Suboptimality and stability analysis for feedback boundary control of heat-diffusion equations

We develop an effective approach to feedback control design of parabolic systems that takes into account specific properties of heat-diffusion and related dynamical processes. Some results obtained in this direction have been reported mostly for the case of Dirichlet boundary controls. Here we pay the main attention to justifying suboptimal characteristics of feedback controllers in Neumann boundary conditions and stability analysis of nonlinear closed-loop control systems obtained in this way. Based on the variational approach to the stability analysis and monotonicity properties of transients, we are able to reduce stability questions in the closed-loop nonlinear system to considering special optimal control problems with infinite horizon