Approximate solutions of the regulator equations for nonlinear DPS

One of our overall research goals is the design of feedback control laws that can be used to solve problems of output regulation for nonlinear distributed parameter systems (DPS). Towards this end, we recast the well-known regulator equations as a nonlinear fixed point problem in terms of which we derive a numerical algorithm for obtaining approximate solutions of the regulator problem for nonlinear DPS. The numerical methods are based on either fixed point or Newton iteration with initial state obtained by solving the regulator equations associated with the corresponding linearized problem. The method is applied to a specific example of a reaction diffusion equation with a quadratic nonlinearity. We present the results of two numerical simulations.