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

• Published in: IET control theory & applications Vol. 12; no. 18; pp. 2541 - 2550
• Main Authors: Dantas, Amanda Danielle O. S, Dantas, André F. O. A, Dórea, Carlos E. T
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 18.12.2018
• Subjects: additive disturbance; constrained linear discrete‐time systems; constrained multiple output systems; control constraints; control system synthesis; discrete time systems; feedback; high online computational cost; k q‐flat data cluster analysis algorithm; large memory capacity; linear discrete‐time systems subject; linear programming; linear systems; measurement noise; mp‐LP problems; multiparametric linear programming; optimal control; optimal control action; output feedback controlled invariant; pattern clustering; piecewise affine function; polyhedral regions; PWA static output feedback control law; PWA sub‐optimal static output feedback control laws; Research Article; static output feedback control design; static output feedback controllers; optimal control action; constrained linear discrete-time systems; linear programming; mp-LP problems; feedback; piecewise affine function; linear discrete-time systems subject; high online computational cost; PWA static output feedback control law; multiparametric linear programming; control constraints; output feedback controlled invariant; static output feedback control design; discrete time systems; measurement noise; control system synthesis; optimal control; linear systems; additive disturbance; large memory capacity; PWA sub-optimal static output feedback control laws; pattern clustering; polyhedral regions; static output feedback controllers; constrained multiple output systems; k q-flat data cluster analysis algorithm
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2018.5744

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.