Abstract
In an earlier paper, the author established a sufficient condition for controllability of systems of the form\(\dot x\)=A(t)x+g(t, u). This condition is a growth condition which generalizes the concept of an asymptotically proper system introduced by LaSalle for linear systems. The purpose of this paper is examine and apply this growth condition. We first show that the condition is also necessary for controllability. Then, we use these results to consider the controllability of perturbations of the above system. The main result of the paper is a class of systems which in many applications can be assumed to be controllable.
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References
LaSalle, J. P.,The Time-Optimal Control Problem, Contribution to Nonlinear Oscillations, Vol. 5, 1959.
Dauer, J. P.,Controllability of Nonlinear Systems Using a Growth Condition, Journal of Optimization Theory and Applications, Vol. 9, No. 2, 1972.
Lee, E. B., andMarkus, L.,Foundations of Optimal Control Theory, John Wiley and Sons, New York, 1967.
Dauer, J. P.,Perturbations of Linear Control Systems, SIAM Journal on Control, Vol. 9, No. 3, 1971.
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Communicated by L. Cesari
During the writing of this paper, the author held a Junior Faculty Summer Fellowship from the Research Council of the University of Nebraska.
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Dauer, J.P. On controllability of systems of the form\(\dot x\)=A(t)x+g(t, u). J Optim Theory Appl 11, 132–138 (1973). https://doi.org/10.1007/BF00935878
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DOI: https://doi.org/10.1007/BF00935878