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NASA NTRS1993

On the robustness of Herlihy's hierarchy

A wait-free hierarchy maps object types to levels in Z(+) U (infinity) and has the following property: if a type T is at level N, and T' is an arbitrary type, then there is a wait-free implementation of an object of type T', for N processes, using only registers and objects of type T. The infinite hierarchy defined by Herlihy is an example of a wait-free hierarchy. A wait-free hierarchy is robust if it has the following property: if T is at level N, and S is a finite set of types belonging to levels N - 1 or lower, then there is no wait-free implementation of an object of type T, for N processes, using any number and any combination of objects belonging to the types in S. Robustness implies that there are no clever ways of combining weak shared objects to obtain stronger ones. Contrary to what many researchers believe, we prove that Herlihy's hierarchy is not robust. We then define some natural variants of Herlihy's hierarchy, which are also infinite wait-free hierarchies. With the exception of one, which is still open, these are not robust either. We conclude with the open question of whether non-trivial robust wait-free hierarchies exist.

Jayanti, Prasad↗

NASA NTRS1994

Designing robust control laws using genetic algorithms

The purpose of this research is to create a method of finding practical, robust control laws. The robustness of a controller is judged by Stochastic Robustness metrics and the level of robustness is optimized by searching for design parameters that minimize a robustness cost function.

Marrison, Chris↗

NASA NTRS1995

Research of Stochastic Robustness: Results and conclusions

With stochastic robustness we are creating tools to design robust compensators for practical systems. During this year, the stochastic robustness research achieved the following results: refined the search tools needed for synthesis; successfully designed robust compensators for the American Controls Conference benchmark problem; and successfully designed robust compensators for a nonlinear hypersonic aircraft model with uncertainties in 28 parameters.

Marrison, Chris↗

NASA NTRS1993

Robust Crossfeed Design for Hovering Rotorcraft

Control law design for rotorcraft fly-by-wire systems normally attempts to decouple angular responses using fixed-gain crossfeeds. This approach can lead to poor decoupling over the frequency range of pilot inputs and increase the load on the feedback loops. In order to improve the decoupling performance, dynamic crossfeeds may be adopted. Moreover, because of the large changes that occur in rotorcraft dynamics due to small changes about the nominal design condition, especially for near-hovering flight, the crossfeed design must be 'robust'. A new low-order matching method is presented here to design robust crossfeed compensators for multi-input, multi-output (MIMO) systems. The technique identifies degrees-of-freedom that can be decoupled using crossfeeds, given an anticipated set of parameter variations for the range of flight conditions of concern. Cross-coupling is then reduced for degrees-of-freedom that can use crossfeed compensation by minimizing off-axis response magnitude average and variance. Results are presented for the analysis of pitch, roll, yaw and heave coupling of the UH-60 Black Hawk helicopter in near-hovering flight. Robust crossfeeds are designed that show significant improvement in decoupling performance and robustness over nominal, single design point, compensators. The design method and results are presented in an easily used graphical format that lends significant physical insight to the design procedure. This plant pre-compensation technique is an appropriate preliminary step to the design of robust feedback control laws for rotorcraft.

Catapang, David R.↗

NASA NTRS2003

Robust Control for Microgravity Vibration Isolation using Fixed Order, Mixed H2/Mu Design

Many space-science experiments need an active isolation system to provide a sufficiently quiescent microgravity environment. Modern control methods provide the potential for both high-performance and robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H(infinity) methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/H(infinity), controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure, for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.

Whorton, Mark↗

NASA NTRS2004

Robust Control for The G-Limit Microgravity Vibration Isolation System

Many microgravity science experiments need an active isolation system to provide a sufficiently quiescent acceleration environment. The g-LIMIT vibration isolation system will provide isolation for Microgravity Science Glovebox experiments in the International Space Station. While standard control system technologies have been demonstrated for these applications, modern control methods have the potential for meeting performance requirements while providing robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H infinity methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/mu controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.

