The theme of this monograph is the adaptive control of systems in a stochastic environment and, more precisely, the study of the tracking problem for ARMAX SISO stochastic systems with time invariant and time varying parameters. Results of simultaneous tracking and parameter identification are included. The author has aimed to (1) provide a reasonably self-contained and up-to-date exposition of the tracking problem after having properly placed it amongst numerous ideas, approaches, and subproblems related to adaptive control, (2) display computer simulation results and discuss their comparative behaviour, (3) introduce a new approach to the stochastic adaptive control with promising results, and (4) qualitatively discuss the adaptive control problem in the hope of improving our understanding of it, stimulate the informed reader to come up with new ideas, and attract newcomers to its study. The reader is assumed to have studied control systems at the graduate level and to have a reasonably good grasp of basic probability theory. Apart from its educational value to the adaptive control student, it is hoped that the accumulation of scattered results and their computer simulation, as well as an extensive reference section will attract the active researcher in this field.

The problem considered in this two-part paper deals with the control of linear, discrete-time, stochastic systems with unknown (possibly time-varying and random) gain parameters. The philosophy of control is based on the use of an open-loop-feedback-optimal (O.L.F.O.) control using a quadratic index of performance. in Part I it is shown that the O.L.F.O. system consists of (1) an identifier that estimates the system state variables and gain parameters, and (2) by a controller described by an 'adaptive' gain and correction term. Several qualitative properties of the overal system are obtained from an interpretation of the equations. Part II deals with the asymptotic properties of the O.L.F.O. adaptive system and with simulation results dealing with the control of stable and unstable third order plants. Comparisons are carried out with the optimal system when the parameters are known. In addition, the simulation results are interpreted in the context of the qualitative conclusions reached in Part I. (Author).

This workshop on stochastic theory and adaptive control assembled many of the leading researchers on stochastic control and stochastic adaptive control to increase scientific exchange and cooperative research between these two subfields of stochastic analysis. The papers included in the proceedings include survey and research. They describe both theoretical results and applications of adaptive control. There are theoretical results in identification, filtering, control, adaptive control and various other related topics. Some applications to manufacturing systems, queues, networks, medicine and other topics are gien.

Over the past decades, although stochastic system control has been studied intensively within the field of control engineering, all the modelling and control strategies developed so far have concentrated on the performance of one or two output properties of the system. such as minimum variance control and mean value control. The general assumption used in the formulation of modelling and control strategies is that the distribution of the random signals involved is Gaussian. In this book, a set of new approaches for the control of the output probability density function of stochastic dynamic systems (those subjected to any bounded random inputs), has been developed. In this context, the purpose of control system design becomes the selection of a control signal that makes the shape of the system outputs p.d.f. as close as possible to a given distribution. The book contains material on the subjects of: - Control of single-input single-output and multiple-input multiple-output stochastic systems; - Stable adaptive control of stochastic distributions; - Model reference adaptive control; - Control of nonlinear dynamic stochastic systems; - Condition monitoring of bounded stochastic distributions; - Control algorithm design; - Singular stochastic systems. A new representation of dynamic stochastic systems is produced by using B-spline functions to descripe the output p.d.f. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

The problem considered in this two-part paper deals with the control of linear, discrete-time, stochastic systems with unknown (possibly time-varying and random) gain parameters. The philosophy of control is based on the use of an open-loop-feedback-optimal (O.L.F.O.) control using a quadratic index of performance. In Part I it is shown that the O.L.F.O. system consists of (1) an identifier that estimates the system state variables and gain parameters, and (2) by a controller described by an 'adaptive' gain and correction term. Several qualitative properties of the overall system are obtained from an interpretation of the equations. Part II deals with the asymptotic properties of the O.L.F.O. adaptive system and with simulation results dealing with the control of stable and unstable third order plants. Comparisons are carried out with the optimal system when the parameters are known. In addition, the simulation results are interpreted in the context of the qualitative conclusions reached in Part I. (Author).