Low‐complexity ISS state estimation approach with bounded disturbances

Abstract

This paper presents a low-complexity input-to-state stable ellipsoidal outer-bounding state estimation approach with unknown but bounded disturbances. The bounds on the noise are specified by ellipsoids. The feasible set is updated through computing the Minkowski sum and intersection of two ellipsoids. At the observation stage, the observation noise bounding ellipsoid is replaced by a parallelotope containing it. Then, each observation update is transformed into multiple consecutive iterations to intersect ellipsoid with strips, which significantly reduces its per-update computational complexity.Furthermore, an adaptive selection scheme of the parameters is derived to ensure the stability of the estimation error. As a result, the proposed approach entails stability and delivers a trade-off between performance and complexity.

Input‐to‐state learning of recurrent neural networks with delay and disturbance

“…This fact has prompted the progress of control over the last several decades, 16‐21 which has been known to possess the advantages of high robustness and low sensitivity to disturbance statistics 22 . Moreover, in view of the fact that the existing disturbance is bounded in most cases, 23 the input‐to‐state stability (ISS), which was first introduced into a nonlinear control system by Sontag, 24 has been extensively accepted as a crucial concept in control engineering and its various extensions have been explored for nonlinear control systems, such as integral ISS, 25 stochastic ISS, 26 exponential ISS, 27 and so forth. In the context of NNs, Bonassi et al 28 proposed a criterion regarding the ISS of long‐short term memory NNs.…”

Bounded-error constrained state estimation in presence of sporadic measurements

“…Remark 3.1 It is worth noting that the volume minimization problem arg min µi det † (Q ki ) has an explicit solution here. If the unknown input vector was bounded by an ellipsoid, as was the case in [11,13,15,22], rather than by an interval-like set, such as a zonotope, µ vol ki would be the unique positive root of an n−order polynomial. Nevertheless, considering that the pseudo-inverse of a n × n matrix is needed at each time step k, in line with (11i), the trace minimization is more appealing, at least from the computational point of view.…”

“…Consequently, in contrast with all the algorithms in the literature, [11,12,13,14], that minimize the size of the ellipsoid Ȇ(β) and where the stability issue was not addressed, the optimal value of β chosen here is the one for which the input-to-state stability of the estimation algorithm to be derived, could be fulfilled, by minimizing some quadratic measure of the estimation error vector 4 in the worst noise case, embodied by ς, in the manner of [15,22], inspired by [27,35,36]. (24b) and its minimum is achieved at…”

Centralized Fusion Methods for Multi-Sensor System With Bounded Disturbances

“…Apparently, the probability-based fusion algorithms have been widely applied, and have excellent fusion estimation results under certain conditions. However, accurate statistical knowledge of process and measurement noise should be known for most probability-based algorithms and such idealized assumptions are difficult to satisfy in certain practical situations, and this may lead to poor performance for the state estimation [16], [17]. But in many engineering applications, it is easier to obtain the bounds of unknown noises.…”