Inverse response problem (control) of dynamic systems via Hamilton's law

Abstract

By using Hamilton's law (of varying action) directly, the solution of a control problem becomes one of solving a set of algebraic equations only; no differential equations are needed. The approach specifies the response as a polynomial in power series of time, the coefficients of which are chosen to yield the desired behavior of the dynamic system. The unknown control inputs are assumed to be also polynomials in power series of time with unknown coefficients. The inverse response (control) problem is solved by finding these unknown input coefficients by an application of Hamilton's law which must always be satisfied by the dynamic system. The feasibility of the method is demonstrated for the control of a spatially discrete nonlinear dynamic system.