×

Physical continuity and uniqueness principle. Exponential natural tracking control. (English) Zbl 0912.93030

Author’s abstract: The physical continuity and uniqueness principle (PCUP) is introduced and defined. It expresses real features of physical variables.
A nonlinear system is modeled by a second order nonlinear vector differential equation and by a nonlinear vector output equation. A complete lack of information is allowed about the real forms and values of the external disturbances and all the system nonlinearities except the matrix function \(A(\cdot)\) mutliplying the second derivative of the interval dynamics vector function \(q(\cdot)\) and the matrix \(B\) expressing the static characteristics of the final (executing) controller devices. Such models characterize a large class of engineering systems. Their variables obey the PCUP.
A necessary condition is proved for the system to possess a qualitative property called natural trackability that permits existence of control obeying the PCUP, which can be generated under such a lack of information and which can exponentially steer the error vector to the origin. The condition is used to synthesize such a control called natural tracking control. The control algorithms are developed by using the PCUP with or without a combination with the Lyapunov method. The algorithms guarantee both elementwise global asymptotic stability and elementwise global exponential tracking.
Reviewer: D.Franke (Hamburg)

MSC:

93C10 Nonlinear systems in control theory
93B51 Design techniques (robust design, computer-aided design, etc.)
PDFBibTeX XMLCite