State estimation in the presence of bounded disturbances

Ellipsoidal set based robust particle filtering for recursive Bayesian state estimation

“…Choice of ρ depends on the minimization criterion for the resultant ellipsoid E i [5], [9]. Figure 2 illustrates the ellipsoid intersection.…”

“…In most cases, Ψ s is not an ellipsoid; its outer bounding ellipsoid is denoted as where α ∈ (0, 1) is a scalar parameter depending on the optimality criterion for the resultant ellipsoid E s [8], [9]. Figure 1 shows the geometric description of the vector sum of two ellipsoids.…”

Adaptive robust tracking for uncertain system

“…coefficient ω is selected based on Lemma 2 in [3]. One advantage of using the procedure in [3] is to ensure the stability of estimation error, as evidenced from the convergence results in [3] for sufficiently large t.…”

“…Besides the two methods mentioned above, an alternative procedure is suggested recently in [3] to computeP t andp t as follows:…”

“…While the size of the uncertainty set can be reduced by utilizing the information observed from the control process, such an updating may further improve the overall performance of the robust control law, especially reducing the conservativeness induced by the robust control. On the other hand, the theory of set membership-based estimation has been well developed during the past 35 years, see, for example, [6] [9] [19] [12] [3] and these techniques provide us a systematic way to deal with the estimation problem with bounded uncertainties. Several studies in the literature have attempted to integrate set-membership estimation with model predictive control in designing controllers for complicated systems [21][4] [8].…”