Nonlinear Controllability and Lie Series Representations: Survey and Tutorial

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1 Title 2 Outline 3 Sundry Definitions 4 Sundry Definitions (cont'd) 5 Chen-Fliess Series 6 Chen-Fliess Series (cont'd) 7 Chen-Fliess Series (cont'd) 8 Chen-Fliess Series of Linear System 9 Lie Algebra Representation 10 Lie Algebra Representation (cont'd) 11 Lie Algebra Representation (cont'd) 12 Lie Algebra Representation (cont'd) 13 Lie Algebra Representation (cont'd) 14 Lie Algebra Representation (cont'd) 15 Vector Field Dilations 16 Controllability Definitions 17 Necessary & Sufficient Condition for AP 18 AP Does Not Imply STLC 19 Necessary Conditions for STLC 20 Sufficient Conditions for STLC 21 Sufficient Conditions for STLC (cont'd) 22 Sufficient Conditions for STLC (cont'd) 23 Sufficient Conditions for STLC (cont'd) 24 Sufficient Conditions for STLC (cont'd) 25 Extensions