Extremum Search Methods and Multivariate Control System Synthesis

Control system design based on the mathematical theory of optimality so far exhibits two practical shortcomings. First, due to analytical difficulties it is not always possible to carry the solution to the end, especially in the case of nonlinear problems. Second, even if such a solution is obtained, it must necessarily be based on knowledge of the characteristics of the controlled plant. However, incomplete knowledge of such properties is the typical situation in control system design. This need not be a disadvantage, since the classical basis of control systems, i.e., the principle of feedback, allows one to largely overcome these difficulties, because a system with feedback can achieve the control objective even when the plant characteristics vary over a wide range.