Numerical solution of constrained optimal control problems with parameters

Fabien, Brian C.

doi:10.1016/0096-3003(95)00280-4

Cited by 36 publications

(27 citation statements)

References 12 publications

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“…However, the weakness of these methods is that they produce less accurate solutions than the indirect methods, in addition to the fact that the discretized optimal control problems might have sometimes several minima [9][10]. In this paper, the proposed method, which is considered as a direct optimal control problem solver, overcomes the major drawbacks and limitations of the existing direct and indirect methods.…”

Section: A Set Of Boundary Conditions On the State Variables Which Gimentioning

confidence: 96%

“…To overcome these drawbacks, many researchers proposed the use of the direct methods to solve the optimal control problems [9][10]. However, the weakness of these methods is that they produce less accurate solutions than the indirect methods, in addition to the fact that the discretized optimal control problems might have sometimes several minima [9][10].…”

Section: A Set Of Boundary Conditions On the State Variables Which Gimentioning

confidence: 99%

“…ILLUSTRATIVE EXAMPLE In this sub-section, we consider the Van Der Pol oscillator problem [9]. The system state equations are:…”

Section: Is the Gaussian Mutation Function D Represents A Random Nmentioning

confidence: 99%

“…Therefore, the proposed method is intended for very accurate and off-line desired solutions. In order to investigate the efficiency of the algorithm, we consider the Van Der Pol oscillator problem [9]. The problem was solved using the proposed algorithm and then compared with the shooting and gradient algorithms and the Sequential Unconstrained Minimization Technique (SUMT) [9][10].…”

Section: A Set Of Boundary Conditions On the State Variables Which Gimentioning

confidence: 99%

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Intelligent computational technique with CGA approach for optimal solutions

Alsmadi

Abo-Hammoud

Al-Smadi

2013

2013 IEEE 20th International Conference on Electronics, Circuits, and Systems (ICECS)

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In this paper, Continuous Genetic Algorithms (CGAs) are used as an intelligent computational technique to provide a problem optimal solution. The problem is formulated as an optimization problem by the direct minimization of the performance index subject to constraints, and is then solved using a CGA. The presented approach has some advantages over the other existing direct and indirect methods which either suffer from low accuracy or lack of robustness. One advantage is that our method can be applied without any limitation on the nature of the problem (number of control signals and mesh points). Another advantage is that high accuracy can be achieved in that the performance index is globally minimized.

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Section: A Set Of Boundary Conditions On the State Variables Which Gimentioning

confidence: 96%

Section: A Set Of Boundary Conditions On the State Variables Which Gimentioning

confidence: 99%

“…ILLUSTRATIVE EXAMPLE In this sub-section, we consider the Van Der Pol oscillator problem [9]. The system state equations are:…”

Section: Is the Gaussian Mutation Function D Represents A Random Nmentioning

confidence: 99%

Section: A Set Of Boundary Conditions On the State Variables Which Gimentioning

confidence: 99%

See 2 more Smart Citations

Intelligent computational technique with CGA approach for optimal solutions

Alsmadi

Abo-Hammoud

Al-Smadi

2013

2013 IEEE 20th International Conference on Electronics, Circuits, and Systems (ICECS)

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“…SQP is an iterative algorithm for solving nonlinear programming (NLP) problems, which uses gradient information. It can moreover be used for solving NOCPs, see [10,14,26]. For decreasing the running time in the early generations (iterations) of MHGA, a less number of iterations for SQP was used and then, when the promising region of search space was found, we increase the number of iterations of SQP, gradually.…”

Section: Introductionmentioning

confidence: 99%

Integrating PSO with modified hybrid GA for solving nonlinear optimal control problems

Ghanbari

Nezhadhosein

Heidari

2014

IJAMR

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Here, a two-phase algorithm based on integrating particle swarm optimization (PSO) with modified hybrid genetic algorithm (MHGA) is proposed for solving the associated nonlinear programming problem of a nonlinear optimal control problem. In the first phase, PSO starts with a completely random initial swarm of particles, where each of them contains two random matrices in time nodes. After phase 1, to achieve more accurate solutions, the number of time nodes is increased. The values of the associated new control inputs are estimated by linear or spline interpolations using the curves computed in the phase 1. In addition, to maintain the diversity in the population, some additional individuals are added randomly. Next, in the second phase, MHGA, starts by the new population constructed by the above procedure and tries to improve the obtained solutions at the end of phase 1. MHGA combines a GA with a successive quadratic programming, SQP, as a local search. Finally, we implement the proposed algorithm on some well-known nonlinear optimal control problems. The numerical results show that the proposed algorithm can find almost better solution than other proposed algorithms.

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Parallel indirect solution of optimal control problems

Fabien

2013

Optim Control Appl Methods

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SUMMARYThis paper presents an algorithm for the indirect solution of optimal control problems that contain mixed state and control variable inequality constraints. The necessary conditions for optimality lead to an inequality constrained two‐point BVP with index‐1 differential‐algebraic equations (BVP‐DAEs). These BVP‐DAEs are solved using a multiple shooting method where the DAEs are approximated using a single‐step linearly implicit Runge–Kutta (Rosenbrock–Wanner) method. An interior‐point Newton method is used to solve the residual equations associated with the multiple shooting discretization. The elements of the residual equations, and the Jacobian of the residual equations, are constructed in parallel. The search direction for the interior‐point method is computed by solving a sparse bordered almost block diagonal (BABD) linear system. Here, a parallel‐structured orthogonal factorization algorithm is used to solve the BABD system. Examples are presented to illustrate the efficiency of the parallel algorithm. It is shown that an American National Standards Institute C implementation of the parallel algorithm achieves significant speedup with the increase in the number of processors used. Copyright © 2013 John Wiley & Sons, Ltd.

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Numerical solution of constrained optimal control problems with parameters

Cited by 36 publications

References 12 publications

Intelligent computational technique with CGA approach for optimal solutions

Intelligent computational technique with CGA approach for optimal solutions

Integrating PSO with modified hybrid GA for solving nonlinear optimal control problems

Parallel indirect solution of optimal control problems

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