Linear quadratic regulation for linear time-varying systems with multiple input delays

Zhang, Huanshui; Duan, Guang‐Ren; Xie, Lihua

doi:10.1016/j.automatica.2006.04.007

Cited by 130 publications

(113 citation statements)

References 13 publications

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“…It is not difficult to see that the system considered in [7,32] is a special case of system (1) and the controller derivation method in [7,32] cannot be readily extended for (1) as it will involve a constrained optimization. Recall that the class of the systems considered in [7,32] is of the form:…”

Section: Remark 21mentioning

confidence: 99%

“…We note that the linear quadratic regulation (LQR) problem for systems with single delay in each of the multiple input channels has been considered [7,32].…”

Section: Remark 21mentioning

confidence: 99%

“…This paper studies the optimal tracking problem for linear discrete-time systems with known multiple delays in single input channel which can be encountered in many applications such as traffic control, irrigation systems, economic systems, and networked control systems [29][30][31]. The class of systems under investigation contains those in [17,21,32] as special cases. The tracking problem will be structured such that the state vector x(k) will be driven as close as possible to a desired state vectorx(k) under the requirement that the control input u(k) does not deviate too much from a given control inputū(k).…”

Section: Introductionmentioning

confidence: 99%

“…However, the system of the present paper is that of [21] with the constraint that the inputs of all the channels must be the same. This constraint poses a significant challenge and cannot be addressed using the approach of [21,32] as it will lead to a constrained optimization problem to which no analytical solution can be obtained. Using a reorganized output approach, we first decouple the input signals at various delayed time instants and establish a duality between the linear quadratic tracking problem and a state and white noise smoothing problem for an associated backward stochastic system.…”

Section: Introductionmentioning

confidence: 99%

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Linear quadratic tracking problem for discrete‐time systems with multiple delays in single input channel

Liu

Xie

Zhang

2010

Intl J Robust & Nonlinear

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SUMMARYThe linear quadratic tracking problem for discrete-time systems with multiple delays in single input channel is considered. In this paper, we provide an approach without resorting to system state augmentation. The optimal tracking control is given in terms of the current state, the previous inputs, and the output of an auxiliary backward deterministic delay system which is formulated for the first time in this paper. The solution relies on a Riccati difference equation of the same dimension as the plant (ignoring the delays). The key to our development is the establishment of a duality between the optimal tracking control and the optimal smoothing estimation of an associated stochastic backward system as well as the introduction of the auxiliary backward deterministic delay system. An analysis of the computational complexity of the proposed approach and its comparison with that of the augmentation method, which is to incorporate the delayed inputs into the augmented state, are provided. An example is given to demonstrate the effectiveness of the results.

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Section: Remark 21mentioning

confidence: 99%

“…We note that the linear quadratic regulation (LQR) problem for systems with single delay in each of the multiple input channels has been considered [7,32].…”

Section: Remark 21mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Linear quadratic tracking problem for discrete‐time systems with multiple delays in single input channel

Liu

Xie

Zhang

2010

Intl J Robust & Nonlinear

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“…[11], however, since these computations are performed off-line, we merely note that computable solutions exist for large h.…”

Section: Example: Lqr Controlmentioning

confidence: 99%

Sampling and controlling faster than the computational delay

Buchstaller

Kerrigan

Constantinides

2012

IET Control Theory Appl.

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Linear quadratic regulation for discrete‐time systems with multiplicative noise and multiple input delays

Zhang

2016

Optim Control Appl Methods

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SUMMARYThis paper is concerned with the optimal linear quadratic regulation problem for discrete-time systems with state and control dependent noises and multiple delays in the input. We show that the problem admits a unique solution if and only if a sequence of matrices, which are determined by coupled difference equations developed in this paper, are positive definite. Under this condition, the optimal feedback controller and the optimal cost are presented via some coupled difference equations. Our approach is based on the stochastic maximum principle. The key technique is to establish relations between the costate and the state. Copyright

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Linear quadratic regulation for linear time-varying systems with multiple input delays

Cited by 130 publications

References 13 publications

Linear quadratic tracking problem for discrete‐time systems with multiple delays in single input channel

Linear quadratic tracking problem for discrete‐time systems with multiple delays in single input channel

Sampling and controlling faster than the computational delay

Linear quadratic regulation for discrete‐time systems with multiplicative noise and multiple input delays

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