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Covering method for terminal control with regard of constraints

  • Control Theory
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Abstract

We suggest a new method for solving the terminal control problem for dynamical systems by supplementing the original system with equations for derivatives of the control and by replacing the terminal problem by two coupled Cauchy problems. We show that, in the case of flat systems, the suggested method permits one to find a solution of the terminal problem in the set of solutions of an arbitrary dynamical system of sufficiently large dimension rather than only in the set of polynomials as in a well-known method. By an example, we show how to use the result for taking into account constraints for the terminal control of a flat system: in this case, a solution of the terminal problem is sought in the set of solutions of a system that has an invariant set all of whose points satisfy the constraints of the problem. The trajectory found by the method lies in this invariant set.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, Russia

    Yu. S. Belinskaya & V. N. Chetverikov

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  1. Yu. S. Belinskaya
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  2. V. N. Chetverikov
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Correspondence to Yu. S. Belinskaya.

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Original Russian Text © Yu.S. Belinskaya, V.N. Chetverikov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 12, pp. 1629–1639.

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Belinskaya, Y.S., Chetverikov, V.N. Covering method for terminal control with regard of constraints. Diff Equat 50, 1632–1642 (2014). https://doi.org/10.1134/S0012266114120076

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  • DOI: https://doi.org/10.1134/S0012266114120076

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