19,303 research outputs found
Robust filtering for bilinear uncertain stochastic discrete-time systems
Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper deals with the robust filtering problem for uncertain bilinear stochastic discrete-time systems with estimation error variance constraints. The uncertainties are allowed to be norm-bounded and enter into both the state and measurement matrices. We focus on the design of linear filters, such that for all admissible parameter uncertainties, the error state of the bilinear stochastic system is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prespecified value. It is shown that the design of the robust filters can be carried out by solving some algebraic quadratic matrix inequalities. In particular, we establish both the existence conditions and the explicit expression of desired robust filters. A numerical example is included to show the applicability of the present method
Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems
Learning-based control algorithms require data collection with abundant
supervision for training. Safe exploration algorithms ensure the safety of this
data collection process even when only partial knowledge is available. We
present a new approach for optimal motion planning with safe exploration that
integrates chance-constrained stochastic optimal control with dynamics learning
and feedback control. We derive an iterative convex optimization algorithm that
solves an \underline{Info}rmation-cost \underline{S}tochastic
\underline{N}onlinear \underline{O}ptimal \underline{C}ontrol problem
(Info-SNOC). The optimization objective encodes both optimal performance and
exploration for learning, and the safety is incorporated as distributionally
robust chance constraints. The dynamics are predicted from a robust regression
model that is learned from data. The Info-SNOC algorithm is used to compute a
sub-optimal pool of safe motion plans that aid in exploration for learning
unknown residual dynamics under safety constraints. A stable feedback
controller is used to execute the motion plan and collect data for model
learning. We prove the safety of rollout from our exploration method and
reduction in uncertainty over epochs, thereby guaranteeing the consistency of
our learning method. We validate the effectiveness of Info-SNOC by designing
and implementing a pool of safe trajectories for a planar robot. We demonstrate
that our approach has higher success rate in ensuring safety when compared to a
deterministic trajectory optimization approach.Comment: Submitted to RA-L 2020, review-
Robust Linear Precoder Design for Multi-cell Downlink Transmission
Coordinated information processing by the base stations of multi-cell
wireless networks enhances the overall quality of communication in the network.
Such coordinations for optimizing any desired network-wide quality of service
(QoS) necessitate the base stations to acquire and share some channel state
information (CSI). With perfect knowledge of channel states, the base stations
can adjust their transmissions for achieving a network-wise QoS optimality. In
practice, however, the CSI can be obtained only imperfectly. As a result, due
to the uncertainties involved, the network is not guaranteed to benefit from a
globally optimal QoS. Nevertheless, if the channel estimation perturbations are
confined within bounded regions, the QoS measure will also lie within a bounded
region. Therefore, by exploiting the notion of robustness in the worst-case
sense some worst-case QoS guarantees for the network can be asserted. We adopt
a popular model for noisy channel estimates that assumes that estimation noise
terms lie within known hyper-spheres. We aim to design linear transceivers that
optimize a worst-case QoS measure in downlink transmissions. In particular, we
focus on maximizing the worst-case weighted sum-rate of the network and the
minimum worst-case rate of the network. For obtaining such transceiver designs,
we offer several centralized (fully cooperative) and distributed (limited
cooperation) algorithms which entail different levels of complexity and
information exchange among the base stations.Comment: 38 Pages, 7 Figures, To appear in the IEEE Transactions on Signal
Processin
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Mixed H2/H∞ filtering for uncertain systems with regional pole assignment
Copyright [2005] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.The mixed H2/H∞ filtering problem for uncertain linear continuous-time systems with regional pole assignment is considered. The purpose of the problem is to design an uncertainty-independent filter such that, for all admissible parameter uncertainties, the following filtering requirements are simultaneously satisfied: 1) the filtering process is asymptotically stable; 2) the poles of the filtering matrix are located inside a prescribed region that compasses the vertical strips, horizontal strips, disks, or conic sectors; 3) both the H2 norm and the H∞ norm on the respective transfer functions are not more than the specified upper bound constraints. We establish a general framework to solve the addressed multiobjective filtering problem completely. In particular, we derive necessary and sufficient conditions for the solvability of the problem in terms of a set of feasible linear matrix inequalities (LMIs). An illustrative example is given to illustrate the design procedures and performances of the proposed method
Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation
Copyright [2001] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.We investigate the robust filter design problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, unknown state time-delay, parameter uncertainties, and unknown nonlinear disturbances, which are all often encountered in practice and the sources of instability. The aim of this problem is to design a linear, delayless, uncertainty-independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the existence of desired robust exponential filters, which are derived in terms of the solutions to algebraic Riccati inequalities. The developed theory is illustrated by numerical simulatio
Output Filter Aware Optimization of the Noise Shaping Properties of {\Delta}{\Sigma} Modulators via Semi-Definite Programming
The Noise Transfer Function (NTF) of {\Delta}{\Sigma} modulators is typically
designed after the features of the input signal. We suggest that in many
applications, and notably those involving D/D and D/A conversion or actuation,
the NTF should instead be shaped after the properties of the
output/reconstruction filter. To this aim, we propose a framework for optimal
design based on the Kalman-Yakubovich-Popov (KYP) lemma and semi-definite
programming. Some examples illustrate how in practical cases the proposed
strategy can outperform more standard approaches.Comment: 14 pages, 18 figures, journal. Code accompanying the paper is
available at http://pydsm.googlecode.co
Optimal and Robust Transmit Designs for MISO Channel Secrecy by Semidefinite Programming
In recent years there has been growing interest in study of multi-antenna
transmit designs for providing secure communication over the physical layer.
This paper considers the scenario of an intended multi-input single-output
channel overheard by multiple multi-antenna eavesdroppers. Specifically, we
address the transmit covariance optimization for secrecy-rate maximization
(SRM) of that scenario. The challenge of this problem is that it is a nonconvex
optimization problem. This paper shows that the SRM problem can actually be
solved in a convex and tractable fashion, by recasting the SRM problem as a
semidefinite program (SDP). The SRM problem we solve is under the premise of
perfect channel state information (CSI). This paper also deals with the
imperfect CSI case. We consider a worst-case robust SRM formulation under
spherical CSI uncertainties, and we develop an optimal solution to it, again
via SDP. Moreover, our analysis reveals that transmit beamforming is generally
the optimal transmit strategy for SRM of the considered scenario, for both the
perfect and imperfect CSI cases. Simulation results are provided to illustrate
the secrecy-rate performance gains of the proposed SDP solutions compared to
some suboptimal transmit designs.Comment: 32 pages, 5 figures; to appear, IEEE Transactions on Signal
Processing, 201
Simple Approximations of Semialgebraic Sets and their Applications to Control
Many uncertainty sets encountered in control systems analysis and design can
be expressed in terms of semialgebraic sets, that is as the intersection of
sets described by means of polynomial inequalities. Important examples are for
instance the solution set of linear matrix inequalities or the Schur/Hurwitz
stability domains. These sets often have very complicated shapes (non-convex,
and even non-connected), which renders very difficult their manipulation. It is
therefore of considerable importance to find simple-enough approximations of
these sets, able to capture their main characteristics while maintaining a low
level of complexity. For these reasons, in the past years several convex
approximations, based for instance on hyperrect-angles, polytopes, or
ellipsoids have been proposed. In this work, we move a step further, and
propose possibly non-convex approximations , based on a small volume polynomial
superlevel set of a single positive polynomial of given degree. We show how
these sets can be easily approximated by minimizing the L1 norm of the
polynomial over the semialgebraic set, subject to positivity constraints.
Intuitively, this corresponds to the trace minimization heuristic commonly
encounter in minimum volume ellipsoid problems. From a computational viewpoint,
we design a hierarchy of linear matrix inequality problems to generate these
approximations, and we provide theoretically rigorous convergence results, in
the sense that the hierarchy of outer approximations converges in volume (or,
equivalently, almost everywhere and almost uniformly) to the original set. Two
main applications of the proposed approach are considered. The first one aims
at reconstruction/approximation of sets from a finite number of samples. In the
second one, we show how the concept of polynomial superlevel set can be used to
generate samples uniformly distributed on a given semialgebraic set. The
efficiency of the proposed approach is demonstrated by different numerical
examples
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