An algorithm for the pseudoinversion of dynamic systems

The problem of the pseudoinversion of a dynamic system (the reconstruction of an normal input of a system by the results of measurement of its output) is considered. The input is understood as a pair: the initial state of the system and an input action onto the system (control, perturbation, etc.). The normal input is one having minimal norm on a set of all inputs consistent with the output. The system output is a function of a time, a system state and an input action. The dynamics of the system is specified by a linear ordinary differential equation. The pseudoinversion problem is solved by the reduction of the original dynamic system to some equivalent system, enabling to obtain an normal input in an explicit form. The reduction is performed using a finite number of algebraic and differentiation operations. The explicit form of the normal input of the reduced system is deduced from a explicit form of a solution of some auxiliary parametric problem of optimal control by passage to the limit.