Nonsmooth Analysis in Control Theory: A Survey
In the classical calculus of variations, the question of regularity (smoothness or otherwise of certain functions) plays a dominant role. This same issue, although it emerges in different guises, has turned out to be crucial in nonlinear control theory, in contexts as various as necessary conditions...
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| Published in | European journal of control Vol. 7; no. 2-3; pp. 145 - 159 |
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| Main Author | |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
Cachan
Elsevier Ltd
2001
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| Abstract | In the classical calculus of variations, the question of regularity (smoothness or otherwise of certain functions) plays a dominant role. This same issue, although it emerges in different guises, has turned out to be crucial in nonlinear control theory, in contexts as various as necessary conditions for optimal control, the existence of Lyapunov functions, and the construction of stabilizing feedbacks. In this report we give an overview of the subject, and of some recent developments. |
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| AbstractList | In the classical calculus of variations, the question of regularity (smoothness or otherwise of certain functions) plays a dominant role. This same issue, although it emerges in different guises, has turned out to be crucial in nonlinear control theory, in contexts as various as necessary conditions for optimal control, the existence of Lyapunov functions, and the construction of stabilizing feedbacks. In this report we give an overview of the subject, and of some recent developments. |
| Author | Clarke, Francis |
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| Cites_doi | 10.1016/0362-546X(83)90049-4 10.1137/0324014 10.1016/S0362-546X(98)00075-3 10.1137/S0363012999352297 10.1137/0321028 10.1109/9.633828 10.1007/BF01189393 10.1137/S0363012999356039 10.1090/S0002-9939-1991-1076572-8 10.1137/S0363012996299338 10.1137/S0363012993259981 10.1137/0329068 10.1090/S0002-9947-1977-0442784-4 10.1006/jdeq.1998.3476 10.1137/0314067 10.1137/S0363012995283972 10.1023/A:1004608800846 10.1137/S0363012992235432 10.1007/BF02741887 10.1090/S0002-9947-1983-0690039-8 10.1137/0327053 10.1109/TAC.1986.1104318 10.1090/S0002-9947-1987-0879580-6 10.1051/cocv:2000113 10.1016/S0167-6911(00)00084-0 10.1016/0362-546X(93)90098-D 10.1090/S0002-9947-1975-0367131-6 10.1016/0167-6911(95)00041-0 |
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| Issue | 2-3 |
| Keywords | Nonsmooth analysis Proximal analysis Feedback Stabilization Optimal control Generalised gradients Lyapunov function Proximal Generalized gradient Non linear control Lyapunov method Review |
| Language | English |
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| SubjectTerms | Applied sciences Computer science; control theory; systems Control system synthesis Control theory. Systems Exact sciences and technology Feedback Generalised gradients Lyapunov function Nonsmooth analysis Optimal control Proximal analysis Stabilization |
| Title | Nonsmooth Analysis in Control Theory: A Survey |
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