On convergence of the Monotone Structural Evolution

• Autorzy: Korytowski A. , Szymkat M.
• Języki publikacji: EN

Abstrakty

EN

The paper studies convergenceof the Monotone Structural Evolution (MSE), a computational method of optimal control. The principles of MSE are described and an expository example presents the method in action. It is then proved that under appropriate assumptions the method is convergent to the decision space stationarity conditions. Observations on finite convergence and on connections with Pontryagin’s maximum principle are also provided.

Słowa kluczowe

EN

optimal control; direct computational methods; gradient optimization; monotone structural evolution

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2016
• Tom: Vol. 45, no. 4
• Strony: 483--512
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Korytowski A.

• AGH University of Science and Technology, Cracow, Poland

autor

Szymkat M.

• AGH University of Science and Technology, Cracow, Poland

Bibliografia

• [1] Axelsson, H., Wardi, Y., Egerstedt, M. and Verriest, E.I. (2008) Gradient descent approach to optimal mode scheduling in hybrid dynamical systems. Journal of Optimization Theory and Applications, 136 (2), 167–186.
• [2] Korytowski, A. and Szymkat, M. (2010) Consistent Control Procedures in the Monotone Structural Evolution. Part 1: Theory. In: M. Diehl et al., Recent Advances in Optimization and its Applications in Engineering, Springer, 247–256.
• [3] Osmolovskii, N.P. and Maurer, H. (2012) Applications to Regular and Bang–Bang Control: Second-Order Necessary and Sufficient Optimality Conditions in Calculus of Variations and Optimal Control.SIAM Advances in Design and Control. DC 24, SIAM Publications, Philadelphia.
• [4] Schättler, H. and Ledzewicz, U. (2012) Geometric Optimal Control. Theory, Methods and Examples. Springer.
• [5] Sirisena, H.R. (1974) A gradient method for computing optimal bang-bang control. International Journal of Control, 19, 257-264.
• [6] Szymkat, M. and Korytowski, A. (2003) Method of monotone structural evolution for control and state constrained optimal control problems. European Control Conference ECC 2003, University of Cambridge, U.K., September 1-4.
• [7] Szymkat, M. and Korytowski, A. (2007) Evolution of structure for direct control optimization. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 27, 165–193.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).