Zonotopic set-membership estimation for interval dynamic systems

Abstract

This paper presents an improved method for guaranteed state estimation of discrete-time linear-time varying systems affected by disturbances, noises and structured uncertainties modeled as interval uncertainties. Under the hypothesis that the disturbances and the noises are bounded, a zonotopic outer approximation of the state estimation domain is computed offering good performance and low complexity compared to the existing methods. The size of this zonotope is decreased by solving an off-line optimization problem. The advantages of the proposed approach are illustrated via a numerical example.

On robust interval observer design for uncertain systems subject to both time-invariant and time-varying uncertainties

“…Consequently, this approach overcomes the wrapping effect and preserves the uncertain parameter time dependency, but in the case of the trajectory function, the problem of the interval function range evaluation still remains. On the other hand, set-based interval observer approaches present a lower computational complexity than trajectory-based interval observer approaches and, consequently, they seem to be more suitable for real-time applications (Kolev & Petrakieva, 2005;Le et al, 2012).…”

Ellipsoidal Set-Membership State Estimation for Multi-Output Systems with Interval Uncertainties

“…Several domain representations are used to bound the set of all possible states of the system consistent with the measurements and perturbations, such as polytopes [10], parallelotopes [7], zonotopes [11], [12], [13], [14], [15], [16] and ellipsoids [17], [18], [19], [20]. Ellipsoidal estimation has increased the attention among researchers in the last decades.…”

Improved set-membership guaranteed state estimation for uncertain non-linear systems

“…As in the previous method, the time-varying nature of parameters is taken into account in a non-conservative way by a zonotope (Chai et al, 2011). A zonotope size criterion called the P-radius is used for state estimation of a linear discrete-time varying system (Le et al, 2012). An improved approach for guaranteed state estimation combining set-membership estimation techniques based on zonotopes and ellipsoids is proposed, applied to linear discrete-time systems with unknown but bounded perturbations and noises.…”