Abstract
We have examined the problem of decentralized adaptive control in the presence of bounded disturbances and parasitics modeled as multiparameter singular perturbations. Sufficient conditions are obtained which guarantee boundedness and convergence to a residual set when parasitics are absent. When parasitics are present the stability properties are no longer global. However, under the same sufficient conditions, a region of attraction is shown to exist from which all signals converge to a residual set. The size of the residual set is a function of the reference input signal characteristics, the magnitude of the disturbance and some design parameters. The size of the region of attraction is a function of the frequency of parasitics and as the parasitics become infinitely fast this region becomes the whole space. One of the crucial results of this chapter is the use of local filters for the strongly observable parasitics and output disturbances. This is done at the expense of increasing the order of the local dominant part of each subsystem. Without the filters the stability of the adaptive control design in this chapter cannot be assured.
The extension of the results of this chapter to a wider class of large scale system is a topic for future research.
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8.7. References
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(1983). 8. Reduced order-decentralized adaptive control. In: Ioannou, P.A., Kokotovic, P.V. (eds) Adaptive Systems with Reduced Models. Lecture Notes in Control and Information Sciences, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006365
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DOI: https://doi.org/10.1007/BFb0006365
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