Stability and Multi-Models in Model Reference Adaptive Systems.
ILLINOIS UNIV AT URBANA-CHAMPAIGN COORDINATED SCIENCE LAB
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Several problems related to model reference adaptive systems MRAS are investigated. The MRAS finds application both in control system design in an uncertain environment and in parameter identification. The development here is based on a parallel MRAS structure whose adaptation design guarantees that the MRAS is hyperstable. A method is found, based on controllability conditions of a particular MRAS subsystem state representation, to produce a reduced-order reference model without losing the inherent hyperstable property of the MRAS design. For MRAS applied to parameter identification, we consider two problems. Necessary and sufficient conditions guaranteeing asymptotic stability of the parameter-error are found. For a specific discrete-time hyperstable MRAS, we consider the difficulty in realizing the hyperstable design due to the nature of the identification problem. An alternate design is proposed and a strategy for investigating its stability properties is described. For a continuous-time MRAS control system with discontinuous adaptation, variable structure system theory is used to establish its stability.
- Theoretical Mathematics