35,858 research outputs found
Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties
This paper presents a robust adaptive control solution for linear
parameter-varying (LPV) systems with unknown input gain and unmatched nonlinear
(state- and time-dependent) uncertainties based on the adaptive
control architecture and peak-to-peak gain (PPG) analysis/minimization from
robust control. Specifically, we introduce new tools for stability and
performance analysis leveraging the PPG bound of an LPV system that is
computable using linear matrix inequality (LMI) techniques. A
piecewise-constant estimation law is introduced to estimate the lumped
uncertainty with quantifiable error bounds, which can be systematically
improved by reducing the estimation sampling time. We also present a new
approach to attenuate the unmatched uncertainty based on the PPG minimization
that is applicable to a broad class of systems with linear nominal dynamics. In
addition, we derive transient and steady-state performance bounds in terms of
the input and output signals of the actual closed-loop system as compared to
the same signals of a virtual reference system that represents the possibly
best achievable performance. Under mild assumptions, we prove that the
transient performance bounds can be uniformly reduced by decreasing the
estimation sampling time, which is subject only to hardware limitations. The
theoretical development is validated by extensive simulations on the
short-period dynamics of an F-16 aircraft
A unified framework for solving a general class of conditional and robust set-membership estimation problems
In this paper we present a unified framework for solving a general class of
problems arising in the context of set-membership estimation/identification
theory. More precisely, the paper aims at providing an original approach for
the computation of optimal conditional and robust projection estimates in a
nonlinear estimation setting where the operator relating the data and the
parameter to be estimated is assumed to be a generic multivariate polynomial
function and the uncertainties affecting the data are assumed to belong to
semialgebraic sets. By noticing that the computation of both the conditional
and the robust projection optimal estimators requires the solution to min-max
optimization problems that share the same structure, we propose a unified
two-stage approach based on semidefinite-relaxation techniques for solving such
estimation problems. The key idea of the proposed procedure is to recognize
that the optimal functional of the inner optimization problems can be
approximated to any desired precision by a multivariate polynomial function by
suitably exploiting recently proposed results in the field of parametric
optimization. Two simulation examples are reported to show the effectiveness of
the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic
Control (2014
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An LFT/SDP approach to the uncertainty analysis for state
A state estimator is an algorithm that computes the current state of a time-varying system from on-line measurements. Physical quantities such as measurements and parameters are characterised by uncertainty. Understanding how uncertainty affects the accuracy of state estimates is therefore a pre-requisite to the application of such techniques to real systems. In this paper we develop a method of uncertainty analysis based on linear fractional transformations (LFT) and obtain ellipsoid-of-confidence bounds by recasting the LFT problem into a semidefinite programming problem (SDP). The ideas are illustrated by applying them to a simple water distribution network
Robust Region-of-Attraction Estimation
We propose a method to compute invariant subsets of the region-of-attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty. Parameter-independent Lyapunov functions are used to characterize invariant subsets of the robust region-of-attraction. A branch-and-bound type refinement procedure reduces the conservatism. We demonstrate the method on an example from the literature and uncertain controlled short-period aircraft dynamics
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
Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version)
A new framework is developed for control of constrained nonlinear systems
with structured parametric uncertainties. Forward invariance of a safe set is
achieved through online parameter adaptation and data-driven model estimation.
The new adaptive data-driven safety paradigm is merged with a recent adaptive
control algorithm for systems nominally contracting in closed-loop. This
unification is more general than other safety controllers as closed-loop
contraction does not require the system be invertible or in a particular form.
Additionally, the approach is less expensive than nonlinear model predictive
control as it does not require a full desired trajectory, but rather only a
desired terminal state. The approach is illustrated on the pitch dynamics of an
aircraft with uncertain nonlinear aerodynamics.Comment: Added aCBF non-Lipschitz example and discussion on approach
implementatio
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Uncertainty modelling in power system state estimation
A method for uncertainty analysis in power system state estimation is proposed. The two-step method uses static weighted least-squares analysis to compute 'point' state estimates. Linear programming is then employed to obtain the upper and lower bounds of the uncertainty interval. It is shown that the method can provide useful additional information for both metered and nonmetered elements of the system. The effects of network parameter errors are also studied. For illustrative purposed, the proposed method is tested using the six-bus and IEEE 30-bus standard systems. Results show that the proposed method is an accurate and reliable tool for estimating the uncertainty bounds in power system state estimation
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