An approach to the synthesis of fuzzy stabilization systems with a priori unknown model of an object

A method of synthesis of fuzzy stabilization systems for a broad class of dynamic objects under the assumption that the mathematical model of the object is not known a priori is proposed. The control is formulated in the form of a proportional law of adjustment as a function of a macro-variable; the square of the Euclidean norm of the phase variables is adopted as the macro-variable. An analogous variable characterizes the distance of the object from the equilibrium position. Despite the simplicity of the control law, its sign remains constant due to the fact that the macro-variable is positive-definite over the entire phase space. The switching times of the signals are determined by fuzzy identification of the system’s dynamic modes on the basis of measurement of the derivatives of the macro-variable.