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  • 1
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    Interval Predictor Models with a Formal Characterization of Uncertainty and Reliability (2014)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: This paper develops techniques for constructing empirical predictor models based on observations. By contrast to standard models, which yield a single predicted output at each value of the model's inputs, Interval Predictors Models (IPM) yield an interval into which the unobserved output is predicted to fall. The IPMs proposed prescribe the output as an interval valued function of the model's inputs, render a formal description of both the uncertainty in the model's parameters and of the spread in the predicted output. Uncertainty is prescribed as a hyper-rectangular set in the space of model's parameters. The propagation of this set through the empirical model yields a range of outputs of minimal spread containing all (or, depending on the formulation, most) of the observations. Optimization-based strategies for calculating IPMs and eliminating the effects of outliers are proposed. Outliers are identified by evaluating the extent by which they degrade the tightness of the prediction. This evaluation can be carried out while the IPM is calculated. When the data satisfies mild stochastic assumptions, and the optimization program used for calculating the IPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the model's reliability (that is, the probability that a future observation would be within the predicted range of outputs) can be bounded rigorously by a non-asymptotic formula.
    Keywords: Statistics and Probability
    Type: NF1676L-18492 , IEEE Conference on Decision and Control; Dec 15, 2014 - Dec 17, 2014; Los Angeles, CA; United States
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  • 2
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    Uncertainty Quantification for Polynomial Systems via Bernstein Expansions (2012)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: This paper presents a unifying framework to uncertainty quantification for systems having polynomial response metrics that depend on both aleatory and epistemic uncertainties. The approach proposed, which is based on the Bernstein expansions of polynomials, enables bounding the range of moments and failure probabilities of response metrics as well as finding supersets of the extreme epistemic realizations where the limits of such ranges occur. These bounds and supersets, whose analytical structure renders them free of approximation error, can be made arbitrarily tight with additional computational effort. Furthermore, this framework enables determining the importance of particular uncertain parameters according to the extent to which they affect the first two moments of response metrics and failure probabilities. This analysis enables determining the parameters that should be considered uncertain as well as those that can be assumed to be constants without incurring significant error. The analytical nature of the approach eliminates the numerical error that characterizes the sampling-based techniques commonly used to propagate aleatory uncertainties as well as the possibility of under predicting the range of the statistic of interest that may result from searching for the best- and worstcase epistemic values via nonlinear optimization or sampling.
    Keywords: Numerical Analysis
    Type: AIAA Paper 2012-1851 , NF1676L-13334 , 13th AIAA Gossamer Systems Forum; Apr 03, 2012 - Apr 26, 2012; Honolulu, HI; United States|53rd Structures, Structural Dynamics, and Materials Conference (SDM); Apr 23, 2012 - Apr 26, 2012; Honolulu, HI; United States|20th AIAA/ASME/AHS Adaptive Structures Conference; Apr 23, 2012 - Apr 26, 2012; Honolulu, HI; United States|14th AIAA Non-Deterministic Approaches Conference; Apr 23, 2012 - Apr 26, 2012; Honolulu, HI; United States
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  • 3
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    Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares (2012)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.
    Keywords: Mathematical and Computer Sciences (General)
    Type: AIAA Paper 2012-1431 , NF1676L-13308 , 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference; Apr 23, 2012 - Apr 26, 2012; Honolulu, HI; United States
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  • 4
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    Robust Control Design for Uncertain Nonlinear Dynamic Systems (2012)
    In:  CASI
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    Publication Date: 2019-07-13
    Description: Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.
    Keywords: Mechanical Engineering
    Type: NF1676L-12813 , IMAC 30th - A Conference and Exposition on Structural Dynamics; Jan 30, 2012; Jacksonville, FL; United States
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  • 5
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    Uncertainty Analysis via Failure Domain Characterization: Polynomial Requirement Functions (2011)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: This paper proposes an uncertainty analysis framework based on the characterization of the uncertain parameter space. This characterization enables the identification of worst-case uncertainty combinations and the approximation of the failure and safe domains with a high level of accuracy. Because these approximations are comprised of subsets of readily computable probability, they enable the calculation of arbitrarily tight upper and lower bounds to the failure probability. A Bernstein expansion approach is used to size hyper-rectangular subsets while a sum of squares programming approach is used to size quasi-ellipsoidal subsets. These methods are applicable to requirement functions whose functional dependency on the uncertainty is a known polynomial. Some of the most prominent features of the methodology are the substantial desensitization of the calculations from the uncertainty model assumed (i.e., the probability distribution describing the uncertainty) as well as the accommodation for changes in such a model with a practically insignificant amount of computational effort.
