Robust Pointwise Min-Norm Control of Distributed Systems with Fluid Flow

This paper reports a Pointwise Min-Norm control (PWMN) general result for a class of distributed systems that include transport phenomena associated with fluid flow in pipes and open pool canals. The main goal is to find a numerical control scheme that ultimately can be embedded in a more general Nonlinear Model Predictive Control formulation as an alternative to ensure closed-loop stability, for moderate values of the receding horizon without increasing dramatically the computational effort. In fact the PWMN control can be viewed as the NMPC limit stabilizing solution when the predictive horizon value goes to zero. A tubular system with finite escape traveling time is used to illustrate the control performance. An application to a canal pool modeled by Saint-Venant's equations is also given. Canals are formed by a sequence of pools separated by gates. Water distribution canals provide interesting examples of distributed parameter plants for nonlinear control application.