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ASPR based Adaptive Output Regulation for Systems with Input Saturation
Ikuro Mizumoto, Kazui Yamada

Last modified: 2023-05-15


The system is said to be `Almost Strictly Positive Real' or ASPR if there exists a static output feedback control such that the resulting closed-loop system is strictly positive real (SPR).  It has been well recognized that one can easily design a simple adaptive output feedback control for ASPR systems and it has strong robustness with respect to disturbances and systems uncertainties. The usefulness of the method to practical systems has also been confirmed through several kinds of practical applications. Unfortunately, however, since most practical systems do not satisfy the ASPR conditions, in the practical application of the ASPR-based adaptive control, we have to consider alleviation methods for the ASPR restriction. One of the simple and powerful methods to alleviate the ASPR restriction on the controlled system is the introduction of a parallel feedforward compensator (PFC). By introducing the PFC in parallel with the controlled system so as to render the resulting augmented system ASPR, one can apply the ASPR-based adaptive output feedback control strategy to the ASPR augmented systems. In this case however, since the control system is designed to the ASPR augmented system, the performance of the practical system may degrade even though the acceptable control performance has been obtained for the augmented system. One of the solution to this problem for attaining output regulation is the introduction of an pre compensator with the integral action. We can alleviate the affects from PFC output and the performance of the practical system can be improved.
On the other hand, windup problem to systems with input saturation will occur in this ASPR-based adaptive output feedback method too, especially for systems with integral action. In this paper, we provide a novel anti-windup control method for ASPR-based adaptive output feedback control system with a PFC and a pre compensator with integral action. An adaptive anti-windup control for adaptive output feedback control under ASPR conditions is proposed based on model recovery anti-windup control technique It will be shown that the proposed adaptive anti-windup control drastically improves the control performance under the existence of the input saturations. The stability of the obtained augmented adaptive anti-windup control will also be shown and the effectiveness of the proposed method will be confirmed through numerical simulations.