Adaptive Control

Abstract

Adaptive control provides techniques for the automatic adjustment of control parameters in real time either to achieve or to maintain a desired level of control system performance when the dynamic parameters of the process to be controlled are unknown and/or time-varying. The main characteristic of these techniques is the ability to extract significant information from real data in order to tune the controller and they feature a mechanism for adjusting the parameters of either the plant model or the controller. The history of adaptive control is long, significant progress in understanding and applying its ideas having begun in the early nineteen-seventies. The growing availability of digital computers has also contributed to the progression of the field. The early applications provided important feedback for the development of the field and theoretical innovations allowed a number of basic problems to be solved. The aim of this book is to provide a coherent and comprehensive treatment of the field of adaptive control. The presentation takes the reader from basic problem formulation to analytical solutions the practical significance of which is illustrated by applications. A unified presentation of adaptive control is not obvious. One reason for this is that several design steps are involved and this increases the number of degrees of freedom. Another is that methods have been proposed having different applications in mind but without a clear motivation for the intermediate design steps. It is our belief, however, that a coherent presentation of the basic techniques of adaptive control is now possible. We have adopted a discrete-time formulation for the problems and solutions described to reflect the importance of digital computers in the application of adaptive control techniques and we share our understanding and practical experience of the soundness of various control designs with the reader. Throughout the book, the mathematical aspects of the synthesis and analysis of various algorithms are emphasized; however, this does not mean that they are sufficient in themselves for solving practical problems or that ad hoc modifications of the algorithms for specific applications are not possible. To guide readers, the book contains various applications of control techniques but it is our belief that without a solid mathematical understanding of the adaptation techniques available, they will not be able to apply them creatively to new and difficult situations. The book has grown out of several survey papers, tutorial and courses delivered to various audiences (graduate students, practicing engineers, etc.

Robust and Adaptive Feedback Noise Attenuation in Ducts

“…where Q is the unknown optimal filter, and η(t) tends asymptotically towards zero (see [20] for details).…”

“…For the stability analysis of this algorithm, see [20]. In adaptive regulation applications, one uses in general the constant trace algorithm.…”

H∞ gain-scheduled controller design for rejection of time-varying narrow-band disturbances applied to a benchmark problem

“…Estimation of the parameters of N p and D p could be performed by the standard Recursive Extended Least Squares method [13], if p(t) was measured. Since p(t) is not available, it is estimated using the measured signal y(t) and the known model of the secondary path.…”

“…Filtered observation vector ψ f (t) is used to ensure the stability and convergence properties of the adaptation algorithm ( [13]). The other condition for the convergence, namely the richness of excitation, is satisfied as long as disturbance is not zero.…”

Optimal model distributions in supervisory adaptive control

“…The emerging field of multi-model adaptive control has successfully mitigated classical adaptive control limitations by introducing logic-based adaptation [1]: instead of a single controller where the parameters vary and adapt with time multiple controllers, each one pertaining to a different operating regime (i.e. to a different model) and whose parameters are fixed, are used.…”