Optimal Control of Linear Time-Delayed Systems by Linear Legendre Multiwavelets

Khellat, Farhad

doi:10.1007/s10957-009-9548-x

Cited by 54 publications

(54 citation statements)

References 15 publications

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“…Example 3 is a twodimensional optimal control problem of a harmonic oscillator with retarded damping and was considered in [29][30][31]. Examples 1 and 3 were also solved in [3] by using the set of eight basis functions of linear Legendre multiwavelets. For these examples, we compare our findings with the numerical results in [3], which have been shown to be comparable or superior to those of [28] and [29][30][31].…”

Section: Illustrative Examplementioning

confidence: 99%

“…This example was considered in [28] and also studied in [3]. Consider the optimal control problem of a time-varying delay system described bẏ…”

Section: Examplementioning

confidence: 99%

“…is still open [3], depending on the delay type, specific system equation, criterion, etc. The application of Pontryagin's maximum principle to the optimization of control systems with time delays, as outlined by Kharatishvili [4], results in a system of coupled two-point boundary-value (TPBV) problem involving both delay and advance terms whose exact solution, except in very special cases, is very difficult.…”

mentioning

confidence: 99%

“…The methods presented in [6] is also a sensitivity approach in which the original system is embedded in a class of nondelay systems using an appropriate parameter. A reference book in the area ( [7] and references therein), discussing the Pontryagin's maximum principle or the dynamic programming method for systems with delays, states that finding a particular explicit form of the criterion must also be taken into account: the studies mostly focused on the time-optimal criterion for quadratic systems [3,[8][9][10][11].…”

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confidence: 99%

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Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Haddadi

Ordokhani

Razzaghi

2011

J Optim Theory Appl

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In this paper, a new numerical method for solving the optimal control of linear time-varying delay systems with quadratic performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions, consisting of block-pulse functions and Bernoulli polynomials, are presented. The operational matrices of integration, product, delay and the integration of the cross product of two hybrid functions of block-pulse and Bernoulli polynomials vectors are given. These matrices are then utilized to reduce the solution of the optimal control of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Section: Illustrative Examplementioning

confidence: 99%

“…This example was considered in [28] and also studied in [3]. Consider the optimal control problem of a time-varying delay system described bẏ…”

Section: Examplementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Haddadi

Ordokhani

Razzaghi

2011

J Optim Theory Appl

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“…To show the high accuracy and efficiency of the proposed method, the developed method is applied to a harmonic oscillator with retarded damping. [69] Consider the problem:…”

Section: Numerical Examplementioning

confidence: 99%

Time-Delay Switch Attack on Networked Control Systems, Effects and Countermeasures

Sargolzaei¹

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An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

Jajarmi

Hajipour

2016

Asian Journal of Control

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In this paper, an efficient finite difference method is presented for the solution of time‐delay optimal control problems with time‐varying delay in the state. By using the Pontryagin's maximum principle, the original time‐delay optimal control problem is first transformed into a system of coupled two‐point boundary value problems involving both delay and advance terms. Then the derived system is converted into a system of linear algebraic equations by using a second‐order finite difference formula and a Hermite interpolation polynomial for the first‐order derivatives and delay terms, respectively. The convergence analysis of the proposed approach is provided. The new scheme is also successful for the optimal control of time‐delay systems affected by external persistent disturbances. Numerical examples are included to demonstrate the validity and applicability of the new technique. Some comparative results are included to illustrate the effectiveness of the proposed method.

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Optimal Control of Linear Time-Delayed Systems by Linear Legendre Multiwavelets

Cited by 54 publications

References 15 publications

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Time-Delay Switch Attack on Networked Control Systems, Effects and Countermeasures

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

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