Control of differentially flat linear delay systems with constraints

Abstract : We consider the control of differentially flat linear delay systems with constraints. The constraints can be given on the state and/or on the control. Linear delay systems are here envisioned as modules over a ring of differential and distributed delay operators. Due to the nice Bezout property that this ring enjoys, the controllability notions of freeness, projectivity and torsion freeness coincide. Thanks to the flatness (corresponding to freeness for linear systems) property, all constraints are reported through the flat output (the basis of the corresponding module). We then make use of polynomial B-splines as specialisations for the flat output; the constraints are then expressed as inequalities in these B-splines control points. Some examples illustrate the effectiveness of the approach.