| The control of distributed parameter systems (DPS) is an interesting and challenging research field studied since the 1960s. An increasing number of DPS control problems in aerospace, materials, chemistry, biology, and other disciplines have attracted many mathematicians and engineers to this field in recent years. Many of these applications have been driven by new technologies for manufacturing, actuation, and sensing. Especially interesting are spatial field control problems that are challenging due to having a very large number of degrees of freedom, which is in contrast to the boundary control problems commonly investigated in the literature.;Computationally efficient methods for the robust and optimal control of DPS are derived that incorporate such techniques as basis function expansions, method of moments, model predictive control, and analytical function theory. These control methods are demonstrated by application to linear and nonlinear DPS described by reaction-diffusion-convection equations, including for some boundary and spatial field control problems that have not been investigated in the literature. Initially open-loop optimal control solutions are derived for a linear PDE, followed by generalizations to nonlinear reaction kinetics, coupled reactions, and feedback. The results also include an extension of internal model control that is applicable to linear infinite-dimensional systems.;While DPS control problems can be highly sensitive to uncertainties, robust control theory for DPS is not as well developed as for lumped parameter systems. Nonconservative approaches are derived for the analysis and control for DPS with worst-case uncertainties that are fairly general in terms of both the uncertainty description and the dynamics of the DPS. These methods provide the same level of assurance for model uncertainties in DPS as what was previously available only for lumped parameter systems. |
