Analytical Solution for Optimal Control by the Second Kind Chebyshev Polynomials Expansion
| Autor: | Navid Razmjooy, Mehdi Ramezani |
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| Rok vydání: | 2017 |
| Předmět: |
Equioscillation theorem
Chebyshev polynomials General Mathematics 05 social sciences Mathematical analysis General Physics and Astronomy 020101 civil engineering Chebyshev iteration 02 engineering and technology General Chemistry 0201 civil engineering ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0502 economics and business Chebyshev pseudospectral method Orthogonal polynomials General Earth and Planetary Sciences General Agricultural and Biological Sciences Chebyshev nodes Chebyshev equation 050203 business & management Mathematics Clenshaw algorithm |
| Zdroj: | Iranian Journal of Science and Technology, Transactions A: Science. 41:1017-1026 |
| ISSN: | 2364-1819 1028-6276 |
| DOI: | 10.1007/s40995-017-0336-4 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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