Approximations of thermoelastic and viscoelastic control systems

This paper deals with the development and analysis of well-posed models and computational algorithms for control of a class of partial differential equations that describe the motions of thermo-viscoelastic structures. We first present an abstract “state space” framework and a general well-posedness result that can be applied to a large class of thermo-elastic and thermo-viscoelastic models. This state space framework is used in the development of a computational scheme to be used in the solution of an LQR control problem. A detailed convergence proof is provided for the viscoelastic model, and several numerical results are presented to illustrate the theory and to analyze problems for which the theory is incomplete.