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Abstract
Most real world systems are at least somewhat nonlinear. Various methods have been proposed for controlling these nonlinear systems. A method, referred to as dynamic linearization, of controlling these systems is developed here. The method finds a feedback controller which forces the response of a given nonlinear system to follow the response of a predetermined linear system. This linear system will have been selected to meet some predetermined design criteria. A test is provided that gives sufficient conditions for the existence of such a control. Algorithms are also given that allow implementation on a digital computer, both for cases that satisfy the sufficient conditions and those that do not.
In addition to the deterministic case, the stochastic case is also presented. Separability is assumed and the dynamic linearization technique is coupled with an extended Kalman filter. To allow the control to have a dual effect, a term proportional to a function of the covariance matrix is added to the performance criterion. This case is also presented in a form for implementation on a digital computer.
An overview of the current research in the control of deterministic nonlinear systems and in the stochastic control problem is also presented. Several illustrative examples and a more complex application to an aircraft landing system are also found here. In addition, some areas for further research are suggested.
