Phase Space in the Theory of Optimum Control†

Phase space is an essential concept in the theory of optimum non-linear control, but has been given only cursory exposition hitherto. This paper attempts to bridge the gap between the control engineer who uses phase space heuristically and the mathematician who adopts phase space as an arbitrary starting point. A history of the phase-space concept is given. It is shown how to define and measure the phase coordinates of linear and non-linear systems. A special treatment of electrical networks is given.