WHAT YOU WILL LEARN:

That LQG and Kalman theory are history, what the new theory is all about, where it's likely to go, and how to use it to design your own regulators and observers.

WHO SHOULD ATTEND:

• Estimation and controls practitioners who wish to get much better performance from their systems, by merely using better feedback gain matrices.
• Those interested in continuing the research.

LQG theory for regulators and Kalman theory for observers both require you to believe that all process and measurement noise is white and Gaussian, when no physical noise has either property. Further, LQG theory forces you to accept that minimizing the trace of a weighted covariance of the state variables is what's good for you, while Kalman theory relies on minimizing the trace of the measurement error weighted residuals, whose relation to engineering desires is tenuous at best. This course is designed to show you how to design optimal regulators and observers for stationary systems, based on knowledge of the all the noise power spectra, and using performance measures that are much more sensitive to your actual engineering needs. You will also see that, by your own measure, performance is likely to be greatly improved, relative to LQG or Kalman-derived feedback gains. While several papers and seminars have been given on this subject, this is the first course offered on how to do it, along with the current status of the theory. Throughout, obscure matrix relations are introduced as needed. Caveat: This theory is all analog. It's the oversampling limit of a system with infinite computational resources. A discussion will be given on directions for future research.

COURSE MATERIALS:

Include extensive notes and reference materials, plus a set of the graphics displayed during the course.

Tuition: $1,595. (Early-registration and group discounts apply)

COURSE OUTLINE:

1. On the properties of noise--random processes, ergodicity, expectation, stationarity, autocorrelation, one-sided Fourier transforms, theoretical power spectra, the noise effect integrals.
2. The perfect regulator--terminal state covariance, settling time, the optimal gains, LQG theory, last rites for 'Certainty-Equivalence,' the general first order problem, examples.
3. The optimal observer--dynamic estimation, the Separation Theorem, terminal error covariance, settling time, Kalman theory, the optimal gains, examples.
4. The combined observer and regulator--the one-way Separation Theorem, settling time, terminal state covariance, the optimal gains, examples.
5. A few words on software--Scaling, optimizing functions with discontinuous derivatives, Lyapunov equations.
6. My crystal ball--non-stationary systems, discrete systems.

INSTRUCTOR: David Sonnabend, Ph.D., PE, has over 40 years' experience in space systems, controls and estimation, instrument design, and navigation, including 16 years at JPL. He is currently the President of Analytical Engineering. This course has evolved over the last several years, from various studies, papers, and seminars, to the point where the book describing the new theory, 'Regulators, Observers, and Power Spectra,' has just been published. Dr. Sonnabend is presently engaged in extending that work. He holds a BA in Physics from UCLA, and an MS and Ph.D. in engineering from Stanford University. He is also a Registered Professional Engineer in Colorado.