Early Developments in Nonlinear Control

This article presents a review of some of the early develop­ ments in nonlinear control engineering. It begins by briefly examining the status prior to World War II and then concentrates on the developments in approximately the following two dec­ ades. A significant amount of the work will be seen to have as its foundation the need to obtain methods to solve wartime problems related to servomechanisms, fire control, and missile controL The major analytical techuiques of the phase plaue, the describ­ ing function and Tsypkin's method for relay systems, are dis­ cussed at length. Two important aspects in obtaining control engineering solutions to problems, which are often forgotten by theoreticians , are the existence of simulation facilities and the capabilities of the available hardware to implement specific solutions at an allowable cost. Later sections therefore comment on these aspects. Also, a brief review of some of the early papers on nonlinear control is given, and finally some comments are provided on the continuing relevance of these early methods and some still unsolved problems.