Optimal input system identification for homogeneous and nonhomogeneous boundary conditions

Abstract

A recent paper by Mehra has considered the design of optimal inputs for linear system identification. The method proposed involves the solution of homogeneous linear differential equations with homogeneous boundary conditions. In this paper, a method of solution is considered for similar-type problems with nonhomogeneous boundary conditions. The methods of solution are compared for the homogeneous and nonhomogeneous cases, and it is shown that, for a simple numerical example, the optimal input for the nonhomogeneous case is almost identical to the homogeneous optimal input when the former has a small initial condition, terminal time near the critical length, and energy input the same as for the homogeneous case. Thus tentatively, solving the nonhomogeneous problem appears to offer an attractive alternative to solving Mehra's homogeneous problem.