Whorton, Mark S.↗

NASA NTRS2004

Robust Timing Synchronization in Aeronautical Mobile Communication Systems

This work details a study of robust synchronization schemes suitable for satellite to mobile aeronautical applications. A new scheme, the Modified Sliding Window Synchronizer (MSWS), is devised and compared with existing schemes, including the traditional Early-Late Gate Synchronizer (ELGS), the Gardner Zero-Crossing Detector (GZCD), and the Sliding Window Synchronizer (SWS). Performance of the synchronization schemes is evaluated by a set of metrics that indicate performance in digital communications systems. The metrics are convergence time, mean square phase error (or root mean-square phase error), lowest SNR for locking, initial frequency offset performance, midstream frequency offset performance, and system complexity. The performance of the synchronizers is evaluated by means of Matlab simulation models. A simulation platform is devised to model the satellite to mobile aeronautical channel, consisting of a Quadrature Phase Shift Keying modulator, an additive white Gaussian noise channel, and a demodulator front end. Simulation results show that the MSWS provides the most robust performance at the cost of system complexity. The GZCD provides a good tradeoff between robustness and system complexity for communication systems that require high symbol rates or low overall system costs. The ELGS has a high system complexity despite its average performance. Overall, the SWS, originally designed for multi-carrier systems, performs very poorly in single-carrier communications systems. Table 5.1 in Section 5 provides a ranking of each of the synchronization schemes in terms of the metrics set forth in Section 4.1. Details of comparison are given in Section 5. Based on the results presented in Table 5, it is safe to say that the most robust synchronization scheme examined in this work is the high-sample-rate Modified Sliding Window Synchronizer. A close second is its low-sample-rate cousin. The tradeoff between complexity and lowest mean-square phase error determines the rankings of the Gardner Zero-Crossing Detector and both versions of the Early-Late Gate Synchronizer. The least robust models are the high and low-sample-rate Sliding Window Synchronizers. Consequently, the recommended replacement synchronizer for NASA's Advanced Air Transportation Technologies mobile aeronautical communications system is the high-sample-rate Modified Sliding Window Synchronizer. By incorporating this synchronizer into their system, NASA can be assured that their system will be operational in extremely adverse conditions. The quick convergence time of the MSWS should allow the use of high-level protocols. However, if NASA feels that reduced system complexity is the most important aspect of their replacement synchronizer, the Gardner Zero-Crossing Detector would be the best choice.

Xiong, Fu-Qin↗

NASA NTRS2009

Trading Robustness Requirements in Mars Entry Trajectory Design

One of the most important metrics characterizing an atmospheric entry trajectory in preliminary design is the size of its predicted landing ellipse. Often, requirements for this ellipse are set early in design and significantly influence both the expected scientific return from a particular mission and the cost of development. Requirements typically specify a certain probability level (6-level) for the prescribed ellipse, and frequently this latter requirement is taken at 36. However, searches for the justification of 36 as a robustness requirement suggest it is an empirical rule of thumb borrowed from non-aerospace fields. This paper presents an investigation into the sensitivity of trajectory performance to varying robustness (6-level) requirements. The treatment of robustness as a distinct objective is discussed, and an analysis framework is presented involving the manipulation of design variables to effect trades between performance and robustness objectives. The scenario for which this method is illustrated is the ballistic entry of an MSL-class Mars entry vehicle. Here, the design variable is entry flight path angle, and objectives are parachute deploy altitude performance and error ellipse robustness. Resulting plots show the sensitivities between these objectives and trends in the entry flight path angles required to design to these objectives. Relevance to the trajectory designer is discussed, as are potential steps for further development and use of this type of analysis.

Lafleur, Jarret M.↗

NASA NTRSDate not supplied

Going beyond reliability to robustness and resilience in space systems

The words reliability, robustness, and resilience, are often used interchangeably to describe tough and dependable systems but the distinctions between them suggest how to design more serviceable space systems. Reliability is simply the quality of consistently performing well. A system that dependably meets its design requirements in the specified environments is reliable. The designers may not consider themselves responsible for failures under unanticipated conditions. Robustness is the capability of performing without failure under a wide range of conditions, which can go beyond the expected range to include possible off-nominal conditions. Resilience is the ability to recover from or adapt to damaging events, such as failures, accidents, external disruptions, and repurposing. Such changes are usually unanticipated. They often invalidate the usual operating assumptions and cause system failure. Reliability, robustness, and resilience describe dependable performance under increasingly difficult conditions, first the specified environment, then a wider possible environment, and finally unanticipated damaging events. These three are increasingly desirable and increasingly difficult to achieve. Engineering for resilience would design systems that can ignore or repair failures, survive accidents, and recover from disruptions. Increasing the resilience of space systems, the ability to perform after unanticipated events, would greatly increase space crew safety. Improving reliability and robustness can be done by dealing with known sources of problems, but improving resilience requires implementing a general approach to reducing the impact of unknown future events. Two contrasting approaches are reducing system complexity and adding supervisory control. The need for resilience has been claimed for decades but little has been accomplished. Systems designers assume that they understand requirements, technologies, designs, architectures, integration, testing, operations, and environments. The potential problems of changes, failures, accidents, unknown environments, and unknown unknowns are ignored. Systems designers are typically overconfident and ignore the need for robustness and resilience.

