Approximation of autonomous affine control systems in the sense of time optimality and algebraic approximation
Abstract
In the paper conditions are given under which, for autonomous affine control systems, approximation in the sense of time optimality implies the algebraic approximation.Downloads
References
Sklyar G. M., Ignatovich S. Yu. Approximation of time-optimal control problems via nonlinear power moment min-problems // SIAM J. Control Optim. -- 2003. - V. 42. -- P. 1325--1346.
Sklyar G. M., Ignatovich S. Yu. Representations of control systems in the Fliess algebra and in the algebra of nonlinear power moments // Systems Control Lett. - 2002. - V. 47. - P. 227-235.
Reutenauer C. Free Lie Algebras. -- Clarendon Press, Oxford. -- 1993.
Melan\c{c}on G., Reutenauer C. Lyndon words, free algebras and shuffes // Canad. J. Math. -- 1989. -- V. 41. -- P. 577--591.
Ignatovich, S. Yu. On a connection between approximation of nonlinear systems in the sense of time optimality and their algebraic approximation // Mat. Fiz. Anal. Geom. -- 2005. -- V. 12, no. 2. -- P. 158--172.
Sklyar G. M., Ignatovich S. Yu., Shugaryov~S. E. Time-optimal control problem for a special class of control systems: optimal controls and approximation in the sense of time optimality // J. Optim. Theory Appl. -- 2015. - Vol. 165. - P. 62--77.
Ignatovich, S. Yu. Explicit solution of the time-optimal control problem for one nonlinear three-dimensional system // Visnyk of V.N.Karazin Kharkiv National University, Ser. Mathematics, Applied Mathematics and Mechanics. 2016, Vol. 83, P. 21-46.
The copyright holder is the author.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal. (Attribution-Noncommercial-No Derivative Works licence).
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (see The Effect of Open Access).
