Algorithms for Robust Inversion of Dynamical Systems

Abstract

A new methodology for solving inverse dynamics problem is developed. The methodology is based on using a mathematical model of a dynamical system and robust stabilization methods for a system under uncertainty.

Most exhaustively the theory is described for linear finite-dimensional time-invariant scalar systems and multiple-input multiple-output systems.

The study shows that with this approach, the zero dynamics of the original system is of crucial significance. This dynamics, if exists, is assumed to be exponentially stable.

It is established that zero-dynamics, relative order, and the corresponding equations of motion cannot be defined correctly in multiple-input multiple-output systems. For correct inverse transformation of the solution of the problem, additional assumptions have to be introduced, which generally limits the inverse system category.

Special attention is given to the synthesis of elementary (minimal) inverters, i.e., least-order dynamical systems that solve the transformation problem.

It is also established that the inversion methods sustain the efficiency with finite parameter variations in the initial system as well as with uncontrolled exogenous impulses having no impact on the system’s internal dynamics.