A numerical method for solving optimal control problems using state parametrization

Mehne, Hamed Hashemi; Borzabadi, Akbar Hashemi

doi:10.1007/s11075-006-9035-5

Cited by 27 publications

(19 citation statements)

References 8 publications

(11 reference statements)

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“…for optimal solution [29,30]. In [15], an algorithm for solving optimal control problems and the controlled Duffing oscillator is presented; in the algorithm the solution is based on state parameterization such that the state variable can be considered as a linear combination of Chebyshev polynomials with unknown coefficients and later, extended state parameterization to solve nonlinear optimal control problems and the controlled Duffing oscillator [31].…”

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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Section: Introductionmentioning

confidence: 99%

Restarted State Parameterization Method For Optimal Control Problems

Kafash¹,

Delavarkhalafi²

2015

J. Math. Computer Sci.

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“…In [10] the problem is converted to measure space and then solved and in [11] the problem is solved by genetic algorithm, Others deal with the optimal control problem directly. For example see [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Solving the Optimal Control of Linear Systems via Homotopy Perturbation Method

Ghomanjani¹,

Ghaderi²,

Farahi

2012

ICA

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In this paper, Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems. In this method the initial approximations are freely chosen, and a Homotopy is constructed with an embedding parameter , which is considered as a “small parameter”. Some examples are given in order to find the approximate solution and verify the efficiency of the proposed method

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“…In contrast to indirect methods 13 , approaches characterized by discretization and following parameter optimization are usually referred to as direct methods 14 . In this work, trajectory segmentation and state parameterization [15][16][17][18] are employed to convert the original infinitedimensional optimal control problem into a finite-dimensional parameter optimization problem which is then solved using genetic algorithms.…”

Section: Introductionmentioning

confidence: 99%

Noise Abatement Trajectory Optimization using Genetic Algorithms

Mulder

2012

AIAA Guidance, Navigation, and Control Conference

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The noise issue generated by approaching and departing aircraft attracts wild attention since it impacts both physical and emotional health of the residents living within the vicinities of civil airports. In this work, a technique is presented to minimize the noise nuisance by optimizing the trajectory of the aircraft for a single event. A level flight at constant speed is discussed although there can be as many as six scenarios within the terminal airspace. First, the trajectory is segmented in such a way that it is only consisted of a series of straight-line segments which are connected by fly-by waypoints. Then, state parameterization is applied for each straight-line segment to convert the original optimal control problem into a parameter optimization problem. Finally, the optimization problem with a finite number of parameters is solved using genetic algorithms. Importantly, all associated models should be built into replaceable modules so that the technique has great generality. The trajectory of a Boeing 747-400 aircraft approaching one of the runways at Amsterdam Airport Schiphol in the Netherlands is optimized to demonstrate the feasibility of the proposed technique. The results from a numerical simulation show that there are multiple local optima. Since genetic algorithms may converge at any one of them, optimization algorithms that guarantee finding the unique global optimum need to be developed.

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A numerical method for solving optimal control problems using state parametrization

Cited by 27 publications

References 8 publications

Restarted State Parameterization Method For Optimal Control Problems

Restarted State Parameterization Method For Optimal Control Problems

Solving the Optimal Control of Linear Systems via Homotopy Perturbation Method

Noise Abatement Trajectory Optimization using Genetic Algorithms

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