Abstract
Adaptive mixing control (AMC) is a recently developed control scheme for uncertain plants, where the control action coming from a bank of precomputed controller is mixed based on the parameter estimates generated by an on-line parameter estimator. Even if the stability of the control scheme, also in the presence of modeling errors and disturbances, has been shown analytically, its transient performance might be sensitive to the initial conditions of the parameter estimator. In particular, for some initial conditions, transient oscillations may not be acceptable in practical applications. In order to account for such a possible phenomenon and to improve the learning capability of the adaptive scheme, in this paper a new mixing architecture is developed, involving the use of parallel parameter estimators, or multi-estimators, each one working on a small subset of the uncertainty set. A supervisory logic, using performance signals based on the past and present estimation error, selects the parameter estimate to determine the mixing of the controllers. The stability and robustness properties of the resulting approach, referred to as multi-estimator adaptive mixing control (Multi-AMC), are analytically established. Besides, extensive simulations demonstrate that the scheme improves the transient performance of the original AMC with a single estimator. The control scheme and the analysis are carried out in a discrete-time framework, for easier implementation of the method in digital control.
Highlights
It is well known that, in feedback control design, unknown values of the physical variables of the plant dynamics may lead to a large parametric uncertainty that cannot be handled by a single fixed
The multiple model architecture comprises a multicontroller consisting of a family of precomputed candidate controllers and some logic that influences the control by selecting the candidate controllers based on processed plant input/output data
A recent adaptive control scheme involving the use of precalculated candidate controllers is adaptive control with mixing (AMC), developed both for continuous-time [11] and discrete-time SISO plants [12]
Summary
It is well known that, in feedback control design, unknown values of the physical variables of the plant dynamics may lead to a large parametric uncertainty that cannot be handled by a single fixed. A recent adaptive control scheme involving the use of precalculated candidate controllers is adaptive control with mixing (AMC), developed both for continuous-time [11] and discrete-time SISO plants [12]. If the I/O data that the on-line adaptive law processes provide little information about the unknown plant dynamics, or if the true parameter vector is far from the initial estimated parameter vector, some undesirable transient can occur before the regulation/tracking task is achieved. In order to account for such a possible phenomenon, a new AMC architecture is developed, involving the use of parallel parameter estimators, or multi-estimators, each one working on a small subset of the uncertainty set.
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