Corresponding author:Kuzmenko Andrew A., Ph. D., Associate Professor, Southern Federal University, Institute of Computer Technologies and Information Security, Taganrog, 347922, Russian Federation, e-mail: aakuzmenko@sfedu.ru

Received on May 25, 2016
Accepted on June 04, 2016

In the paper the authors compare the known method of Analytical Design of the Aggregated Regulators (ADAR) with the method of Analytical Design of the Optimal Regulators (ADOR). The ADAR method has significant advantages: (i) easier procedure of analytical design of the nonlinear laws of the optimal control; (ii) physically clear presentation of the weight factors of the optimality criterions; and (iii) stability of the closed-loop optimal system. As opposed to the method of the optimal control, the ADAR method is free from the demand to solve Riccati's equation and Bellman's equation, and the procedure of the control laws' analytical design is easier. The control laws designed with ADAR method also may ensure sub-optimal transients in a system: time optimal and energy optimal in the mode of big deviations from the desired final state, as well as optimal to the quadratic criterion of the generalized work (criterion of A. A. Krasovskii) in the mode of small deviations. The provided numerical examples display equivalency of these methods, as well as a significant difference in the approaches used for the analytical design of the control laws, i.e. in contrast to ADOR, in the ADAR method the optimizing functional is a constructed performance criteria, the structure and the parameters of which are defined by the designer of the control system in accordance with the object's physical properties and the desired engineering requirements.
Keywords: control design, nonlinear control systems, optimal control, synergetic control theory

Acknowledgements: This work was supported by RFBR (grant № 14-08-00782-a).

For citation:
Kolesnikov A. A., Kolesnikov A. A., Kuz'menko A. A. The ADAR Method and Theory of Optimal Control in the Problems of Synthesis of the Nonlinear Control Systems, Mekhatronika, Avtomatizatsiya, Upravlenie, 2016, vol. 17, no. 10, pp. 657—669.

DOI: 10.17587/mau.17.657-669

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