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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Comparison of organ-at-risk sparing and plan robustness for spot-scanning proton therapy and volumetric modulated arc photon therapy in head-and-neck cancer

Purpose: Proton radiotherapy for head-and-neck cancer (HNC) aims to improve organ-at-risk (OAR) sparing over photon radiotherapy. However, it may be less robust for setup and range uncertainties. The authors investigated OAR sparing and plan robustness for spot-scanning proton planning techniques and compared these with volumetric modulated arc therapy (VMAT) photon plans. Methods: Ten HNC patients were replanned using two arc VMAT (RapidArc) and spot-scanning proton techniques. OARs to be spared included the contra- and ipsilateral parotid and submandibular glands and individual swallowing muscles. Proton plans were made using Multifield Optimization (MFO, using three, five, and seven fields) and Single-field Optimization (SFO, using three fields). OAR sparing was evaluated using mean dose to composite salivary glands (Comp{sub Sal}) and composite swallowing muscles (Comp{sub Swal}). Plan robustness was determined for setup and range uncertainties (±3 mm for setup, ±3% HU) evaluating V95% and V107% for clinical target volumes. Results: Averaged over all patients Comp{sub Sal}/Comp{sub Swal} mean doses were lower for the three-field MFO plans (14.6/16.4 Gy) compared to the three-field SFO plans (20.0/23.7 Gy) and VMAT plans (23.0/25.3 Gy). Using more than three fields resulted in differences in OAR sparing of less than 1.5 Gy between plans. SFO plans were significantly more robust than MFO plans. VMAT plans were the most robust. Conclusions: MFO plans had improved OAR sparing but were less robust than SFO and VMAT plans, while SFO plans were more robust than MFO plans but resulted in less OAR sparing. Robustness of the MFO plans did not increase with more fields.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-187: Quantifying Normal Tissue Sparing with 4D Robust Optimization of Intensity Modulated Proton Therapy

Purpose: To report an approach to quantify the normal tissue sparing for 4D robustly-optimized versus PTV-optimized IMPT plans. Methods: We generated two sets of 90 DVHs from a patient’s 10-phase 4D CT set; one by conventional PTV-based optimization done in the Eclipse treatment planning system, and the other by an in-house robust optimization algorithm. The 90 DVHs were created for the following scenarios in each of the ten phases of the 4DCT: ± 5mm shift along x, y, z; ± 3.5% range uncertainty and a nominal scenario. A Matlab function written by Gay and Niemierko was modified to calculate EUD for each DVH for the following structures: esophagus, heart, ipsilateral lung and spinal cord. An F-test determined whether or not the variances of each structure’s DVHs were statistically different. Then a t-test determined if the average EUDs for each optimization algorithm were statistically significantly different. Results: T-test results showed each structure had a statistically significant difference in average EUD when comparing robust optimization versus PTV-based optimization. Under robust optimization all structures except the spinal cord received lower EUDs than PTV-based optimization. Using robust optimization the average EUDs decreased 1.45% for the esophagus, 1.54% for the heart and 5.45% for the ipsilateral lung. The average EUD to the spinal cord increased 24.86% but was still well below tolerance. Conclusion: This work has helped quantify a qualitative relationship noted earlier in our work: that robust optimization leads to plans with greater normal tissue sparing compared to PTV-based optimization. Except in the case of the spinal cord all structures received a lower EUD under robust optimization and these results are statistically significant. While the average EUD to the spinal cord increased to 25.06 Gy under robust optimization it is still well under the TD50 value of 66.5 Gy from Emami et al. Supported in part by the NCI U19 CA021239.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1989

Application of stochastic robustness to aircraft control systems

Stochastic robustness, a simple numerical procedure for estimating the stability robustness of linear, time-invariant systems, is applied to a forward-swept-wing aircraft control system. Based on Monte Carlo evaluation of the system's closed-loop eignevalues, this analysis approach introduces the probability of instability as a scalar stability robustness measure. The related stochastic root locus provides insight into robustness characteristics of the closed-loop system. Three Linear Quadratic controllers of decreasing robustness are chosen to demonstrate the use of stochastic robustness to analyze and compare control designs. Examples are presented illustrating the use of stochastic robustness analysis to address the effects of actuator dynamics and unmodeled dynamics on the stability robustness of the forward-swept-wing aircraft.

