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All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Technology Development of Automated Rendezvous and Docking/Capture Sensors and Docking Mechanism for the Asteroid Redirect Crewed Mission

This paper will describe the technology development efforts NASA has underway for Automated Rendezvous and Docking/Capture (AR&D/C) sensors and a docking mechanism and the challenges involved. The paper will additionally address how these technologies will be extended to other missions requiring AR&D/C whether robotic or manned. NASA needs AR&D/C sensors for both the robotic and crewed segments of the Asteroid Redirect Mission (ARM). NASA recently conducted a commonality assessment of the concept of operations for the robotic Asteroid Redirect Vehicle (ARV) and the crewed mission segment using the Orion crew vehicle. The commonality assessment also considered several future exploration and science missions requiring an AR&D/C capability. Missions considered were asteroid sample return, satellite servicing, and planetary entry, descent, and landing. This assessment determined that a common sensor suite consisting of one or more visible wavelength cameras, a threedimensional LIDAR along with long-wavelength infrared cameras for robustness and situational awareness could be used on each mission to eliminate the cost of multiple sensor developments and qualifications. By choosing sensor parameters at build time instead of at design time and, without having to requalify flight hardware, a specific mission can design overlapping bearing, range, relative attitude, and position measurement availability to suit their mission requirements with minimal nonrecurring engineering costs. The resulting common sensor specification provides the union of all performance requirements for each mission and represents an improvement over the current systems used for AR&D/C today. These sensor specifications are tightly coupled to the docking system capabilities and requirements for final docking conditions. The paper will describe NASA's efforts to develop a standard docking system for use across NASA human spaceflight missions to multiple destinations. It will describe the current design status and the considerations and technologies involved in developing this docking mechanism.

Hinkel, Heather↗
NASA NTRS2015

Technology Development of Automated Rendezvous and Docking/Capture Sensors and Docking Mechanism for the Asteroid Redirect Crewed Mission

This paper will describe the technology development efforts NASA has underway for Automated Rendezvous and Docking/Capture (AR and D/C) sensors and a docking mechanism and the challenges involved. The paper will additionally address how these technologies will be extended to other missions requiring AR and D/C whether robotic or manned. NASA needs AR&D/C sensors for both the robotic and crewed segments of the Asteroid Redirect Mission (ARM). NASA recently conducted a commonality assessment of the concept of operations for the robotic Asteroid Redirect Vehicle (ARV) and the crewed mission segment using the Orion crew vehicle. The commonality assessment also considered several future exploration and science missions requiring an AR and D/C capability. Missions considered were asteroid sample return, satellite servicing, and planetary entry, descent, and landing. This assessment determined that a common sensor suite consisting of one or more visible wavelength cameras, a threedimensional LIDAR along with long-wavelength infrared cameras for robustness and situational awareness could be used on each mission to eliminate the cost of multiple sensor developments and qualifications. By choosing sensor parameters at build time instead of at design time and, without having to requalify flight hardware, a specific mission can design overlapping bearing, range, relative attitude, and position measurement availability to suit their mission requirements with minimal nonrecurring engineering costs. The resulting common sensor specification provides the union of all performance requirements for each mission and represents an improvement over the current systems used for AR and D/C today. These sensor specifications are tightly coupled to the docking system capabilities and requirements for final docking conditions. The paper will describe NASA's efforts to develop a standard docking system for use across NASA human spaceflight missions to multiple destinations. It will describe the current design status and the considerations and technologies involved in developing this docking mechanism.

Hinkel, Heather↗
NASA NTRS1991

Reliable numerical computation in an optimal output-feedback design

This paper presents a reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. The algorithm has been included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.

Vansteenwyk, Brett↗
NASA NTRS1985

Automatic control design procedures for restructurable aircraft control

A simple, reliable automatic redesign procedure for restructurable control is discussed. This procedure is based on Linear Quadratic (LQ) design methodologies. It employs a robust control system design for the unfailed aircraft to minimize the effects of failed surfaces and to extend the time available for restructuring the Flight Control System. The procedure uses the LQ design parameters for the unfailed system as a basis for choosing the design parameters of the failed system. This philosophy alloys the engineering trade-offs that were present in the nominal design to the inherited by the restructurable design. In particular, it alloys bandwidth limitations and performance trade-offs to be incorporated in the redesigned system. The procedure also has several other desirable features. It effectively redistributes authority among the available control effectors to maximize the system performance subject to actuator limitations and constraints. It provides a graceful performance degradation as the amount of control authority lessens. When given the parameters of the unfailed aircraft, the automatic redesign procedure reproduces the nominal control system design.

