DIRECT ADAPTIVE CONTROL IN HILBERT SPACE.

摘要

Though great advances have been reported in adaptive control for single-input/single-output (SISO) systems and some multi-input/multi-output (MIMO) systems, a large amount of a priori structural information of the plant is needed for most of the methods proposed. This is unsatisfying because all physical systems have some unmodelled dynamics and structure and operate in noisy environment. In fact, in many high performance control system design, the distributed nature of the plant must be taken into account. These distributed parameter systems may be modelled by delayed differential equations, partial differential equations or integral equations. They must be analysed in the appropriate infinite-dimensional state space.; A particular approach, model reference adaptive control (MRAC) with command generator tracker (CGT) concept, adopts a set of assumptions that are not system dimension dependent. The method has been applied successfully to some finite-dimensional systems and show promise for the infinite-dimensional state space generalization. In this thesis, the scheme is modified in order to make the transition of this theory from finite dimensions to the infinite-dimensional Hilbert Space mathematically rigorous. As a bonus, the modified scheme also improves performance in the finite-dimensional case in terms of rate of convergence, robustness with respect to unmodelled dynamics, input and output disturbances and parameter variation. We have also relaxed the model matching condition to an asymptotic form. The proposed modification can also be applied to other adaptive control schemes yielding improvement in robustness. Three DPS examples, heat equation and beam equation with marginally stable rigidbody modes and first order delay equation, and many finite-dimensional examples are given to illustrate the application of this scheme.