Analytical Solution for Optimal Control by the Second kind Chebyshev Polynomials Expansion

Document Type : Regular Paper

Authors

1 Department of Electrical Engineering, University of Tafresh, Tafresh, Iran

2 Department of Mathematics, University of Tafresh, Tafresh, Iran.

Abstract

Second kind Chebyshev polynomials are modified set of defined Chebyshev polynomials by a slightly different generating function. This paper presents new and efficient algorithm for achieving an analytical approximate solution to optimal control problems. The proposed solution is based on state parameterization, such that the state variable is approximated by the second kind Chebyshev polynomials with unknown coefficients.
At first, the equation of motion, boundary conditions and performance index are changed into some algebraic equations. This task converts the optimal control problem into an optimization problem, which can then be solved easily. The presented technique approximates the control and state variables as a function of time. After optimizing, the system is converted into a feedback mode for having the closed loop profits. The results proved the algorithm convergence. Finally by analyzing two numerical examples, the reliability and effectiveness of the proposed method by comparing two different methods is demonstrated.

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Iranian Journal of Science

Articles in Press, Accepted Manuscript
Available Online from 23 January 2016

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