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Constructive methods of control optimization in nonlinear systems

  • Approximate and Numerical Methods
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Abstract

The paper investigates methods of optimal program and point-to-point control in nonlinear differential systems. The proposed methods are based on the idea of discretizing the continuous-time problem. In case of program control, the method of projected Lagrangian is used, which involves solution of an auxiliary problem with linearized constraints by the reduced gradient method; in case of point-to-point control, Bellman’s optimality principle is employed for a “grid” over an approximating solvability tube of the system for a specified goal set with approximation of the point-to-point control by families of controlling function or parameters. An example is given, where the optimal point-to-point control is calculated for a model of maneuvering aircraft.

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Authors and Affiliations

  1. Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia

    A. I. Tyatyushkin

  2. Buryat State University, Ulan-Ude, Russia

    O. V. Morzhin

Authors
  1. A. I. Tyatyushkin
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  2. O. V. Morzhin
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Additional information

Original Russian Text © A.I. Tyatyushkin, O.V. Morzhin, 2009, published in Avtomatika i Telemekhanika, 2009, No. 5, pp. 35–50.

This work was supported in part by the Program of President of Russia “State Support for Leading Scientific Schools,” project no. NSH-1676.2008.1, and Russian Foundation for Basic Research, projects nos. 07-01-90101-Mong-a and 08-01-00945-a.

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Tyatyushkin, A.I., Morzhin, O.V. Constructive methods of control optimization in nonlinear systems. Autom Remote Control 70, 772–786 (2009). https://doi.org/10.1134/S0005117909050063

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