Stengel, Robert F.↗
NASA NTRS1993

A comparative study of multivariable robustness analysis methods as applied to integrated flight and propulsion control

Three multivariable robustness analysis methods are compared and contrasted. The focus of the analysis is on system stability and performance robustness to uncertainty in the coupling dynamics between two interacting subsystems. Of particular interest is interacting airframe and engine subsystems, and an example airframe/engine vehicle configuration is utilized in the demonstration of these approaches. The singular value (SV) and structured singular value (SSV) analysis methods are compared to a method especially well suited for analysis of robustness to uncertainties in subsystem interactions. This approach is referred to here as the interacting subsystem (IS) analysis method. This method has been used previously to analyze airframe/engine systems, emphasizing the study of stability robustness. However, performance robustness is also investigated here, and a new measure of allowable uncertainty for acceptable performance robustness is introduced. The IS methodology does not require plant uncertainty models to measure the robustness of the system, and is shown to yield valuable information regarding the effects of subsystem interactions. In contrast, the SV and SSV methods allow for the evaluation of the robustness of the system to particular models of uncertainty, and do not directly indicate how the airframe (engine) subsystem interacts with the engine (airframe) subsystem.

Schierman, John D.↗
NASA NTRS2006

Towards Robust Designs Via Multiple-Objective Optimization Methods

Fabricating and operating complex systems involves dealing with uncertainty in the relevant variables. In the case of aircraft, flow conditions are subject to change during operation. Efficiency and engine noise may be different from the expected values because of manufacturing tolerances and normal wear and tear. Engine components may have a shorter life than expected because of manufacturing tolerances. In spite of the important effect of operating- and manufacturing-uncertainty on the performance and expected life of the component or system, traditional aerodynamic shape optimization has focused on obtaining the best design given a set of deterministic flow conditions. Clearly it is important to both maintain near-optimal performance levels at off-design operating conditions, and, ensure that performance does not degrade appreciably when the component shape differs from the optimal shape due to manufacturing tolerances and normal wear and tear. These requirements naturally lead to the idea of robust optimal design wherein the concept of robustness to various perturbations is built into the design optimization procedure. The basic ideas involved in robust optimal design will be included in this lecture. The imposition of the additional requirement of robustness results in a multiple-objective optimization problem requiring appropriate solution procedures. Typically the costs associated with multiple-objective optimization are substantial. Therefore efficient multiple-objective optimization procedures are crucial to the rapid deployment of the principles of robust design in industry. Hence the companion set of lecture notes (Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks ) deals with methodology for solving multiple-objective Optimization problems efficiently, reliably and with little user intervention. Applications of the methodologies presented in the companion lecture to robust design will be included here. The evolutionary method (DE) is first used to solve a relatively difficult problem in extended surface heat transfer wherein optimal fin geometries are obtained for different safe operating base temperatures. The objective of maximizing the safe operating base temperature range is in direct conflict with the objective of maximizing fin heat transfer. This problem is a good example of achieving robustness in the context of changing operating conditions. The evolutionary method is then used to design a turbine airfoil; the two objectives being reduced sensitivity of the pressure distribution to small changes in the airfoil shape and the maximization of the trailing edge wedge angle with the consequent increase in airfoil thickness and strength. This is a relevant example of achieving robustness to manufacturing tolerances and wear and tear in the presence of other objectives.

Man Mohan, Rai↗
DOE OSTI2013

Stretching the limits of forming processes by robust optimization: A demonstrator

Robust design of forming processes using numerical simulations is gaining attention throughout the industry. In this work, it is demonstrated how robust optimization can assist in further stretching the limits of metal forming processes. A deterministic and a robust optimization study are performed, considering a stretch-drawing process of a hemispherical cup product. For the robust optimization study, both the effect of material and process scatter are taken into account. For quantifying the material scatter, samples of 41 coils of a drawing quality forming steel have been collected. The stochastic material behavior is obtained by a hybrid approach, combining mechanical testing and texture analysis, and efficiently implemented in a metamodel based optimization strategy. The deterministic and robust optimization results are subsequently presented and compared, demonstrating an increased process robustness and decreased number of product rejects by application of the robust optimization approach.