Looze, D. P.↗
NASA NTRS1991

Reliable numerical computation in an optimal output-feedback design

A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.

Vansteenwyk, Brett↗
NASA NTRS1991

Advanced rotorcraft control using parameter optimization

A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.

Vansteenwyk, Brett↗
NASA NTRS2016

Technology Development of Automated Rendezvous and Docking/Capture Sensors and Docking Mechanism for the Asteroid Redirect Crewed Mission

This paper will describe the technology development efforts NASA has underway for Automated Rendezvous and Docking/Capture (AR&D/C) sensors and a docking mechanism and the challenges involved. The paper will additionally address how these technologies will be extended to other missions requiring AR&D/C whether robotic or manned. NASA needs AR&D/C sensors for both the robotic and crewed segments of the Asteroid Redirect Mission (ARM). NASA recently conducted a commonality assessment of the concept of operations for the robotic Asteroid Redirect Vehicle (ARV) and the crewed mission segment using the Orion spacecraft. The commonality assessment also considered several future exploration and science missions requiring an AR&D/C capability. Missions considered were asteroid sample return, satellite servicing, and planetary entry, descent, and landing. This assessment determined that a common sensor suite consisting of one or more visible wavelength cameras, a three-dimensional LIDAR along with long-wavelength infrared cameras for robustness and situational awareness could be used on each mission to eliminate the cost of multiple sensor developments and qualifications. By choosing sensor parameters at build-time instead of at design-time and, without having to requalify flight hardware, a specific mission can design overlapping bearing, range, relative attitude, and position measurement availability to suit their mission requirements with minimal non-recurring engineering costs. The resulting common sensor specification provides the union of all performance requirements for each mission and represents an improvement over the current systems used for AR&D/C today. These sensor specifications are tightly coupled to the docking system capabilities and requirements for final docking conditions. The paper will describe NASA's efforts to develop a standard docking system for use across NASA human spaceflight missions to multiple destinations. It will describe the current design status and the considerations and technologies involved in developing this docking mechanism.

Hinkel, Heather↗
NASA NTRS2017

SLS-SPEC-159 Cross-Program Design Specification for Natural Environments (DSNE) Revision E

The DSNE completes environment-related specifications for architecture, system-level, and lower-tier documents by specifying the ranges of environmental conditions that must be accounted for by NASA ESD Programs. To assure clarity and consistency, and to prevent requirements documents from becoming cluttered with extensive amounts of technical material, natural environment specifications have been compiled into this document. The intent is to keep a unified specification for natural environments that each Program calls out for appropriate application. This document defines the natural environments parameter limits (maximum and minimum values, energy spectra, or precise model inputs, assumptions, model options, etc.), for all ESD Programs. These environments are developed by the NASA Marshall Space Flight Center (MSFC) Natural Environments Branch (MSFC organization code: EV44). Many of the parameter limits are based on experience with previous programs, such as the Space Shuttle Program. The parameter limits contain no margin and are meant to be evaluated individually to ensure they are reasonable (i.e., do not apply unrealistic extreme-on-extreme conditions). The natural environments specifications in this document should be accounted for by robust design of the flight vehicle and support systems. However, it is understood that in some cases the Programs will find it more effective to account for portions of the environment ranges by operational mitigation or acceptance of risk in accordance with an appropriate program risk management plan and/or hazard analysis process. The DSNE is not intended as a definition of operational models or operational constraints, nor is it adequate, alone, for ground facilities which may have additional requirements (for example, building codes and local environmental constraints). "Natural environments," as the term is used here, refers to the environments that are not the result of intended human activity or intervention. It consists of a variety of external environmental factors (most of natural origin and a few of human origin) which impose restrictions or otherwise impact the development or operation of flight vehicles and destination surface systems.

