Parameterized polyhedra approach for robust constrained generalized predictive control

The paper considers the discrete time-invariant linear systems affected by input disturbances and construct the explicit description of the constrained generalized predictive control (GPC) law taking in account the constraints existence from the design stage. The explicit formulation of the predictive controllers gives a useful insight on the closed loop capabilities. The GPC is a special case of model predictive control (MPC) whose explicit formulation is known to be a piecewise affine function of state. As novelty the present work shows that this piecewise linear dependence on the context parameters can be found by exploiting the fact that the optimum of a min-max multiparametric program is placed on the vertices of a parameterized polyhedron. As these parameterized vertices have specific validity domains, the control law is expressed as a piecewise linear function of the current system parameters. The resulting GPC law is formulated in terms of a look-up table with two-degree of freedom polynomials in the backward shift operator (also known as the RST formulation)