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Adaptive control of time-varying systems with time-varying delays. (English) Zbl 1076.93026

This paper presents a pole-placement-based robust stable adaptive method for time-varying linear plants subject to a set of possibly unbounded point time delays, under unmodeled dynamics and bounded disturbances. Plant parameters are permitted to be impulsive of limited size and frequency. Known values of time delays are not required. The mechanism used to achieve robust adaptive stabilization includes a dead zone. This dead zone freezes the adaptation when the adaptive error is small compared to the estimated contribution of uncertainty to the filtered output. This strategy insures that parameter estimation is not disrupted by small identification errors. The proposed estimation algorithm combines the use of the dead zone with a modified rule for updating parameter estimates and with a modification of classical least squares updating of the covariance matrix. The estimation algorithm has the standard desirable properties of boundedness and closed-loop stability in the presence of delays. The covariance matrix is positive definite for all time for appropriate initial conditions.

MSC:

93C40 Adaptive control/observation systems
93B55 Pole and zero placement problems
93C23 Control/observation systems governed by functional-differential equations
93D21 Adaptive or robust stabilization
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