Scalable command governor via semi-ellipsoidal set for linear systems with time-varying soft constraints

This paper provides a solution for a command governor (CG) that employs a semi-ellipsoidal set. The motivation is driven by the need to address the shortcomings of polyhedral and ellipsoidal sets widely used in CG. In particular for many applications, polyhedral sets require a large number of linear inequality constraints while ellipsoidal sets are too conservative. Furthermore, both types of sets are generally designed for systems with time-invariant and hard constraints. The contributions of the paper are: (i) we provide new convex conditions to construct an invariant and constraint-admissible semi-ellipsoidal set for discrete-time linear systems with time-varying soft constraints; (ii) we propose a computationally efficient procedure to solve the online optimization problem associated with the newly introduced semi-ellipsoidal set in CG. Three numerical examples with comparison to earlier solutions from the literature illustrate the effectiveness of the proposed approach.