Journal ArticleDOI
Robust filtering for discrete-time systems with bounded noise and parametric uncertainty
TLDR
The main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using interior-point methods for convex optimization.Abstract:
This note presents a new approach to finite-horizon guaranteed state prediction for discrete-time systems affected by bounded noise and unknown-but-bounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the state-space matrices on the uncertain parameters. The main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using interior-point methods for convex optimization. With n states, l uncertain parameters appearing linearly in the state-space matrices, with rank-one matrix coefficients, the worst-case complexity grows as O(l(n + l)/sup 3.5/) With unstructured uncertainty in all system matrices, the worst-case complexity reduces to O(n/sup 3.5/).read more
Citations
More filters
Journal ArticleDOI
Uncertain convex programs: randomized solutions and confidence levels
TL;DR: This paper considers an alternative ‘randomized’ or ‘scenario’ approach for dealing with uncertainty in optimization, based on constraint sampling, and studies the constrained optimization problem resulting by taking into account only a finite set of N constraints, chosen at random among the possible constraint instances of the uncertain problem.
Journal ArticleDOI
The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs
Marco C. Campi,Simone Garatti +1 more
TL;DR: It is proven that the feasibility of the randomized solutions for all other convex programs can be bounded based on the feasibility for the prototype class of fully-supported problems, which means that all fully- supported problems share the same feasibility properties.
Journal ArticleDOI
Brief Guaranteed state estimation by zonotopes
TL;DR: This paper presents a new approach to guaranteed state estimation for non-linear discrete-time systems with a bounded description of noise and parameters with an algorithm to compute a set that contains the states consistent with the measured output and the given Noise and parameters.
Journal ArticleDOI
A Dynamic Event-Triggered Transmission Scheme for Distributed Set-Membership Estimation Over Wireless Sensor Networks
TL;DR: The proposed dynamic ETS is applied to address the distributed set-membership estimation problem for a discrete-time linear time-varying system with a nonlinearity satisfying a sector constraint.
Journal ArticleDOI
Selected topics in robust convex optimization
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: This paper overviews several selected topics in this popular area, specifically, recent extensions of the basic concept of robust counterpart of an optimization problem with uncertain data, tractability of robust counterparts, links between RO and traditional chance constrained settings of problems with stochastic data, and a novel generic application of the RO methodology in Robust Linear Control.
References
More filters
Book
Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Journal Article
Optimal Filtering
TL;DR: This book helps to fill the void in the market and does that in a superb manner by covering the standard topics such as Kalman filtering, innovations processes, smoothing, and adaptive and nonlinear estimation.
Journal ArticleDOI
Semidefinite programming
Lieven Vandenberghe,Stephen Boyd +1 more
TL;DR: A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given.