Linear Quadratic Regulation for Discrete-time Systems with Multiple Delays in Single Input Channel

This paper is concerned with the linear quadratic regulation (LQR) problem for both linear discrete-time systems and linear continuous-time systems with multiple delays in a single input channel. Our solution is given in terms of the solution to a two-dimensional Riccati difference equation for the discrete-time case and a Riccati partial differential equation for the continuous-time case. The conditions for convergence and stability are provided.

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“…Motivated by [19], if we consider system (1) starting from an arbitrarily given time s > 0, we rewrite the system as…”

Section: Lqr For Discrete-time Systemsmentioning

confidence: 99%

“…Conclusions are drawn in Section 5. The discretetime part of the paper was previously presented at a conference [19].…”

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confidence: 99%

Infinite horizon LQR for systems with multiple delays in a single input channel

Liu

Xie

Zhang

2010

J. Control Theory Appl.

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“…(62) Then, the recursive equations (23)-(25) can be rewritten equivalently as [27] P (k + 1) =ĀP (k)Ā +CQw(k)C +K(k)Q e (k)K (k), (63) where Q e (k) is as in (20), andK(k) is given as…”

Section: Asymptotic Stabilitymentioning

confidence: 99%

Optimal linear estimator for discrete-time systems with random delays

Han

Zhang

Feng

2011

J. Control Theory Appl.

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In this paper, optimal estimation for discrete-time linear time-varying systems with randomly state and measurement delays is considered. By introducing a set of binary random variables, the system is converted into the one with both multiplicative noises and constant delays. Then, an estimator which includes the cases of smoothing and filtering, is derived via the projection formula, and the solution is given in terms of a partial difference Riccati equation with boundary conditions. A predictor for such systems is also presented based on the proposed filter and smoother. The obtained estimators have the same dimension as the original state. Conditions for existence, uniqueness, and stability of the steady-state optimal estimators are studied for time-invariant cases. In this case, the obtained estimators are very easy to implement and all calculations can be performed off line, leading to a linear time-invariant estimator.

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“…Furthermore, we consider the linear quadratic tracking in this paper which is more difficult than the LQR problem considered in [8]. The result in [8] cannot be directly extended to the proposed tracking problem since there are extra termsx andū in the cost function (2). In the following, we shall provide an explicit feedback control law by introducing an auxiliary backward deterministic delay system which is formulated for the first time in this paper.…”

Section: Remark 21mentioning

confidence: 99%

“…A lot of studies have been focused on analysis and control problems of input delay systems; see, e.g. [3][4][5][6][7][8] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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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Linear Quadratic Regulation for Discrete-time Systems with Multiple Delays in Single Input Channel

Cited by 8 publications

References 9 publications

Infinite horizon LQR for systems with multiple delays in a single input channel

Infinite horizon LQR for systems with multiple delays in a single input channel

Optimal linear estimator for discrete-time systems with random delays

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

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