36 MATERIALS SCIENCE↗
DOE OSTI2012

A characterization of robust radiation therapy treatment planning methods-from expected value to worst case optimization

Purpose: To characterize a class of optimization formulations used to handle systematic and random errors in radiation therapy, and to study the differences between the methods within this class. Methods: The class of robust methods that can be formulated as minimax stochastic programs is studied. This class generalizes many previously used methods, ranging between optimization of the expected and the worst case objective value. The robust methods are used to plan intensity-modulated proton therapy (IMPT) treatments for a case subject to systematic setup and range errors, random setup errors with and without uncertain probability distribution, and combinations thereof. As reference, plans resulting from a conventional method that uses a margin to account for errors are shown. Results: For all types of errors, target coverage robustness increased with the conservativeness of the method. For systematic errors, best case organ at risk (OAR) doses increased and worst case doses decreased with the conservativeness. Accounting for random errors of fixed probability distribution resulted in heterogeneous dose. The heterogeneities were reduced when uncertainty in the probability distribution was accounted for. Doing so, the OAR doses decreased with the conservativeness. All robust methods studied resulted in more robust target coverage and lower OAR doses than the conventional method. Conclusions: Accounting for uncertainties is essential to ensure plan quality in complex radiation therapy such as IMPT. The utilization of more information than conventional in the optimization can lead to robust target coverage and low OAR doses. Increased target coverage robustness can be achieved by more conservative methods.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

TH-C-BRD-10: An Evaluation of Three Robust Optimization Approaches in IMPT Treatment Planning

Purpose: Various robust optimization approaches have been proposed to ensure the robustness of intensity modulated proton therapy (IMPT) in the face of uncertainty. In this study, we aim to investigate the performance of three classes of robust optimization approaches regarding plan optimality and robustness. Methods: Three robust optimization models were implemented in our in-house IMPT treatment planning system: 1) L2 optimization based on worst-case dose; 2) L2 optimization based on minmax objective; and 3) L1 optimization with constraints on all uncertain doses. The first model was solved by a L-BFGS algorithm; the second was solved by a gradient projection algorithm; and the third was solved by an interior point method. One nominal scenario and eight maximum uncertainty scenarios (proton range over and under 3.5%, and setup error of 5 mm for x, y, z directions) were considered in optimization. Dosimetric measurements of optimized plans from the three approaches were compared for four prostate cancer patients retrospectively selected at our institution. Results: For the nominal scenario, all three optimization approaches yielded the same coverage to the clinical treatment volume (CTV) and the L2 worst-case approach demonstrated better rectum and bladder sparing than others. For the uncertainty scenarios, the L1 approach resulted in the most robust CTV coverage against uncertainties, while the plans from L2 worst-case were less robust than others. In addition, we observed that the number of scanning spots with positive MUs from the L2 approaches was approximately twice as many as that from the L1 approach. This indicates that L1 optimization may lead to more efficient IMPT delivery. Conclusion: Our study indicated that the L1 approach best conserved the target coverage in the face of uncertainty but its resulting OAR sparing was slightly inferior to other two approaches.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

TU-EF-304-03: 4D Monte Carlo Robustness Test for Proton Therapy

Purpose: Breathing motion and approximate dose calculation engines may increase proton range uncertainties. We address these two issues using a comprehensive 4D robustness evaluation tool based on an efficient Monte Carlo (MC) engine, which can simulate breathing with no significant increase in computation time. Methods: To assess the robustness of the treatment plan, multiple scenarios of uncertainties are simulated, taking into account the systematic and random setup errors, range uncertainties, and organ motion. Our fast MC dose engine, called MCsquare, implements optimized models on a massively-parallel computation architecture and allows us to accurately simulate a scenario in less than one minute. The deviations of the uncertainty scenarios are then reported on a DVH-band and compared to the nominal plan.The robustness evaluation tool is illustrated in a lung case by comparing three 60Gy treatment plans. First, a plan is optimized on a PTV obtained by extending the CTV with an 8mm margin, in order to take into account systematic geometrical uncertainties, like in our current practice in radiotherapy. No specific strategy is employed to correct for tumor and organ motions. The second plan involves a PTV generated from the ITV, which encompasses the tumor volume in all breathing phases. The last plan results from robust optimization performed on the ITV, with robustness parameters of 3% for tissue density and 8 mm for positioning errors. Results: The robustness test revealed that the first two plans could not properly cover the target in the presence of uncertainties. CTV-coverage (D95) in the three plans ranged respectively between 39.4–55.5Gy, 50.2–57.5Gy, and 55.1–58.6Gy. Conclusion: A realistic robustness verification tool based on a fast MC dose engine has been developed. This test is essential to assess the quality of proton therapy plan and very useful to study various planning strategies for mobile tumors. This work is partly funded by IBA (Louvain-la-Neuve, Belgium)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-R-31: Identification of Robust Normal Lung CT Texture Features for the Prediction of Radiation-Induced Lung Disease