Roberts, Barry C.↗
NASA NTRS1985

Decomposition and state variable feedback control of elastic robotic systems

Energy-efficient, lightweight robot arms for space applications have considerable structural flexibility. An approach to control of a class of flexible robotic systems is presented. A control law is derived which decouples the joint-angle motion from the flexible motion and, in addition, asymptotically decomposes the elastic dynamics into two subsystems. This allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertaintly in system parameters. Simulation results show that the combination of nonlinear decoupling and elastic stabilization permits rapid, accurate tracking of large joint angle commands with well damped elastic response, in spite of space vehicle motion and payload uncertainty.

Singh, S. N.↗
NASA NTRS1986

Control of elastic robotic systems by nonlinear inversion and modal damping

Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.

Singh, S. N.↗
NASA NTRS1996

Parametric Robust Control and System Identification: Unified Approach

During the period of this support, a new control system design and analysis method has been studied. This approach deals with control systems containing uncertainties that are represented in terms of its transfer function parameters. Such a representation of the control system is common and many physical parameter variations fall into this type of uncertainty. Techniques developed here are capable of providing nonconservative analysis of such control systems with parameter variations. We have also developed techniques to deal with control systems when their state space representations are given rather than transfer functions. In this case, the plant parameters will appear as entries of state space matrices. Finally, a system modeling technique to construct such systems from the raw input - output frequency domain data has been developed.

Keel, L. H.↗
NASA NTRS1988

Robust control with structured perturbations

Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general.

Keel, Leehyun↗
NASA NTRS2015

SLS-SPEC-159 Cross-Program Design Specification for Natural Environments (DSNE) Revision D

This document is derived from the former National Aeronautics and Space Administration (NASA) Constellation Program (CxP) document CxP 70023, titled "The Design Specification for Natural Environments (DSNE), Revision C." The original document has been modified to represent updated Design Reference Missions (DRMs) for the NASA Exploration Systems Development (ESD) Programs. The DSNE completes environment-related specifications for architecture, system-level, and lower-tier documents by specifying the ranges of environmental conditions that must be accounted for by NASA ESD Programs. To assure clarity and consistency, and to prevent requirements documents from becoming cluttered with extensive amounts of technical material, natural environment specifications have been compiled into this document. The intent is to keep a unified specification for natural environments that each Program calls out for appropriate application. This document defines the natural environments parameter limits (maximum and minimum values, energy spectra, or precise model inputs, assumptions, model options, etc.), for all ESD Programs. These environments are developed by the NASA Marshall Space Flight Center (MSFC) Natural Environments Branch (MSFC organization code: EV44). Many of the parameter limits are based on experience with previous programs, such as the Space Shuttle Program. The parameter limits contain no margin and are meant to be evaluated individually to ensure they are reasonable (i.e., do not apply unrealistic extreme-on-extreme conditions). The natural environments specifications in this document should be accounted for by robust design of the flight vehicle and support systems. However, it is understood that in some cases the Programs will find it more effective to account for portions of the environment ranges by operational mitigation or acceptance of risk in accordance with an appropriate program risk management plan and/or hazard analysis process. The DSNE is not intended as a definition of operational models or operational constraints, nor is it adequate, alone, for ground facilities which may have additional requirements (for example, building codes and local environmental constraints). "Natural environments," as the term is used here, refers to the environments that are not the result of intended human activity or intervention. It consists of a variety of external environmental factors (most of natural origin and a few of human origin) which impose restrictions or otherwise impact the development or operation of flight vehicles and destination surface systems. These natural environments include the following types of environments: Terrestrial environments at launch, abort, and normal landing sites (winds, temperatures, pressures, surface roughness, sea conditions, etc.); Space environments (ionizing radiation, orbital debris, meteoroids, thermosphere density, plasma, solar, Earth, and lunar-emitted thermal radiation, etc.); Destination environments (Lunar surface and orbital, Mars atmosphere and surface, near Earth asteroids, etc.). Many of the environmental specifications in this document are based on models, data, and environment descriptions contained in the CxP 70044, Constellation Program Natural Environment Definition for Design (NEDD). The NEDD provides additional detailed environment data and model descriptions to support analytical studies for ESD Programs. For background information on specific environments and their effects on spacecraft design and operations, the environment models, and the data used to generate the specifications contained in the DSNE, the reader is referred to the NEDD paragraphs listed in each section of the DSNE. Also, most of the environmental specifications in this document are tied specifically to the ESD DRMs in ESD-10012, Revision B, Exploration Systems Development Concept of Operations (ConOps). Coordination between these environment specifications and the DRMs must be maintained. This document should be compatible with the current ESD DRMs, but updates to the mission definitions and variations in interpretation may require adjustments to the environment specifications.

