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On convergence of the Monotone Structural Evolution

Korytowski A., Szymkat M.

Control and Cybernetics

2016

Vol. 45, no. 4

483--512

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.

A simple proof of the maximum principle with endpoint constraints

Korytowski A.

Control and Cybernetics

2014

Vol. 43, no. 1

5--13

The paper presents a new, relatively simple proof of Pontryagin’s maximum principle for the canonical problem of optimal control, with equality and inequality constraints imposed on the trajectory endpoints. The proof combines together two ideas, which appeared separately in the earlier works: application of the Karush-John conditions for finite-dimensional problems, and using packages of needle variations.