Full Text: PDF
In this paper we consider nonlinear systems using infinite Volterra series describing the input-output model. We present sufficient conditions under which the nonlinear operator determined by the infinite Volterra series maps L_2 space into itself. Using output feedback we arrive at a nonlinear integral equation of the second kind. We prove existence of solutions of this equation and local input-output stability. Then we consider a control problem where the input is to be chosen to optimize certain objective functional. We prove existence of suboptimal control (or input) policy from the class of regular controls. We discuss the question of nonexistence of optimal policy from the class of regular controls, and then prove the existence of an optimal relaxed control from the class of finitely additive measures defined on a related compact Hausdorff space (the space of regular controls endowed with the weak topology). Next we consider the inverse problem identifying the kernels of the Volterra series. These results are then extended to an infinite dimensional Hilbert space.
How to Cite this Article:
N. U. Ahmed, Volterra series and nonlinear integral equations of the second kind arising from output feedback and their optimal control, Journal of Nonlinear Functional Analysis 2016 (2016), Article ID 40.