Roberts, Barry C.↗
NASA NTRS1991

Dynamic dissipative compensator design for large space structures

Control system design is considered for attitude control and vibration suppression of flexible space structures. The problem addressed is that of controlling both the zero-frequency rigid-body modes and the elastic modes. Model-based compensators, which employ observers tuned to the plant parameters, are first investigated. Such compensators are shown to generally exhibit high sensitivity to the knowledge of the parameters, especially the elastic mode frequencies. To overcome this problem a class of dynamic dissipative compensators is next proposed, which robustly stabilize the plant in the presence of unmodeled dynamics and parametric uncertainties. An analytical proof of robust stability is given, and a method of implementing the controller as a strictly proper compensator is given. Methods of designing such controllers to obtain optimal performance and robust stability are presented. Numerical and experimental results of application of the methods are presented, which indicate that dynamic dissipative controllers can simultaneously provide excellent performance and robustness.

Joshi, S. M.↗
NASA NTRS2005

Robust Load-Sharing Control of Spacecraft Formations

This paper focuses on the design of autonomous and collaborative control strategies to govern the relative distances among multiple spacecraft in formation with no ground intervention. A coordinate load-sharing control structure for formation flying and a methodology to control their dynamic models with slow time-varying and uncertain parameters are the main objectives of this work. The method is applied to a deep space formation example, where the uncertainty in spacecraft fuel masses is also considered.

multi spacecraft↗
NASA NTRSDate not supplied

Thermal Protection System to Enable Ice Giant Aerocapture Mission for Delivering Both an Orbiter and an In Situ Probe

The Ice Giants have been identified as high priority science destinations in the last Decadal Survey [1] and could benefit from aerocapture as the primary method for orbit insertion [2]. A mass-efficient aerocapture system will enable the delivery of an orbiter along with an atmospheric probe (for in situ measurements to anchor global data collected by the orbiter) and possibly a lander at Triton [3]. Aerocapture could be executed either using low L/D rigid aeroshell with lift modulation (LMA) [4] or using deployable aeroshell using drag modulation (DMA) [3]. Nearly two decades ago, a NASA-funded team performed Neptune-Triton aerocapture studies with a mid-L/D lifting configuration [5] for achieving orbit using LMA. This study showed aerocapture challenges. Due to very high peak entry conditions combined with very high heat-load, a suite of TPS materials was required and this suite was deemed problematic from a qualification perspective, due test facility limitations. In the past 20 years, progress made in GN&C for lift-guided entry missions such as MSL, Orion EFT1, Mars 2020 and the upcoming Artemis missions, and the expertise in blunt body aerodynamics at large scale (~ 5m) has led the EDL community to conclude that aerocapture is a “go do” engineering activity and most technologies are in hand to propose missions with aerocapture [6] [7]. Aerocapture using DMA, currently in development, is an option for Ice Giant Missions. While DMA is simpler in some sense, due to ballistic entry and no need for lift-guided maneuvering, it has challenges and it’s maturity is lower. LMA and DMA both require one or more ablative Thermal Protection System (TPS) materials for the rigid aeroshell element. The ablative TPS needs to be robust and mass efficient due to the high heat loads and size of the rigid aeroshell. Currently, there are capable ablative thermal protection materials, e.g., Heatshield for Extreme Entry Environments Technology (HEEET), 3-D woven Mid-Density Carbon- Phenolic (3MDCP), and PICA (Phenolic-Impregnated Carbon Ablator) that are mature, i.e., at TRL 6 or higher. NASA also invested in Conformal PICA that was matured to TRL 5. Our goal is to evaluate the applicability of high TRL TPS and consider other design options. We first establish bounding aerocapture trajectories for a wide range of arrival conditions and the associated aerothermal environment. Based on the environments, we then determine the predicted TPS mass for the aeroshell [4]. In this presentation, we will outline the process by which we establish bounding aerocapture trajectories for hyperbolic excess velocities ranging from 27 km/s to 35 km/s, which are shown to be a range of velocities that can reduce the trip time from ~14 years to 8 years. The above velocity range translates to ~12 km/s to ~24 km/s arrival velocities at the planetary entry interface [2]. The velocity reduction required to achieve orbit ranges between ~2.5 km/s to 9.5 km/s for both Neptune and Triton. Propulsive insertion alone, due to the amount of fuel required to achieve the required velocity reduction, limits the science returned [2]. We establish the bounding aerocapture trajectories for a low L/D (~ 0.4) configuration for three different ballistic coefficients. The ballistic coefficient range is determined from three different aeroshell diameters of 3m, 4m and 5m and with an entry system mass of 2200 kg. With the above range of design parameters, we then determine conservative/bounding estimates of aerothermal environments by using a combination of CFD simulations and stagnation point heating estimates [7]. This engineering approach allows us to first assess the TPS need vs. TPS capability and determine the applicability of existing TPS. Once an applicable suite of TPS is determined, the TPS thickness and mass are computed. We show that the TPS mass fraction can be as low as 5% to as high as 20%, depending on total trip time reduction and other design parameters for a range of TPS. This is a large range for TPS mass fraction. We show PICA and HEEET can indeed enable aerocapture missions, but the missions incur a mass penalty. TPS mass savings, can be further reduced with the use of conformal PICA. Advancing the development of Conformal PICA to make it robust across the entire aerothermal environment (peak heat-flux, pressure and shear) range will result in TPS mass fractions of < 10% for Ice Giant aerocapture missions such as the Neptune-Triton mission. Aerocapture allows for not only shortening the trip time but enables larger mass to be placed in orbit. Furthermore, probes deployed from orbit will benefit in reduced entry environments allowing for a lower risk TPS implementation as compared to mission designs where the probe is released prior to orbit insertion. One of the challenges for the Ice Giant community is to ensure mission designs that maximize science and allow flexibility in the placement of the entry probe. The traditional approach to release the probe ahead of the orbiter may not optimize returned science. In this presentation, we will make the case for mature TPS such as HEEET and PICA. While these materials can enable aerocapture missions, completing the development of conformal PICA and extending Conformal PICA to be more robust, will have significant impact to TPS mass efficiency and significantly enhance science return for future Gas- and Ice-Giant missions.