Harry W Jones↗

NASA NTRSDate not supplied

Robust Design Under Uncertainty of Hypersonic Inlets

The objective of this work is to optimize scramjet inlet designs under uncertainty at multiple fidelity levels. Optimizations are performed for both deterministic and stochastic conditions. For stochastic conditions, robust design is used to minimize the variance in system performance in addition to optimizing mean system performance. Uncertainty quantification is performed using non-intrusive polynomial chaos. Comparisons are made between low-fidelity analysis and high-fidelity analysis, as well as deterministic optimization and robust optimization. Results indicate that the general design trend of previous inlet optimization techniques is recovered for the external compression portion of an inlet. For the internal compression portion of an inlet, when viscous effects become more significant and boundary layer separation becomes more likely, the optimal trend departs from previous results. Multifidelity uncertainty quantification methods are found to substantially reduce the computation time of robust design while obtaining results that nearly match those of high-fidelity analysis. Robust optimization is found to decrease the standard deviation of throat Mach number by up to 40% compared to deterministic optimization. Changes in the design variables and total turning that lead to robust scramjet inlets are identified and linked back to fundamental physical principles through the theta-beta-Mach function.

Hypersonic↗

NASA NTRS2022

Robust Controller Synthesis for Vision-based Spacecraft Guidance and Control

This work develops a method for Robust Controller for Vision-based Spacecraft (RCVS) guidance and control, integral to the robust autonomy framework for multi-spacecraft for- mation control and reconfiguration applications. The method is built around the use of a photo-realistic simulator, where a camera is deployed on a tracking spacecraft (ego) in order to observe an uncontrolled spacecraft (target) in a Low Earth Orbit (LEO). In this direction, the proposed approach performs the relative state (attitude and position) estimation of the target spacecraft using Convolutional Neural Network (CNN). The state estimation error is then modeled and the corresponding error-bounds are obtained around a nominal trajectory of the ego and target spacecraft. Next, this work proposes a linear matrix inequalities (LMIs) based approach to controller synthesis, guaranteed to be robust against both model uncertainties and measurement errors, resulting from vision-based estimation. This controller is comprised of two distinct components, one synthesized based on the nominal trajectory, while the “robust” component corrects for deviations from the nominal trajectory. Finally, a tracking scenario that directly utilize the image data for spacecraft guidance and control, is presented to showcase the performance of the proposed robust autonomy framework.

Rahmani, Amir↗

NASA NTRS1974

Robust design of dynamic observers

The two (identity) observer realizations z = Mz + Ky and z = transpose of Az + transpose of K(y - transpose of Cz), respectively called the open loop and closed loop realizations, for the linear system x = Ax, y = Cx are analyzed with respect to the requirement of robustness; i.e., the requirement that the observer continue to regulate the error x - z satisfactorily despite small variations in the observer parameters from the projected design values. The results show that the open loop realization is never robust, that robustness requires a closed loop implementation, and that the closed loop realization is robust with respect to small perturbations in the gains transpose of K if and only if the observer can be built to contain an exact replica of the unstable and underdamped dynamics of the system being observed. These results clarify the stringent accuracy requirements on both models and hardware that must be met before an observer can be considered for use in a control system.

