensor selection LQ problem

A study for sensor selection LQ problem

A Study for Sensor Selection LQ Problem

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