E Venkatapathy↗
NASA NTRS1990

Dissipative compensators for flexible spacecraft control

The problem of controller design for flexible spacecraft is addressed. Model-based compensators, which rely on the knowledge of the system parameters to tune the state estimator, are considered. The instability mechanisms resulting from high sensitivity to parameter uncertainties are investigated. Dissipative controllers, which use collocated actuators and sensors, are also considered, and the robustness properties of constant-gain dissipative controllers in the presence of unmodeled elastic-mode dynamics, sensor/actuator nonlinearities, and actuator dynamics are summarized. In order to improve the performance without sacrificing robustness, a class of dissipative dynamic compensators is proposed and is shown to retain robust stability in the presence of second-order actuator dynamics if acceleration feedback is employed. A class of dissipative dynamic controllers is proposed which consists of a low-authority, constant-gain controller and a high-authority dynamic compensator. A procedure for designing an optimal dissipative dynamic compensator is given which minimizes a quadratic performance criterion. Such compensators offer the promise of better performance while still retaining robust stability.

Joshi, S. M.↗
NASA NTRS1993

A new approach to mixed H2/H infinity controller synthesis using gradient-based parameter optimization methods

In the past few years, the mixed H(sub 2)/H-infinity control problem has been the object of much research interest since it allows the incorporation of robust stability into the LQG framework. The general mixed H(sub 2)/H-infinity design problem has yet to be solved analytically. Numerous schemes have considered upper bounds for the H(sub 2)-performance criterion and/or imposed restrictive constraints on the class of systems under investigation. Furthermore, many modern control applications rely on dynamic models obtained from finite-element analysis and thus involve high-order plant models. Hence the capability to design low-order (fixed-order) controllers is of great importance. In this research a new design method was developed that optimizes the exact H(sub 2)-norm of a certain subsystem subject to robust stability in terms of H-infinity constraints and a minimal number of system assumptions. The derived algorithm is based on a differentiable scalar time-domain penalty function to represent the H-infinity constraints in the overall optimization. The scheme is capable of handling multiple plant conditions and hence multiple performance criteria and H-infinity constraints and incorporates additional constraints such as fixed-order and/or fixed structure controllers. The defined penalty function is applicable to any constraint that is expressible in form of a real symmetric matrix-inequity.

Ly, Uy-Loi↗