A Bessel collocation method for solving fractional optimal control problems

Tohidi, Emran; Nik, Hassan Saberi

doi:10.1016/j.apm.2014.06.003

Cited by 74 publications

(31 citation statements)

References 21 publications

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“…Next, in this example, we use the numerical results of linear programming. The exact solution of equation (39) for ¼ 1 is equal to: Keshavarz et al (2015) Number of solution by Tohidi and Nik (2015) Number of solution by Jafari and Tajadodi (2014) Number of solution by Lotfi et al (2011) 0.1 2.39 Â 10 À6 -1.34 Â 10 À5 1.34 Â 10 À5 0.2 1.21 Â 10 À6 6.2315. 10 À8 2.12 Â 10 À5 2.12 Â 10 À5 0.3 1.72 Â 10 À6 -3.24 Â 10 À5 3.24 Â 10 À5 0.4 6.82 Â 10 À7 2.4565.…”

Section: Examplementioning

confidence: 99%

An efficient method to solve a fractional differential equation by using linear programming and its application to an optimal control problem

Rakhshan

Kamyad

2015

Journal of Vibration and Control

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This paper presents a new idea to solve fractional differential equations and fractional optimal control problems. The fractional derivative is defined in the Grunwald-Letnikov sense. The method is based on the linear programming problem. In this paper, by using first the concept of fractional derivatives, we will suggest a method where an equation with a fractional derivative is changed to a linear programming problem, and by solving it the fractional derivative will be obtained. Actually this suggested method is based on the minimization of total error. Some numerical examples are provided to confirm the accuracy of the proposed method.

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Section: Examplementioning

confidence: 99%

An efficient method to solve a fractional differential equation by using linear programming and its application to an optimal control problem

Rakhshan

Kamyad

2015

Journal of Vibration and Control

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“…Ref [8] proposed direct multiple shooting based methods with long prediction horizons for nonlinear model predictive control. Direct collocation method [9][10][11] is another direct method which operate by parameterization of both the state and control variables. Two most common forms of direct collocation methods are local collocation and global collocation.…”

Section: Introductionmentioning

confidence: 99%

Optimal trajectory planning for Omni-directional mobile robots using direct solution of optimal control problem

Mohseni

Fakharian

2016

2016 4th International Conference on Control, Instrumentation, and Automation (ICCIA)

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In this paper we address the problem of finding trajectory for Omni-directional mobile robots. The objective of the trajectory planning is moving the robot from its initial position to a final position in the presence of static obstacles while minimizing a quadratic index of performance. Along the trajectory, the robot requires to observe certain velocity and acceleration limitations. This problem can be formulated as a constraint nonlinear optimal control problem. To solve this problem, we employ direct method of numerical solution in which the trajectories are parameterized by parametric polynomial functions. By this transforming, the main optimal control problem converts to a nonlinear programming problem (NLP) by lower computational cost. To solve the NLP and obtaining the trajectories, we utilize a new approach with too small run time. The performance and effectiveness of the proposed method are tested in simulations.

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“…In fact, state and control variables x 1 (t), x 2 (t) and u(t) are plotted for n = 1 and n = 2 in Figure 5. The approximate solution for the performance index as given in [20] is J = 2.1439039 the optimal cost functionalJ, obtained by presented algorithm, is shown in Table 3. …”

Section: Van Der Pol Oscillatormentioning

confidence: 99%

“…In [19], for one-dimensional stochastic linear fractional systems the optimal control is derived and in [20] truncated Bessel series approximation by using collocation scheme, for solving linear and nonlinear fractional optimal control problems (OCPs) indirectly. In particular, the control parameterization technique is used in [21,22] and control parameterization enhancing technique is introduced in [22,23].…”

Section: Introductionmentioning

confidence: 99%

Restarted State Parameterization Method For Optimal Control Problems

Kafash¹,

Delavarkhalafi²

2015

J. Math. Computer Sci.

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In this paper we introduce an efficient algorithm based on state parameterization method to solve optimal control problems and Van Der Pol oscillator. In fact, state variable can be considered as linear combination of polynomials with unknown coefficients. Using this method, an optimal control problem breaks down into an optimization and will be solved via mathematical programming techniques. By this algorithm, the control and state variables can be approximated as a function of time. Finally, some numerical examples are presented to show the validity and efficiency of the proposed method.

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A Bessel collocation method for solving fractional optimal control problems

Cited by 74 publications

References 21 publications

An efficient method to solve a fractional differential equation by using linear programming and its application to an optimal control problem

An efficient method to solve a fractional differential equation by using linear programming and its application to an optimal control problem

Optimal trajectory planning for Omni-directional mobile robots using direct solution of optimal control problem

Restarted State Parameterization Method For Optimal Control Problems

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