Analytical Solutions of Optimal Control Problems with Mixed Constraints

References

[1] Batiha B., Noorani M. S. M. and Hashim I. (2007). Application of VariationalIteration Method to a General Riccati Equation. International Mathematical Forum. Volume 2, Pages 2759-2770.

[2] Castelli, R., Lessard J. and James J. D. M. (2015), Analytic Enclosure of theFundamental Matrix Solution. Conference Applications of Mathematics 2015, inhonor of the birthday anniversaries of Ivo Babuska (90), Milan Prager (85), andEmil Vitasek (85) J. Brandts, S. Korotov, M. Krzek, K. Segeth, J. Sstek, T.Vejchodsky (Eds.) , Institute of Mathematics AS CR, Prague 2015, Pages 1-19.

[3] Claudiu, C. R. (2006), Linear Control. Rhodes University, Grahamstown 6140,South Africa Pages 1-217.

[4] Dmitruk, Andrei V. (2009), On the development of Pontryagin’s Maximum Principle in the works of A.Ya. Dubovitskii and AA Milyutin. Control and cybernetic, Volume 38, Number 4A. Pages 1-38.

[5] Fair, R.C. (1973), On the Solution of Optimal Control Problems as MaximizationProblems. Econometric Research Program, Research Memorandum, Number 146, Pages 1-32.

[6] Ioffe Alexander D. (2020), An Elementary Proof of the Pontryagin’s MaximumPrinciple. Vietnam Journal of Mathematics, 1-10.

[7] Javier, F.R. (2009), Equality-Inequality Mixed Constraints in Optimal Control.International Journal of Mathematical Analysis, Volume 3, Number 28, Pages1369-1387.

[8] Mattheij, R. and Molenaar J. (2002), Ordinary Differential Equations in Theoryand Practice. Society for Industrial and Applied Mathematics (SIAM), Philadelphia Pages 231-237.

[9] Naidu, D.S. (2003), Optimal Control Systems. CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida, Pages 1-96.

[10] Olotu, O. and Adekunle, A. I. (2010), Analytic and Numeric Solutions of Discretized Constrained Optimal Control Problem with Vector-Matrix Coefficients.Mathematics Subject Classification, AMO-Advanced Modeling and Optimization,Volume 12, Number 1, Pages 119-131.

[11] Olotu, O. and Afolabi, A.S. (2014), A New Scheme Using Penalty Functionswith B-Spline Function for Constrained Optimal Control Problems. InternationalJournal of Numerical Mathematics (IJNM), Volume 7, Number 2, 282-300.

[12] Polak, E. (1973), An Historical Survey of Computational Methods in OptimalControl. SIAM Review, Volume 15, Number 2, Pages 552-584.

[13] Polak, E. (1971), Computational Methods in Optimization: A Unified Approach.Academic Press, New York, Pages 1-50.

[14] Radhi, A.Z., Shiv, P.Y and Mohan, C. (1999), Penalty Method for an OptimalControl Problem with Equality and Inequality Constraints. Indian Journal of Pureand Applied Mathematics, Volume 30, Number 1, Pages 1-14.

[15] Serrezuela, R. R. (2016), The K-Exponential Matrix to solve systems of differentialequations deformed. Global Journal of Pure and Applied Mathematics, Volume12, Number 3, Pages 1921-1945. Singiresu, S. R.(1996), Engineering Optimization: Theory and Practice. ThirdEdition, West Lafayette, Indiana, Pages 1-450.

[16] Suha, N. A., Fuad, A. A. and Saba, S. H. (2010), A New Computational Methodfor Optimal Control Problem with B-spline Polynomials. Eng. and Tech Journal,Volume 28, Number 2, Pages 5711-5718.

[17] Vincent, H. (2005), Optimal Control. Retrieved fromhttps://en.wikipedia.org/wiki/Optimal_controlon 13/11/2016 at 22:02 GMT.

@article{1702348,
      author = {Afolabi A. S., Olotu O.},
      title = {Analytical Solutions of Optimal Control Problems with Mixed Constraints},
      journal = {Iconic Research And Engineering Journals},
      year = {2020},
      volume = {3},
      number = {12},
      pages = {37-43},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1702348.pdf},
      abstract = {In this research, the analytical solutions of optimal control problems constrained by ordinary differential equations are examined. The analytical solutions are obtained by applying the first order optimality conditions on the Hamiltonian function and solving the resulting system of first order ordinary differential equations. This leads to the optimal state, controland adjoint variables and hence the optimal objective function value. Two examples of optimal control problems constrained by ordinary differential equations are considered.},
      month = {June},
  }