Algorithms for Robust Inversion of Dynamical Systems

A new methodology for solving inverse dynamics problem is developed. The methodologyis based on using a mathematical model of a dynamical system and robust stabilization methodsfor a system under uncertainty.Most exhaustively the theory is described for linear finite-dimensionaltime-invariant scalar systems and multiple-input multiple-output systems.The study shows that with this approach, the zero dynamics of the original systemis of crucial significance. This dynamics, if exists, is assumed to be exponentially stable.It is established that zero-dynamics, relative order, and the correspondingequations of motion cannot be defined correctly in multiple-input multiple-output systems. Forcorrect inverse transformation of the solution of the problem, additional assumptions have to beintroduced, 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 finiteparameter variations in the initial system as well as with uncontrolled exogenous impulses havingno impact on the system ' s internal dynamics.