Functional Series and the Control of Nonlinear Systems

Nonlinear systems, particularly those with soft nonlinearities, can be characterized by functional series expansions. Commonly used expansions include the Volterra series, the Wiener series, and the Cameron-Martin series. The Cameron-Martin series (analogous to a Fourier series) represents systems by a superposition of specially constructed nonlinear component systems. These component systems form their outputs from products of Hermite polynomials of the outputs of sets of linear filters exhibiting certain useful properties. Consequently, nonlinear system output control objectives can be reformulated in terms of the states and outputs of these linear filters, which can in turn be controlled by conventional linear control methods. Several new results are given.