Comparison of Direct and Indirect Approaches for Numerical Solution of the Optimal Control Problem by Evolutionary Methods

Diveev, Askhat; Shmalko, Elizaveta

doi:10.1007/978-3-030-38603-0_14

Cited by 5 publications

(1 citation statement)

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“…In this paper, it is shown that such control can also provide the required value of the quality criterion, but the mathematical model of the control object turns out to be insensitive to the existing uncertainties and external disturbances. The approach of synthesized optimal control is new, but we have already managed to obtain good experimental results [18,19] confirming the effectiveness of such control. In this paper, we provide mathematical formulations of the approach and give a theoretical substantiation of the efficiency of the synthesized optimal control.…”

Section: Introductionmentioning

confidence: 75%

Fundamentals of Synthesized Optimal Control

et al. 2020

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This paper presents a new formulation of the optimal control problem with uncertainty, in which an additive bounded function is considered as uncertainty. The purpose of the control is to ensure the achievement of terminal conditions with the optimal value of the quality functional, while the uncertainty has a limited impact on the change in the value of the functional. The article introduces the concept of feasibility of the mathematical model of the object, which is associated with the contraction property of mappings if we consider the model of the object as a one-parameter mapping. It is shown that this property is sufficient for the development of stable practical systems. To find a solution to the stated problem, which would ensure the feasibility of the system, the synthesized optimal control method is proposed. This article formulates the theoretical foundations of the synthesized optimal control. The method consists in making the control object stable relative to some point in the state space and to control the object by changing the position of the equilibrium points. The article provides evidence that this approach is insensitive to the uncertainties of the mathematical model of the object. An example of the application of the method for optimal control of a group of robots is given. A comparison of the synthesized optimal control method with the direct method on the model without disturbances and with them is presented.

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Section: Introductionmentioning

confidence: 75%