Purpose: Normal lung CT texture features have been used for the prediction of radiation-induced lung disease (radiation pneumonitis and radiation fibrosis). For these features to be clinically useful, they need to be relatively invariant (robust) to tumor size and not correlated with normal lung volume. Methods: The free-breathing CTs of 14 lung SBRT patients were studied. Different sizes of GTVs were simulated with spheres placed at the upper lobe and lower lobe respectively in the normal lung (contralateral to tumor). 27 texture features (9 from intensity histogram, 8 from grey-level co-occurrence matrix [GLCM] and 10 from grey-level run-length matrix [GLRM]) were extracted from [normal lung-GTV]. To measure the variability of a feature F, the relative difference D=|Fref -Fsim|/Fref*100% was calculated, where Fref was for the entire normal lung and Fsim was for [normal lung-GTV]. A feature was considered as robust if the largest non-outlier (Q3+1.5*IQR) D was less than 5%, and considered as not correlated with normal lung volume when their Pearson correlation was lower than 0.50. Results: Only 11 features were robust. All first-order intensity-histogram features (mean, max, etc.) were robust, while most higher-order features (skewness, kurtosis, etc.) were unrobust. Only two of the GLCM and four of the GLRM features were robust. Larger GTV resulted greater feature variation, this was particularly true for unrobust features. All robust features were not correlated with normal lung volume while three unrobust features showed high correlation. Excessive variations were observed in two low grey-level run features and were later identified to be from one patient with local lung diseases (atelectasis) in the normal lung. There was no dependence on GTV location. Conclusion: We identified 11 robust normal lung CT texture features that can be further examined for the prediction of radiation-induced lung disease. Interestingly, low grey-level run features identified normal lung diseases. This work was supported in part by the National Cancer Institute Grants R01CA172638.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TH-CD-209-04: Fuzzy Robust Optimization in Intensity-Modulated Proton Therapy Planning to Account for Range and Patient Setup Uncertainties

Purpose: We propose to apply a robust optimization model based on fuzzy-logic constraints in the intensity-modulated proton therapy (IMPT) planning subject to range and patient setup uncertainties. The purpose is to ensure the plan robustness under uncertainty and obtain the best trade-off between tumor dose coverage and organ-at-risk(OAR) sparing. Methods: Two IMPT plans were generated for 3 head-and-neck cancer patients: one used the planning target volume(PTV) method; the other used the fuzzy robust optimization method. In the latter method, nine dose distributions were computed - the nominal one and one each for ±3mm setup uncertainties along three cardinal axes and for ±3.5% range uncertainty. For tumors, these nine dose distributions were explicitly controlled by adding hard constraints with adjustable parameters. For OARs, fuzzy constraints that allow the dose to vary within a certain range were used so that the tumor dose distribution was guaranteed by minimum compromise of that of OARs. We rendered this model tractable by converting the fuzzy constraints to linear constraints. The plan quality was evaluated using dose-volume histogram(DVH) indices such as tumor dose coverage(D95%), homogeneity(D5%-D95%), plan robustness(DVH band at D95%), and OAR sparing like D1% of brain and D1% of brainstem. Results: Our model could yield clinically acceptable plans. The fuzzy-logic robust optimization method produced IMPT plans with comparable target dose coverage and homogeneity compared to the PTV method(unit: Gy[RBE]; average[min, max])(CTV D95%: 59 [52.7, 63.5] vs 53.5[46.4, 60.1], CTV D5% - D95%: 11.1[5.3, 18.6] vs 14.4[9.2, 21.5]). It also generated more robust plans(CTV DVH band at D95%: 3.8[1.2, 5.6] vs 11.5[6.2, 16.7]). The parameters of tumor constraints could be adjusted to control the tradeoff between tumor coverage and OAR sparing. Conclusion: The fuzzy-logic robust optimization generates superior IMPT with minimum compromise of OAR sparing. This research was supported by the National Cancer Institute Career Developmental Award K25CA168984, by the Fraternal Order of Eagles Cancer Research Fund Career Development Award, by The Lawrence W. and Marilyn W. Matteson Fund for Cancer Research, by Mayo Arizona State University Seed Grant, and by The Kemper Marley Foundation. eRA Person ID(s) for the Principal Investigator: 11017970 (Research Supported by National Institutes of Health)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

Dual Regulation of Gene Expression Mediated by Extended MAPK Activation and Salicylic Acid Contributes to Robust Innate Immunity in Arabidopsis thaliana

