Zonotopic guaranteed state estimation for uncertain systems

Abstract

International audienceThis paper presents a new approach for guaranteed state estimation based on zonotopes for linear discrete-time multivariable systems with interval multiplicative uncertainties, in the presence of bounded state perturbations and noises. At each sample time, the presented approach computes a zonotope which contains the real system state. A P-radius-based criterion is minimized in order to decrease the size of the zonotope at each sample time and to obtain an increasingly accurate state estimation. The proposed approach allows one to efficiently handle the trade-off between the complexity of the computation and the accuracy of the estimation. An illustrative example is analyzed in order to highlight the advantages of the proposed state estimation technique

On enlarging backward reachable sets via Zonotopic set membership

“…In addition, the second inequality of (26) enables that the backward reachable set Ψ(k, T ) is contained in an ellipsoid x(k)…”

“…Another explanation of (2) is that a zonotope Z(c, G) is an affine image of a unit cube {ζ ∈ R m : ζ ∞ ≤ 1} under a linear mapping G using l ∞ norm, just as an ellipsoid E = {x ∈ R n : x = c + Rζ, ζ 2 ≤ 1} is an affine image of a unit ball {ζ ∈ R m : ζ 2 ≤ 1} under a linear mapping R using the l 2 norm. Note that for a single ellipsoidal representation, the complexity is fixed for a selected n, while the complexity of representations using convex polytopes and zonotopes can be arbitrarily high [26]. In other words, by using polytopes and zonotopes, an increasing accurate representation can be obtained according to a higher userdefined complexity.…”

Set-membership approach and Kalman observer based on zonotopes for discrete-time descriptor systems

“…To reduce the size of the intersection zonotope, the F W -radius [6] and W -radius [15] criteria are considered. The F W -radius criterion is used through the Kalman filtering procedure while the W -radius criterion is taken into account via an optimization problem including linear matrix inequalities (LMIs).…”

Zonotopic fault detection observer with H<inf>−</inf> performance

“…According to [26], the size of the zonotope (10) is measured by the P -radius of the zonotope. There exists a symmetric and positive definite matrix P = P T 0 such that the the P -radius of the zonotope (10) is defined as…”