The principle of contraction mapping in nonlinear and adaptive control systems
- 1 October 1964
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 9 (4) , 393-398
- https://doi.org/10.1109/tac.1964.1105743
Abstract
The principle of contraction mapping is well established in mathematics. It has been used in control theory and its application to control systems considered as recursive processes has been investigated. The principle is valid for nonlinear systems and can be used to establish stability in nonlinear control. Also, because the existence of a solution can be obtained by a recursive algorithm, the principle can be used in adaptive or learning systems to generate a desired output function recursively. In this paper, after reviewing the background and recent results on the application of contraction mapping to control systems, the principle is applied to aircraft terrain following. Next, a scheme is presented for a learning model, involving the control of a system with undetermined parameters. In conclusion, the connection between a discrete iterative process and a continuous operation is discussed.Keywords
This publication has 3 references indexed in Scilit:
- Functional Analysis Applied to Nonlinear Feedback SystemsIEEE Transactions on Circuit Theory, 1963
- Contraction Mapping with Application to Control ProcessesJournal of Electronics and Control, 1963
- Control system analysis and design via the second method of lyapunov: (I) continuous-time systems (II) discrete time systemsIRE Transactions on Automatic Control, 1959