Network robustness is a crucial property of the plant immune signaling network because pathogens are under a strong selection pressure to perturb plant network components to dampen plant immune responses. Nevertheless, modulation of network robustness is an area of network biology that has rarely been explored. While two modes of plant immunity, Effector-Triggered Immunity (ETI) and Pattern-Triggered Immunity (PTI), extensively share signaling machinery, the network output is much more robust against perturbations during ETI than PTI, suggesting modulation of network robustness. Here, we report a molecular mechanism underlying the modulation of the network robustness in Arabidopsis thaliana. The salicylic acid (SA) signaling sector regulates a major portion of the plant immune response and is important in immunity against biotrophic and hemibiotrophic pathogens. In Arabidopsis, SA signaling was required for the proper regulation of the vast majority of SA-responsive genes during PTI. However, during ETI, regulation of most SA-responsive genes, including the canonical SA marker gene PR1, could be controlled by SA-independent mechanisms as well as by SA. The activation of the two immune-related MAPKs, MPK3 and MPK6, persisted for several hours during ETI but less than one hour during PTI. Sustained MAPK activation was sufficient to confer SA-independent regulation of most SA-responsive genes. Furthermore, the MPK3 and SA signaling sectors were compensatory to each other for inhibition of bacterial growth as well as for PR1 expression during ETI. These results indicate that the duration of the MAPK activation is a critical determinant for modulation of robustness of the immune signaling network. Our findings with the plant immune signaling network imply that the robustness level of a biological network can be modulated by the activities of network components.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1981

Practical robustness measures in multivariable control system analysis

The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.

Lehtomaki, N. A.↗
NASA NTRS1981

Robustness tests utilizing the structure of modelling error

The present investigation is essentially concerned with the extension of results presented by Lehtomaki et al. (1981) on the robustness of multivariable linear time invariant feedback control systems. The work reported by Lehtomaki et al. is based on a multivariable version of Nyquist's theorem from which several robustness theorems were derived. In connection with the current investigation a slightly more general approach based on Nyquist's theorem is given in a fundamental robustness theorem from which various robustness tests may be obtained. A fundamental characterization of robustness is considered, and important tools from matrix theory are introduced. Attention is given to robustness tests and unstructured model error, and a robustness analysis for linear systems with structured model error.

Lehtomaki, N. A.↗
NASA NTRS1990

Stochastic performance robustness of aircraft control systems

Stochastic robustness, a simple technique used to estimate the robustness of linear, time-invariant systems, is applied to a twin-jet transport aircraft control system. Concepts behind stochastic stability robustness are extended to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications and measures specific to aircraft handling qualities are introduced. Confidence intervals for both individual stochastic robustness measures and for comparing two measures are presented. The application of stochastic performance robustness, the use of confidence intervals, and tradeoffs between performance objectives are demonstrated by means of the twin-jet aircraft example.

Stengel, Robert F.↗
NASA NTRS1990

Design optimization for cost and quality: The robust design approach

Designing reliable, low cost, and operable space systems has become the key to future space operations. Designing high quality space systems at low cost is an economic and technological challenge to the designer. A systematic and efficient way to meet this challenge is a new method of design optimization for performance, quality, and cost, called Robust Design. Robust Design is an approach for design optimization. It consists of: making system performance insensitive to material and subsystem variation, thus allowing the use of less costly materials and components; making designs less sensitive to the variations in the operating environment, thus improving reliability and reducing operating costs; and using a new structured development process so that engineering time is used most productively. The objective in Robust Design is to select the best combination of controllable design parameters so that the system is most robust to uncontrollable noise factors. The robust design methodology uses a mathematical tool called an orthogonal array, from design of experiments theory, to study a large number of decision variables with a significantly small number of experiments. Robust design also uses a statistical measure of performance, called a signal-to-noise ratio, from electrical control theory, to evaluate the level of performance and the effect of noise factors. The purpose is to investigate the Robust Design methodology for improving quality and cost, demonstrate its application by the use of an example, and suggest its use as an integral part of space system design process.

Unal, Resit↗
NASA NTRS1991

Robust control of systems with real parameter uncertainty and unmodelled dynamics

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.

Chang, Bor-Chin↗
NASA NTRS1993

A Monte Carlo approach to the analysis of control system robustness

Stochastic robustness, a simple technique used to estimate the stability and performance robustness of linear, time-invariant systems, is described. The scalar probability of instability is introduced as a measure of stability robustness. Examples are given of stochastic performance robustness measures based on classical time-domain specifications. The relationship between stochastic robustness measures and control system design parameters is discussed. The technique is demonstrated by analyzing an LQG/LTR system designed for a flexible robot arm. It is concluded that the analysis of stochastic robustness offers a good alternative to existing robustness metrics.

Ray, Laura R.↗