Control of linear extended nD systems with minimized sensitivity to parameter uncertainties

A new view on uncertain system parameters is presented considering them in the same way as other independent variables, e.g., time or space variables. After re-interpreting the well known equations for the sensitivities of a system to parameter changes, we consider the problem of optimal control that takes into account not only the quality of control itself, but also a reduction in the influence of parameter changes. Firstly, we re-derive and elucidate known results for systems described by linear ordinary differential equations in the state-space form. Then, it is shown how to extend the well known theory of designing optimal controllers with quadratic criterion so as to cover the reduction of uncertainties in systems described by a class of linear partial differential equations. As a result, we obtain a controller that has a new modal structure in space. Furthermore, the controller incorporates additional sensitivity signals for each mode.