PrefaceThe engineering objective of high performance control using the tools of optimal control theory, robust control theory, and adaptive control theory is more achievable now than ever before, and the need has never been greater. Of course, when we use the term high performance control we are thinking of achieving this in the real world with all its complexity, uncertainty and variability. Since we do not expect to always achieve our desires, a more complete title for this book could be "Towards High Performance Control".To illustrate our task, consider as an example a disk drive tracking system for a portable computer. The better the controller performance in the presence of eccentricity uncertainties and external disturbances, such as vibrations when operated in a moving vehicle, the more tracks can be used on the disk and the more memory it has. Many systems today are control system limited and the quest is for high performance in the real world.In our other texts Anderson and Moore (1989), Anderson and Moore (1979), Elliott, Aggoun and Moore (1994), Helmke and Moore (1994) and Mareels and Polderman (1996), the emphasis has been on optimization techniques, optimal estimation and control, and adaptive control as separate tools. Of course, robustness issues are addressed in these separate approaches to system design, but the task of blending optimal control and adaptive control in such a way that the strengths of each is exploited to cover the weakness of the other seems to us the only way to achieve high performance control in uncertain and noisy environments.The concepts upon which we build were first tested by one of us, John Moore, on high order NASA flexible wing aircraft models with flutter mode uncertainties. This was at Boeing Commercial Airplane Company in the late 1970s, working with Dagfinn Gangsaas. The engineering intuition seemed to work surprisingly well and indeed 180 • phase margins at high gains was achieved, but there was a shortfall in supporting theory. The first global convergence results of the late 1970s for adaptive control schemes were based on least squares identification. These were harnessed to design adaptive loops and were used in conjunction with vi Preface linear quadratic optimal control with frequency shaping to achieve robustness to flutter phase uncertainty. However, the blending of those methodologies in itself lacked theoretical support at the time, and it was not clear how to proceed to systematic designs with guaranteed stability and performance properties.A study leave at Cambridge University working with Keith Glover allowed time for contemplation and reading the current literature. An interpretation of the Youla-Kučera result on the class of all stabilizing controllers by John Doyle gave a clue. Doyle had characterized the class of stabilizing controllers in terms of a stable filter appended to a standard linear quadratic Gaussian LQG controller design. But this was exactly where our adaptive filters were placed in the designs we developed at Boeing. Could we impro...

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We revisit the extremum seeking scheme whose local stability properties were analyzed in and propose its simplified version that still achieves extremum seeking. We show under slightly stronger conditions that this simplified scheme achieves extremum seeking from arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local convergence result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. Moreover, we show at the same time that reducing the parameters typically slows down the convergence of the extremum seeking controller. Hence, the control designer faces a tradeoff between the size of the domain of attraction and the speed of convergence when tuning the extremum seeking controller. We present a simulation example to illustrate our results.

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