TY - GEN

T1 - A hybrid evolutionary direct search technique for solving optimal control problems

AU - Ghosh, Arnob

AU - Chowdhury, Aritra

AU - Giri, Ritwik

AU - Das, Swagatam

AU - Abraham, Ajith

PY - 2010

Y1 - 2010

N2 - An Optimal Control is a set of differential equations describing the path of the control variables that minimize the cost functional (function of both state and control variables). Direct solution methods for optimal control problems treat them from the perspective of global optimization: perform a global search for the control function that optimizes the required objective. Invasive Weed Optimization (IWO) technique is used here for optimal control. However, the direct solution method operates on discrete n-dimensional vectors, not on continuous functions, and becomes computationally unmanageable for large values of n. Thus, a parameterization technique is required, which can represent control functions using a small number of real-valued parameters. Typically, direct methods using evolutionary techniques parameterize control functions with a piecewise constant approximation. This has obvious limitations, both for accuracy in representing arbitrary functions, and for optimization efficiency. In this paper a new parameterization is introduced, using Bézier curves, which can accurately represent continuous control functions with only a few parameters. It is combined with Invasive Weed Optimization into a new evolutionary direct method for optimal control. The effectiveness of the new method is demonstrated by solving a wide range of optimal control problems.

AB - An Optimal Control is a set of differential equations describing the path of the control variables that minimize the cost functional (function of both state and control variables). Direct solution methods for optimal control problems treat them from the perspective of global optimization: perform a global search for the control function that optimizes the required objective. Invasive Weed Optimization (IWO) technique is used here for optimal control. However, the direct solution method operates on discrete n-dimensional vectors, not on continuous functions, and becomes computationally unmanageable for large values of n. Thus, a parameterization technique is required, which can represent control functions using a small number of real-valued parameters. Typically, direct methods using evolutionary techniques parameterize control functions with a piecewise constant approximation. This has obvious limitations, both for accuracy in representing arbitrary functions, and for optimization efficiency. In this paper a new parameterization is introduced, using Bézier curves, which can accurately represent continuous control functions with only a few parameters. It is combined with Invasive Weed Optimization into a new evolutionary direct method for optimal control. The effectiveness of the new method is demonstrated by solving a wide range of optimal control problems.

KW - Control vector parameterization(CVP)

KW - Differential equations

KW - Genetic algorithms

KW - Optimal control

KW - Optimization method

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U2 - 10.1109/HIS.2010.5600080

DO - 10.1109/HIS.2010.5600080

M3 - Conference contribution

AN - SCOPUS:78650102560

SN - 9781424473656

T3 - 2010 10th International Conference on Hybrid Intelligent Systems, HIS 2010

SP - 125

EP - 130

BT - 2010 10th International Conference on Hybrid Intelligent Systems, HIS 2010

T2 - 2010 10th International Conference on Hybrid Intelligent Systems, HIS 2010

Y2 - 23 August 2010 through 25 August 2010

ER -