A Control Parameterization Method to Solve the Fractional-Order Optimal Control Problem

Mu, Pan; Wang, Lei; Liu, Chongyang

doi:10.1007/s10957-017-1163-7

Cited by 39 publications

(14 citation statements)

References 21 publications

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“…Proof. Letθ ∈ Θ be a duration vector satisfying (22). Suppose that σ κ(sj |θ)+1 = ζ j , s j ∈ [ α j p , α j p + 1), it suffices to show that α j (t…”

Section: Control Parameterizationmentioning

confidence: 99%

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On the optimal control problems with characteristic time control constraints

Yu¹,

Su²,

Bai³

2022

JIMO

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In this paper, we consider a class of optimal control problems with control constraints on a set of characteristic time instants. By applying the control parameterization technique, these constraints are imposed on the subdomains that contain the characteristic time points. The values of the control functions as well as the lengths for their corresponding subdomains become decision variables. Time-scaling transformation is an effective technique to optimize the length of each subdomain in a new time horizon. However, the characteristic time instants in the original time horizon become variable time instants in the new time horizon, and hence the control constraints imposed on these characteristic time points are difficult to be formulated in the new time horizon. We propose a surrogate condition and show that the characteristic time control constraints will be satisfied once the surrogate condition holds. Moreover, this surrogate condition is easy to formulate in the new time horizon. The resulting approximate problem can be readily solved by many existing computational methods for solving constrained optimal control problems. Finally, we conclude this paper by solving two examples.

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“…Proof. Letθ ∈ Θ be a duration vector satisfying (22). Suppose that σ κ(sj |θ)+1 = ζ j , s j ∈ [ α j p , α j p + 1), it suffices to show that α j (t…”

Section: Control Parameterizationmentioning

confidence: 99%

“…Control parameterization method is a popular approach for solving general constrained optimal control problems [7,22,33,37,38]. This method involves approximating the control function by a piecewise constant function.…”

mentioning

confidence: 99%

On the optimal control problems with characteristic time control constraints

Yu¹,

Su²,

Bai³

2022

JIMO

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show abstract

“…After these pioneer works, many other extensive researches have been done on the development of numerical methods for FOCPs. For instance, we can refer to Oustaloup recursive approximation [22], direct methods based on pseudo-state-space formulations of FOCP [36], spectral methods based on orthogonal polynomials and fractional operational matrices [37,38,39,40,41,42,43], Legendre multiwavelet collocation methods [44], direct methods based on Bernstein polynomials [45,46,47], nonstandard finite difference methods [48], linear programming approaches [49], integral fractional pseudospectral methods [50], direct methods based on Ritz's techniques [51,52], the epsilon-Ritz method [53], direct methods based on hybrid block-pulse with other basis functions [54,55], pseudospectral methods based on Legendre Müntz basis functions [56], dynamic Hamilton-Jacobi-Bellman methods [57], penalty and variational methods [58], control parameterization methods [59], differential and integral fractional pseudospectral methods [60], as well as other numerical techniques [61,62,63]. Efforts were also done to derive optimality conditions for special types of FOCPs, such as bang-bang FOCPs [64] and free final and terminal time problems [65,66].…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems

Salati

Shamsi

Torres

2019

Communications in Nonlinear Science and Numerical Simulation

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“…Recently some authors have considered the general model of this problem in fractional area. 27,40,41 This article proposes a new numerical approach for solving multidimensional FOCPs including state and control inequality constraints using new biorthogonal multiwavelets. The wavelet numerical method has several advantages as follows:…”

Section: Introductionmentioning

confidence: 99%

Biorthogonal multiwavelets on the interval for solving multidimensional fractional optimal control problems with inequality constraint

Ashpazzadeh

Lakestani

Yıldırım

2020

Optim Control Appl Methods

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Summary This article proposes a new numerical approach for solving fractional optimal control problems including state and control inequality constraints using new biorthogonal multiwavelets. The properties of biorthogonal multiwavelets are first given. The Riemann‐Liouville fractional integral operator for biorthogonal multiwavelets is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well‐developed algorithms may be applied. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The method is computationally very attractive and gives very accurate results.

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A Control Parameterization Method to Solve the Fractional-Order Optimal Control Problem

Cited by 39 publications

References 21 publications

On the optimal control problems with characteristic time control constraints

On the optimal control problems with characteristic time control constraints

Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems

Biorthogonal multiwavelets on the interval for solving multidimensional fractional optimal control problems with inequality constraint

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