Optimal control of linear time-varying delay systems via single-term walsh series

Palanisamy, K.R.; Balachandran, K.; Ramasamy, R.

doi:10.1049/ip-d.1988.0048

Cited by 10 publications

(12 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the time step size h = 0.4,0.04,0.004, Figs and show the simulation curves of x ( t ) and u ( t ) for the OCP ()‐() with constant time‐delay τ ( t ) = 1 and time‐varying delay

τ (t) = 1 + \frac{1}{2} \frac{t^{2}}{1 + t}

, respectively. These figures indicate that the numerical solution of the new approximation scheme is in good agreement with the available litreture .…”

Section: The Second‐order Two‐step Fd Methodssupporting

confidence: 71%

“…For the time step size h = 0.4, 0.04, 0.004, Figs 1 and 2 show the simulation curves 1+t , respectively. These figures indicate that the numerical solution of the new approximation scheme is in good agreement with the available litreture [5,12,14,18,19,23].…”

Section: Illustrative Examplessupporting

confidence: 71%

“…From Table it is observed that for the time step size h = 0.004 and constant time‐delay τ ( t ) = 1, a minimum value of the cost functional is obtained as J = 4.796786. As it is shown in Table , this value of J computed by the proposed scheme is compared very well with those achieved by the single‐term Walsh series , iterative dynamic programming , Legendre multi‐wavelets , modified line‐up competition algorithm and recursive shooting method . Comparison results reveal the validity of the proposed FD method for solving the TDOCP ()–().…”

Section: The Second‐order Two‐step Fd Methodssupporting

confidence: 59%

See 2 more Smart Citations

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

Jajarmi

Hajipour

2016

Asian Journal of Control

View full text Add to dashboard Cite

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.

show abstract

“…For the time step size h = 0.4,0.04,0.004, Figs and show the simulation curves of x ( t ) and u ( t ) for the OCP ()‐() with constant time‐delay τ ( t ) = 1 and time‐varying delay

τ (t) = 1 + \frac{1}{2} \frac{t^{2}}{1 + t}

, respectively. These figures indicate that the numerical solution of the new approximation scheme is in good agreement with the available litreture .…”

Section: The Second‐order Two‐step Fd Methodssupporting

confidence: 71%

Section: Illustrative Examplessupporting

confidence: 71%

Section: The Second‐order Two‐step Fd Methodssupporting

confidence: 59%

See 1 more Smart Citation

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

Jajarmi

Hajipour

2016

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…By substituting X(t f ) ≈̂T H (t f )X 2 , where X 2 is defined in Equation 38 and U(t) in Equation 29, we get…”

Section: The Performance Index Approximationmentioning

confidence: 99%

“…In Table 4, a comparison is made between the value of I obtained by the present method for M = 2 and J = 4, 5, 6 and the values of I achieved by the Walsh series, 38 Legendre multiwavelets, 12 modified line-up competition, 39 and the recursive shooting method. 40 Table 4 indicates that the results of the proposed method are much better than those achieved by the other existing methods.…”

Section: Examplementioning

confidence: 99%

Optimal control of linear time‐delay systems by a hybrid of block‐pulse functions and biorthogonal cubic Hermite spline multiwavelets

Mohammadzadeh

Lakestani

2017

Optim Control Appl Methods

View full text Add to dashboard Cite

SummaryThis paper proposes a new numerical approach for finding the solution of linear time-delay control systems with a quadratic performance index using new hybrid functions. This method is based on a hybrid of block-pulse functions and biorthogonal multiwavelets that consist of cubic Hermite splines on the primal side. The excellent properties of the hybrid functions together with the operational matrices of integration, product, and delay are presented. Using these matrices, the solution of the optimal control of delay systems is reduced to the solution of algebraic equations. Because of the sparsity nature of these matrices, this method is computationally very attractive and reduces CPU time and computer memory. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The effectiveness of the method and the accuracy of the solution are shown in comparison with some other methods by illustrative examples.

show abstract

Optimal control of time‐delay systems by dynamic programming

Dadebo

Luus

1992

Optim Control Appl Methods

View full text Add to dashboard Cite

SUMMARYThe use of iterative dynamic programming employing systematic region contraction and accessible grid points is investigated for the optimal control of time-delay systems. At the time of generating the grid points for the state variables, the corresponding delayed variables at each time stage are also generated and stored in memory. Then, when applying dynamic programming, a linear approximation is used to obtain the initial profile for the delayed variables during integration. This procedure was tested with four problems of different complexity. In each case the optimal control policy is easily obtained and the results compare very favourably with those reported in the literature using other computational procedures.

show abstract

Optimal control of linear time-varying delay systems via single-term walsh series

Cited by 10 publications

References 0 publications

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

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

Optimal control of linear time‐delay systems by a hybrid of block‐pulse functions and biorthogonal cubic Hermite spline multiwavelets

Optimal control of time‐delay systems by dynamic programming

Contact Info

Product

Resources

About