Maximal Robust Control Invariant Set Research Articles

Computing Robust Controlled Invariant Sets of Linear Systems

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set, while the second method provides an inner approximation. The outer approximation scheme is $\delta$-complete, given that the constraint sets are formulated as finite unions of polytopes.

Set‐theoretic analysis of the isolated ramp metering problem

SummaryAnalysis of ramp metering, as an effective freeway traffic control solution, is focused in the paper. The studied traffic control problem is discussed in a set‐theoretic context in order to quantitatively characterize its effectivenes. The notions of maximal robust controlled invariant set, as well as t‐step robust controllable set are defined and used for analyzing the ramp metering problem independently of the control policy applied. Algorithms are developed to compute these sets, with special attention to their practical interpretations. Numerical examples with graphical representation of the proposed methodology are given to examine local ramp metering and conclude implications to control strategies. Copyright © 2015 John Wiley & Sons, Ltd.

Safety preserving control synthesis for sampled data systems

In sampled data systems the controller receives periodically sampled state feedback about the evolution of a continuous time plant, and must choose a constant control signal to apply between these updates; however, unlike purely discrete time models the evolution of the plant between updates is important. In this paper we describe an abstract algorithm for approximating the discriminating kernel (also known as the maximal robust control invariant set) for a sampled data system with continuous state space, and then use this operator to construct a switched, set-valued feedback control policy which ensures safety. We show that the approximation is conservative for sampled data systems. We then demonstrate that the key operations–the tensor products of two sets, invariance kernels, and a pair of projections–can be implemented in two formulations: one based on the Hamilton–Jacobi partial differential equation which can handle nonlinear dynamics but which scales poorly with state space dimension, and one based on ellipsoids which scales well with state space dimension but which is restricted to linear dynamics. Each version of the algorithm is demonstrated numerically on a simple example.