Static output feedback control design for constrained linear discrete-time systems using data cluster analysis

Methods for the design of static output feedback controllers for linear discrete-time systems subject to state and control constraints, additive disturbance and measurement noise are proposed in this study. First, the authors show how the design can be performed through the construction of an output feedback controlled invariant set together with the solution of several multiparametric linear programming (mp-LP) problems. This technique is commonly used to characterise the optimal control action as a piecewise affine (PWA) function over polyhedral regions. However, when applied to constrained multiple output systems, it may require high online computational cost and large memory capacity, due to the number of polyhedral regions resulting from the mp-LP solution. Within this context, the authors present a new approach to compute a PWA static output feedback control law over a smaller number of polyhedral regions using the K q-flat data cluster analysis algorithm. Optimisation problems to compute PWA sub-optimal static output feedback control laws over an even smaller number of regions are also proposed, and illustrated by numerical examples.