Genetic Algorithm Approach for Optimal Control Problems with Linearly Appearing Controls

Seywald, Hans; Kumar, Renjith R.; Deshpande, Samir M.

doi:10.2514/3.56673

Cited by 34 publications

(13 citation statements)

References 9 publications

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“…A limitation of the proposed method is that the range of operating conditions has been only extended; it applicability for highly nonlinear operating conditions is still to be improved, unlike in [8], which applies to all initial conditions. However, the approach in [8] was an offline solution, while the method herein is onlineimplementable.…”

Section: Concluding Commentsmentioning

confidence: 93%

“…The present paper proposes a simpler, but not as widely applicable method as the one in [8]: make use of the closed form solution (3) that is available for the linearised model. This can serve as a good starting point for generating trial solutions around it, and the best solution can be found thereafter by a stochastic search technique like differential evolution (DE).…”

Section: Problem Formulation 31 the Mayer Type Optimal Control Formumentioning

confidence: 99%

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An online implementable differential evolution tuned optimal guidance law

Raghunathan

Pradeep

2007

Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation

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This paper proposes a novel application of differential evolution to solve a difficult dynamic optimisation or optimal control problem. The miss distance in a missile-target engagement is minimised using differential evolution. The difficulty of solving it by existing conventional techniques in optimal control theory is caused by the nonlinearity of the dynamic constraint equation, inequality constraint on the control input and inequality constraint on another parameter that enters problem indirectly.The optimal control problem of finding the minimum miss distance has an analytical solution subject to several simplifying assumptions. In the approach proposed in this paper, the initial population is generated around the seed value given by this analytical solution. Thereafter, the algorithm progresses to an acceptable final solution within a few generations, satisfying the constraints at every iteration. Since this solution or the control input has to be obtained in real time to be of any use in practice, the feasibility of online implementation is also illustrated.

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Section: Concluding Commentsmentioning

confidence: 93%

Section: Problem Formulation 31 the Mayer Type Optimal Control Formumentioning

confidence: 99%

An online implementable differential evolution tuned optimal guidance law

Raghunathan

Pradeep

2007

Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation

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“…Based on natural selection and survival of the fittest in the biological world, evolutionary algorithms (EAs) [17][18][19][20], a special class of stochastic optimizers, are also applied to the solutions of singular optimal control problems. Compared with traditional direct methods, EAs search a population of solutions instead of a single one.…”

Section: Introductionmentioning

confidence: 99%

The solution of singular optimal control problems using the modified line-up competition algorithm with region-relaxing strategy

Sun

2010

ISA Transactions

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Section: Introductionmentioning

confidence: 99%

“…For the control engineer, EAs present opportunities to address some classes of problems that are not amenable to ef®cient solution by the application of conventional techniques. In recent years, EAs have been applied to a broad range of activities in control system engineering, including parametric optimization [7], robust control analysis [8], system identi®cation [9], and optimal control [10,11].Differential evolution (DE) developed by Stron and Price [6] is one of the most excellent EAs. DE turned out to be one of the best genetic algorithms for solving the real-valued test function suite of the ®rst International Contest on Evolutionary Computation, which was held in Nagoya, Japan, 1996.…”

mentioning

confidence: 99%

Estimation of Monod model parameters by hybrid differential evolution

Chiou

Wang

2001

Bioprocess Biosyst Eng

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A hybrid method based on evolutionary algorithms is developed in this study. Two additional operations, an acceleration operation and a migration operation, are embedded into the original version of differential evolution. These two operations are used for the improvement of the convergence speed without decreasing the diversity among the individuals. The acceleration operation is used to speed up convergence. However, the migration operation is used to increase the diversity among the individuals. The hybrid method is applied to estimate the parameters of the Monod model of a recombinant fermentation process. The model pro®les based on 50% variations of the initial concentrations of glucose can ®t the experimental observations satisfactorily. IntroductionEstimation of kinetic parameters is always required for the development of bioreaction modeling. The mathematical estimation of model parameters is based on minimization of some quantity, which is a function of parameters to be estimated. If the model under consideration is linear, the estimation is generally an easy task. Linear regression or plot procedures are well known and do not pose any important problems of use for such models. There exists, however, no unique method for nonlinear models. Several approaches have been suggested to estimate kinetic parameters of nonlinear models.There has been widespread interest from the control community in applying evolutionary algorithms (EAs) to solve the problem of control system engineering [1]. EAs are a class of stochastic search and optimization methods that includes genetic algorithms [2], evolutionary programming [3], evolution strategies [4], genetic programming [5], and their variants [6]. These algorithms, based on the principles of natural biological evolution, have received considerable and increasing interest over the past decade. Compared to traditional search and optimization methods, such as calculus-based and enumerative strategies, the EAs are robust, global, and generally more straightforward to apply in situations where there is little or no a-priori knowledge about the process to be controlled. For the control engineer, EAs present opportunities to address some classes of problems that are not amenable to ef®cient solution by the application of conventional techniques. In recent years, EAs have been applied to a broad range of activities in control system engineering, including parametric optimization [7], robust control analysis [8], system identi®cation [9], and optimal control [10,11].Differential evolution (DE) developed by Stron and Price [6] is one of the most excellent EAs. DE turned out to be one of the best genetic algorithms for solving the real-valued test function suite of the ®rst International Contest on Evolutionary Computation, which was held in Nagoya, Japan, 1996. This method has proved to be a promising candidate to solve real-valued optimization problems. The computational algorithm of DE is very simple to understand and implement. Only a few parameters in this algorithm are re...

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Genetic Algorithm Approach for Optimal Control Problems with Linearly Appearing Controls

Cited by 34 publications

References 9 publications

An online implementable differential evolution tuned optimal guidance law

An online implementable differential evolution tuned optimal guidance law

The solution of singular optimal control problems using the modified line-up competition algorithm with region-relaxing strategy

Estimation of Monod model parameters by hybrid differential evolution

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