Minimum sensitivity analysis for accurate open-loop controllers in linear systems using weighted gramians

2017 ◽  
Author(s):  
Nak-seung Patrick Hyun ◽  
Vishal Murali ◽  
Erik I. Verriest
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Open Loop ◽  
Minimum Sensitivity ◽  
Open Loop Controllers

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Stability, performance and sensitivity analysis of I.I.D. jump linear systems

2017 ◽  
Vol 91 (6) ◽  
pp. 1460-1472
Author(s):  
Jorge R. Chávez Fuentes ◽  
Oscar R. González ◽  
W. Steven Gray
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Jump Linear Systems ◽  
Stability Performance

FIRST HARMONIC ANALYSIS OF PLANAR LINEAR SYSTEMS WITH SINGLE SATURATED FEEDBACK

1996 ◽  
Vol 06 (12b) ◽  
pp. 2605-2610 ◽  
Author(s):  
RODOLFO SUÁREZ ◽  
JOSÉ ALVAREZ-RAMIREZ ◽  
BALTAZAR AGUIRRE
Keyword(s):  
Linear Systems ◽  
Periodic Orbits ◽  
Function Method ◽  
Open Loop ◽  
Control Parameters ◽  
Describing Function ◽  
Open Loop System ◽  
Unstable Eigenvalue ◽  
Unstable Equilibrium Point ◽  
Describing Function Method

A first harmonic approach (describing function method) is used here to analyze the dependence of periodic orbits on the control parameters of planar linear systems with single saturated feedback. It is shown that, if the open-loop system has at least one unstable eigenvalue, periodic orbits converge monotonically to an unstable equilibrium point as the control gains go to infinity.

scholarly journals The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (nth-CASAM-L): II. Illustrative Application

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8315
Author(s):  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Closed Form ◽  
Linear Systems ◽  
Predictive Modeling ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Third Order ◽  
Analysis Methodology ◽  
Illustrative Application

This work illustrates the application of the nth-order comprehensive adjoint sensitivity analysis methodology for response-coupled forward/adjoint linear systems (abbreviated as “nth-CASAM-L”) to a paradigm model that describes the transmission of particles (neutrons and/or photons) through homogenized materials, as encountered in radiation protection and shielding. The first-, second-, and third-order sensitivities of responses that depend on both the forward and adjoint particle fluxes are obtained exactly, in closed-form, underscoring the principles and methodology underlying the nth-CASAM-L. The results presented in this work underscore the fundamentally important role of the nth-CASAM-L in the quest to overcome the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling.

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