On the use of a Lyapunov function to determine logic for a saturating type control of a non-linear system
Goldsmith, Watson W.
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A method is developed, using the quadratic form of canonical uncoupled state variables as a Lyapunov function to determine the switching logic for a quasi-optimum control of a non-linear dynamic system.# Analytic arguments are presented to support the method, which is capable of being extended to any order system and any number of controls, subject to certain practical limitations noted in the analysis. A computational scheme for determining the canonical state variables and control functions is presented and a topological interpretation is made of the choice of variables used for the control logic calculation. The controller based on the method described is applied to a nonlinear second-order system . Phase trajectories for both the uncontrolled and controlled systems are obtained by means of a digital computer simulation. Various aspects of the theoretical limitations of the method presented are investigated and the experimental results are analyzed with respect to the theoretical predictions. #The system is postulated to be described by a system of differential equations of known form.
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