    Keywords: Mathematical and Computer Sciences (General)
    Type: NF1676L-12499 , ESREL 2011 Annual Conference; Sep 18, 2011 - Sep 22, 2011; Troyes; France
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  • 6
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    Adaptive Control Allocation in the Presence of Actuator Failures (2010)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: In this paper, a novel adaptive control allocation framework is proposed. In the adaptive control allocation structure, cooperative actuators are grouped and treated as an equivalent control effector. A state feedback adaptive control signal is designed for the equivalent effector and allocated to the member actuators adaptively. Two adaptive control allocation algorithms are proposed, which guarantee closed-loop stability and asymptotic state tracking in the presence of uncertain loss of effectiveness and constant-magnitude actuator failures. The proposed algorithms can be shown to reduce the controller complexity with proper grouping of the actuators. The proposed adaptive control allocation schemes are applied to two linearized aircraft models, and the simulation results demonstrate the performance of the proposed algorithms.
    Keywords: Aircraft Stability and Control
    Type: AIAA Paper 2010-7772 , NF1676L-11094 , AIAA Guidance, Navigation and Control Conference; Aug 02, 2010 - Aug 05, 2010; Toronto; Canada
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  • 7
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    Bounding the Failure Probability Range of Polynomial Systems Subject to P-box Uncertainties (2012)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: This paper proposes a reliability analysis framework for systems subject to multiple design requirements that depend polynomially on the uncertainty. Uncertainty is prescribed by probability boxes, also known as p-boxes, whose distribution functions have free or fixed functional forms. An approach based on the Bernstein expansion of polynomials and optimization is proposed. In particular, we search for the elements of a multi-dimensional p-box that minimize (i.e., the best-case) and maximize (i.e., the worst-case) the probability of inner and outer bounding sets of the failure domain. This technique yields intervals that bound the range of failure probabilities. The offset between this bounding interval and the actual failure probability range can be made arbitrarily tight with additional computational effort.
    Keywords: Statistics and Probability
    Type: NF1676L-14093 , ESREL 2012 - Annual European Safety and Reliability Conference; Jun 25, 2012 - Jun 29, 2012; Helsinki; Finland
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  • 8
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    Uncertainty Analysis via Failure Domain Characterization: Unrestricted Requirement Functions (2011)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: This paper proposes an uncertainty analysis framework based on the characterization of the uncertain parameter space. This characterization enables the identification of worst-case uncertainty combinations and the approximation of the failure and safe domains with a high level of accuracy. Because these approximations are comprised of subsets of readily computable probability, they enable the calculation of arbitrarily tight upper and lower bounds to the failure probability. The methods developed herein, which are based on nonlinear constrained optimization, are applicable to requirement functions whose functional dependency on the uncertainty is arbitrary and whose explicit form may even be unknown. Some of the most prominent features of the methodology are the substantial desensitization of the calculations from the assumed uncertainty model (i.e., the probability distribution describing the uncertainty) as well as the accommodation for changes in such a model with a practically insignificant amount of computational effort.
    Keywords: Mathematical and Computer Sciences (General)
    Type: NF1676L-12489 , ESREL 2011 Annual Conference; Sep 18, 2011 - Sep 22, 2011; Troyes; France
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  • 9
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    UQTools: The Uncertainty Quantification Toolbox - Introduction and Tutorial (2012)
    In:  CASI
    Details
    Publication Date: 2019-07-12
    Description: UQTools is the short name for the Uncertainty Quantification Toolbox, a software package designed to efficiently quantify the impact of parametric uncertainty on engineering systems. UQTools is a MATLAB-based software package and was designed to be discipline independent, employing very generic representations of the system models and uncertainty. Specifically, UQTools accepts linear and nonlinear system models and permits arbitrary functional dependencies between the system s measures of interest and the probabilistic or non-probabilistic parametric uncertainty. One of the most significant features incorporated into UQTools is the theoretical development centered on homothetic deformations and their application to set bounding and approximating failure probabilities. Beyond the set bounding technique, UQTools provides a wide range of probabilistic and uncertainty-based tools to solve key problems in science and engineering.
    Keywords: Aircraft Stability and Control
    Type: NASA/TM-2012-217561 , L-20130 , NF1676L-14349
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  • 10
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    Stochastic Optimal Control via Bellman's Principle (2003)
    In:  CASI
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    Publication Date: 2019-07-10
    Description: This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.
    Keywords: Numerical Analysis
    Type: NASA/CR-2003-212419 , NIA Report No. 2003-04 , NAS 1.26:212419
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