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Global controllability of nonlinear control processes with prescribed controls

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Abstract

In this paper, we establish sufficient conditions upon the functionsA(t, x),B(t),g(t, x, u), such that the nonlinear control process

$$x' = A(t,x)x + B(t)u + g(t,x,u)$$

is completely controllable and it is possible to control not only the statex of the system, but also its velocityx′. The method used is a transformation of the given control system into a boundary-value problem similar to one considered by Lukes on perturbed linear control systems. The main tool used is Schaefer's fixed-point argument.

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Authors and Affiliations

  1. Istituto Matematico Ulisse Dini, Universitá di Firenze, Firenze, Italy

    G. Anichini (Assistant Professor)

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  1. G. Anichini
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Communicated by R. Conti

This research was performed under the auspices of GNAFA, CNR, Italy. The author wishes to thank Professor R. Conti and Professor J. D. Schuur for some helpful suggestions.

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Anichini, G. Global controllability of nonlinear control processes with prescribed controls. J Optim Theory Appl 32, 183–199 (1980). https://doi.org/10.1007/BF00934723

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  • DOI: https://doi.org/10.1007/BF00934723

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