Abstract
For a finite-dimensional linear system, in which the control is restricted to belong to a completely arbitrary setJ, we give a simple necessary and sufficient condition for small-time local controllability from a pointp. The condition is equivalent to a characterization of the property that the Bellman function for the corresponding minimum-time optimal control problem is continuous atp.
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References
Sussmann, H. J.,A General Theorem on Local Controllability, SIAM Journal on Control and Optimization, Vol. 25, pp. 158–194, 1987.
Lee, E. B., andMarkus, L.,Foundations of Optimal Control Theory, John Wiley and Sons, New York, New York, 1976.
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Communicated by L. D. Berkovitz
This work was partially supported by the National Science Foundation, Grant No. MCS-78-02442.
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Sussmann, H.J. Small-time local controllability and continuity of the optimal time function for linear systems. J Optim Theory Appl 53, 281–296 (1987). https://doi.org/10.1007/BF00939220
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DOI: https://doi.org/10.1007/BF00939220