## Jason L. Speyer

**Charles Stark**)

**Draper**, whose second volume of his three sequence series on Instrument Engineering (1952) was one the first books on what we know as Classical Control covering such topics as

**[1]****Evens**root locus,

**Bode**plots, Nyquist criterion, and

**Nichols**charts. Doc

**Draper**instituted an undergraduate course in classical control that I took my junior year. This inspired me to take a graduate course and write my undergraduate thesis in controls.

**Richard Bellman**for global sufficiency of an optimal trajectory and the Pontryagin Maximum principle inspired by the deficiency of dynamic programing to solve certain classes of optimization problems. The Bushaw problem of determining the minimum time to the origin of a double integrator was just such a problem, since the optimal return function in dynamic programing is

*not*differentiable at the switching curve and the Bellman theory did not apply. Interestingly, for my bachelor’s thesis I applied the results of the Bushaw problem to the minimum time problem of bringing the yaw and yaw rate of an aircraft to the origin. However, at that time I had no idea about the ramification of the Bushaw problem to optimization theory. I also learned of the work of

**Rudolf**

**Kalman**in estimation, the work of

**Arthur Bryson**and Henry Kelley in the development of numerical methods for determining optimal constrained trajectories, and J. Halcombe (Hal) Laning and Richard Battin on the determination of orbits for moon rendezvous.

**Art Bryson**was a consultant. There, I worked with a student of Bryson, Walter Denham. We were contracted by MIT’s Instrumentation Laboratory, monitored by Richard Battin, to enhance the Apollo autonomous navigation system over the trans-Lunar orbit. We developed a scheme for determining the optimal angle-measurement sequence between the best stars in a catalogue and near and far horizons of the Earth or the Moon using a sextant. This angle-measurement sequence minimized some linear function of the terminal value of the error covariance of position and velocity near the Earth or Moon. Our optimization scheme, which required a matrix dynamic constraint, seemed to be a first. This scheme, used in the Apollo autonomous navigation system, was tested on Apollo 8, and used on every mission thereon. My next task at Raytheon was working on neighboring optimal guidance scheme. This work was with

**Art Bryson**and

**John Breakwell**. I remember travelling to Lockheed’s Palo Alto Research Laboratory and meeting with John, the beginning of a long and delightful collegial relationship.

**Art Bryson**to take me on as a graduate student at Harvard, supported by the Raytheon Fellowship program. To understand the intellectual level I had to contend with, on my doctorial preliminary exam committee, three of the four examiners were recipients of the Richard E. Bellman Control Heritage Award;

**Art Bryson, Larry (Yu-Chi) Ho,**and

**Bob (Kumpati) Narendra,**all of whom have been my life time colleagues. I was also fortunate to take a course taught by

**Rudy Kalman**. Surprisingly, he taught many of the controls areas he had pioneered, except filtering for Gauss-Markov systems (the Kalman filter); the Aizerman conjecture, the Popov criterion and Lyopunov functions, duality in linear systems, optimality for linear-quadratic systems, etc. After finishing my PhD thesis on optimal control problems with state variable inequality constraints, I returned to Raytheon. Fortunately,

**Art Bryson**made me aware of some interest at Raytheon in using modern control theory for developing guidance laws for a new missile. At Raytheon’s Missile Division I worked with Bill O’Halloran on the homing missile guidance system where Bill worked on development of the Kalman filter and I worked on the development of the linear-quadratic

*closed-form*guidance gains that had to include the nonminimal phase autopilot. This homing missile, the Patriot missile system, appears to be the first fielded system using modern control theory.

[1] Boldface names are recipients of the Richard E. Bellman Control Heritage Award.