| Continuous Dependence With Respect to the Input of Trajectories of Control-Affine Systems (1999) | |||||||||||||||
Abstract | |||||||||||||||
| . We study the continuous dependence on the input of trajectories of control-affine systems belonging to the class C 0 (m) of all systems \Sigma of the form \Sigma : x = f 0 (x) + m X i=1 u i (t)f i (x); where f 0 ; : : : ; f m are continuous vector fields on some open subset of IR n and the control functions belong to L 1 ([0; T ]; IR m ). We give a simple necessary and sufficient condition for a control sequence fu j g 1 j=1 to "T 0 -converge" to a control u 1 , i.e. to be such that, for every system \Sigma in C 0 (m), the trajectories generated by the u j converge as j ! 1 to the trajectories generated by u 1 . We also characterize T k -convergence ---i.e. the concept of control convergence that arises when we use, instead of C 0 (m), the class C k (m) of systems \Sigma where the f i are of class C k --- for k 1 in the scalar input case, and explain how the analogous characterization for the multiinput case fails to be true, unless one restricts... | |||||||||||||||
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