Bhattacharyya, S. P.↗

NASA NTRS1986

Robust detection, isolation and accommodation for sensor failures

The objective is to extend the recent advances in robust control system design of multivariable systems to sensor failure detection, isolation, and accommodation (DIA), and estimator design. This effort provides analysis tools to quantify the trade-off between performance robustness and DIA sensitivity, which are to be used to achieve higher levels of performance robustness for given levels of DIA sensitivity. An innovations-based DIA scheme is used. Estimators, which depend upon a model of the process and process inputs and outputs, are used to generate these innovations. Thresholds used to determine failure detection are computed based on bounds on modeling errors, noise properties, and the class of failures. The applicability of the newly developed tools are demonstrated on a multivariable aircraft turbojet engine example. A new concept call the threshold selector was developed. It represents a significant and innovative tool for the analysis and synthesis of DiA algorithms. The estimators were made robust by introduction of an internal model and by frequency shaping. The internal mode provides asymptotically unbiased filter estimates.The incorporation of frequency shaping of the Linear Quadratic Gaussian cost functional modifies the estimator design to make it suitable for sensor failure DIA. The results are compared with previous studies which used thresholds that were selcted empirically. Comparison of these two techniques on a nonlinear dynamic engine simulation shows improved performance of the new method compared to previous techniques

Emami-Naeini, A.↗

NASA NTRS1986

Integrated control/structure design and robustness

When a flexible structure is to be controlled actively, optimum performance is obtained by integrated, or simultaneous, design of the structure and the controller, as opposed to the common practice of designing the structure independently of control consideration and then designing a controller for a fixed structure. The primary design objective from the structural point of view usually is to minimize weight, while the control design objectives depend on the application. An important requirement for a practical control system is robustness with respect to uncertain plant parameters. This paper discusses simultaneous control/structure design when the overall design objective combines the weight of the structure and the robustness of the closed-loop control system. For numerical optimization, robustness is represented by the sensitivity of the closed-loop eigenvalues with respect to uncertain parameters. An example illustrates the optimal design of a flexible structure along with a robust compensator.

Adamian, A.↗

NASA NTRS1987

Lyapunov function gradient generated robust control in the absence of the nominal stabilizing control

A relevant facet of the application of Lyapunov gradient-generated robust control to unstable linear autonomous plants is explored. It is demonstrated that if the plant, the output, and the nominal stabilizing control satisfy certain conditions, then the robust component alone stabilizes the nominal plant. An example characterized by two zero eigenvalues and two negative real value poles is presented. These results assure that the robust component will fulfill the role of nominal stabilization successfully so long as the possible magnitude of the robust component can overcome the contribution of the instability to positiveness of the Lyapunov rate.

Blackwell, C. C.↗

NASA NTRS1988

Robustness analysis based on passivity

A technique of robust stability analysis for multivariable control systems is introduced. Existing tools in the literature are mostly based on small gain type of conditions such as the H(infinity)-norm or mu measure. In contrast, the approach presented is motivated by passivity theory. The natural energy Lyapunov function associated with a passive system allows robustness to be analyzed with Lyapunov stability theory. Consequently, nonlinear and time-varying perturbations can be considered within the same framework. For unstructured uncertainties, the robustness margin is characterized in terms of an index related to the Hermitian part of a transfer function. If the uncertainties contain additional diagonal structure, stability margins are obtained for variations of each uncertain block in both positive and negative directions. Applications of this robustness analysis technique are illustrated.

Wen, John T.↗

NASA NTRS1988

Robust eigenvalue/eigenvector selection in linear state feedback systems

Design procedures are developed to select both eigenvalues and eigenvectors to improve system robustness. A robustness metric based on the determinant of the normalized eigenvector matrix defined. It is shown that this metric significantly speeds up the convergence of robust eigenvector solutions close to the optimal. A procedure to blend multiple inputs to improve achievable system robustness in the lower dimensional pseudo control space has also been derived.

Srinathkumar, S.↗

NASA NTRS1989

Robust control design for aerospace applications

Time-domain control design for stability robustness of linear systems with structured uncertainty is addressed. Upper bounds on the linear perturbation of an asymptotically stable linear system are obtained, making it possible to maintain stability by using the structural information of the uncertainty. A quantitative measure called the stability robustness index is introduced and used to design controllers for robust stability. The proposed state feedback control design algorithm can be used, for a given set of perturbations, to select the range of control effort for which the system is stability-robust. Conversely it can be used, for a given control effort, to determine the size of the tolerable perturbation. The algorithm is illustrated with examples from aircraft control and large-space-structure control problems.

Yedavalli, Rama K.↗