Abstract
As we can observe from results SQA Algorithm is characterized by its big possibility to overcome local minina in conjunction with high convergence speed. These basic characteristics consist an optimization algorithm suitable for problems with high computational cost, such as dynamic problems, and objective functions with many peculiarities.
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References
Polak, E., Computational Methods in Optimization, Academic Press, New York, New York, 1970.
Dunn, J. C., and Bertsekas, D. P., Efficient Dynamic Programming Implementations of Newton's Method for Unconstrained Optimal Control Problems, Journal of Optimization Theory and Applications, Vol.63, pp. 23–38, 1989.
Edge, E. R., and Power, W., F., Functions Space Quasi-Newton Algorithms for Optimal Control Problems with Bounded Controls and Singular Arcs, Journal of Optimization Theory and Applications, Vol. 20, pp. 455–479, 1976.
Kelley, C. T. and Sachs, E. W., A Pointwise Quasi-Newton Method for Unconstrained Optimal Control Problems, Numerische Mathematik, Vol. 55, pp. 159–176, 1989.
Demyanov, V. F., and Rubinov, A. M., Approximate Methods in Optimization Problems, American Elsevier, New York, New York, 1970.
Dunn, J. C., Global and Asymptotic Convergence Rate Estimates for a Class of Projected Gradient Processes. SIAM Journal on Control and Optimization, Vol. 19, pp. 368–400, 1981.
Dunn, J. C., On the Convergence of Projected Gradient Processes to Singular Critical Points, Journal of Optimization Theory and Applications, Vol. 55, pp. 203–216, 1987.
Gafni, E. M., and Bertsekas, D. P., Two-Metric Projection Methods for Constrained Optimization, SIAM Journal on Control and Optimization, Vol. 22, pp. 936–964, 1984.
Dunn, J. C., A Projected Newton Method for Minimization Problems with Nonlinear Inequality Constraints, Numerische Mathematik, Vol. 53, pp. 377–409, 1988.
Wright, S. J., Interior Point Methods for Optimal Control of Discrete Time Systems, Journal of Optimization Theory and Applications, Vol. 77, pp. 161–187, 1993.
Pantoja, J. F. A. D., and Mayne, D. Q., Sequential Quadratic Programming Algorithm for Discrete Optimal Control Problems with Control Inequality Constraints, International Journal of Control, Vol. 53, pp. 823–836, 1991.
Wright, S. J., Solution of Discrete-Time Optimal Control Problems on Parallel Computers, Parallel Computing, Vol. 16, pp. 221–238, 1990.
Wright, S. J., Partitioned Dynamic Programming for Optimal Control, SIAM Journal on Optimization, Vol. 1, pp. 620–642, 1991.
Yang, T. H., Polak, E., and Mayne, D. Q., A Method of Centers Based on Barrier Functions for Solving Optimal Control Problems with Continuum Constraints, Proceedings of the 29th Conference on Decision and Control, pp. 2327–2332, 1990.
Evtushenko, Y. G., Numerical Optimization Techniques, Optimization Software, New York, New York, 1985.
Di Pillo, G. Grippo, L., and Lampariello, F., A Class of Structured Quasi-Newton Algorithms for Optimal Control Problems, Proceedings of the IFAC Conference on Applications of Nonlinear Programming to Optimization and Control, pp. 101–107, 1983.
Teo, K. L., and Jennings, L. S., Nonlinear Optimal Control Problems with Continuous State Inequality Constraints, Journal of Optimization Theory and Applications, Vol. 63, pp. 1–22, 1989.
Goh, C. J., and Teo, K. L., Control Parametrization: A Unified Approach to Optimal Control Problems with General Constraints, Automatica, Vol. 24, pp. 3–18, 1988.
Teo, K. L., and Goh, C. J., A Computational Method for Combined Optimal Parameter Selection and Optimal Control Problems with General Constraints, Journal of the Australian Mathematical Society, Series B, Vol. 30, pp. 350–364, 1989.
Teo, K. L., and Goh, C. J., A Simple Computational Procedure for Optimization Problems with Functional Inequality Constraints, IEEE Transactions on Automatic Control, Vol. 32, pp. 940–941, 1987.
Wong, K. H., Klements, D. J., and Teo, K. L., Optimal Control Computation for Nonlinear Time-Lag Systems, Journal of Optimization Theory and Applications, Vol. 47, pp. 91–107, 1985.
Sirisena, H. R., Computation of Optimal Controls Using a Piecewise Polynomial Parametrization, IEEE Transactions on Automatic Control, Vol. 18, pp. 409–411, 1973.
Sirisena, H. R., and Chou, F. S., Convergence of Control Parametrization Ritz Method for Nonlinear Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 29, pp. 369–382, 1979.
Sisirena, H. R. and Tan, K. S., Computational of Constrained Optimal Controls Using Parametrization Techniques, IEEE Transactions on Automatic Control, Vol. 19, pp. 431–433, 1974.
Teo, K. L., and Womersley, R. S., A Control Parametrization Algorithm for Optimal Control Problems Involving Linear Systems and Linear Inequality Constraints, Numerical Functional Analysis and Optimization, Vol. 6, pp. 291–313, 1983.
Teo, K. L., Wong, K. H., and Clements, D. J., Optimal Control Computation for Linear Time-Lag Systems with Linear Terminal Constraints, Journal of Optimization Theory and Applications, Vol. 44, pp. 509–529, 1984.
Kaji, K., and Wong, K. H., Nonlinearly Constrained Time-Delayed Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 82, pp. 295–313, 1994.
Petridis, A. G., Haralabopoulos, G. N., and Kanarachos, A. E., A New Global Optimization Algorithm Combining the Natural Evolution Model and the Deterministic Newton Methodology, EURISCON’ 98, 1998.
Jacobson, D. H., and Mayne, D. Q., Differential Dynamic Programming, American Elsevier, New York, New York, 1970.
Longsdon, J. S., Efficient Determination of Optimal Control Profiles for Differential Algebraic Systems, PhD Thesis, Carnegie-Mellon University, 1990.
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Petridis, A.G., Charalampopoulos, G.N., Kanarachos, A.E. (1999). Response optimization of a discrete-time bang-bang optimal control problem. In: Tzafestas, S.G., Schmidt, G. (eds) Progress in system and robot analysis and control design. Lecture Notes in Control and Information Sciences, vol 243. Springer, London. https://doi.org/10.1007/BFb0110540
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DOI: https://doi.org/10.1007/BFb0110540
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