Reduced explicit constrained linear quadratic regulators

In this note, it is studied how structural properties of certain linear systems can be exploited to derive reduced dimension multiparametric quadratic programs that lead to explicit piecewise linear feedback solutions to the state and input constrained linear quadratic regulation problem. The reduced dimensionality typically results in suboptimal controllers of lower complexity, with associated computational advantages in the online implementation. At the heart of the methods are state-space projections based on the singular value decomposition.