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Derivation of Coordinate Descent Algorithms from Optimal control Theory

Operations Research Forum 2023年第2期4卷 1-11页

作者： Ross, Isaac M. Control & Optimization Laboratories Naval Postgraduate School 1 University Circle Monterey 93943 CA United States

Recently, it was posited that disparate optimization algorithms may be coalesced in terms of a central source emanating from optimal control theory. Here we further this proposition by showing how coordinate descent algorithms may be derived from this emerging new principle. In particular, we show that basic coordinate descent algorithms can be derived using a maximum principle and a collection of max functions as “control” Lyapunov functions. The convergence of the resulting coordinate descent algorithms is thus connected to the controlled dissipation of their corresponding Lyapunov functions. The operational metric for the search vector in all cases is given by the Hessian of the convex objective function. © 2023, This is a U.S. Government work and not under copyright protection in the US;foreign copyright protection may apply.

关键词： Convex optimization Coordinate descent Machine learning Nonsmooth control Lyapunov functions Singular optimal control theory

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Unscented Hypersonic Trajectory optimization with a Heating-Rate Chance Constraint

Unscented Hypersonic Trajectory Optimization with a Heating-...

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AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2025

作者： Schwartz, E. Karpenko, M. Ross, I.M. Guidance Navigation and Control Department Raytheon An RTX Business TucsonAZ85756 United States Control and Optimization Laboratories Department of Mechanical and Aerospace Engineering Naval Postgraduate School MontereyCA93943 United States

ISBN: (数字)9781624107238

ISBN: (纸本)9781624107238

The aerothermal load on an aerospace vehicle is one of the most critical conditions during hypersonic flight. To maximize performance, a typical hypersonic vehicle rides the maximum allowable value of the heating-rate constraint during a portion of its flight. Because atmospheric density has high uncertainty, guiding a hypersonic vehicle along a deterministic optimal trajectory will violate the maximum heating-rate limit with an unacceptable probability. To address this problem, we pose the maximum heating-rate on the vehicle as a chance constraint in a tychastic trajectory optimization problem (from Tyche, the Greek goddess of chance). To generate a tractable problem formulation, the chance constraint is mapped to a constraint on a deviation measure of the heating-rate. The resulting tychastic problem is transcribed to a constrained unscented trajectory optimization problem and solved using DIDO. The validity of these transcriptions and approximations is verified via Monte Carlo analysis. Sample numerical results demonstrate how risk can be reduced from unsafe (i.e., 70% risk) to safe (i.e., near 0% risk) operations. © 2025, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

关键词： Atmospheric density

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Unscented Trajectory optimization

arXiv

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arXiv 2024年

作者： Ross, I.M. Proulx, R.J. Karpenko, M. Naval Postgraduate School MontereyCA93943 United States Control and Optimization Department of Mechanical and Aerospace Engineering United States Control and Optimization Laboratories Space Systems Academic Group United States Control and Optimization Laboratories Department of Mechanical and Aerospace Engineering United States

In a nutshell, unscented trajectory optimization is the generation of optimal trajectories through the use of an unscented transform. Although unscented trajectory optimization was introduced by the authors about a decade ago, it is reintroduced in this paper as a special instantiation of tychastic optimal control theory. Tychastic optimal control theory (from Tyche, the Greek goddess of chance) avoids the use of a Brownian motion and the resulting Itô calculus even though it uses random variables across the entire spectrum of a problem formulation. This approach circumvents the enormous technical and numerical challenges associated with stochastic trajectory optimization. Furthermore, it is shown how a tychastic optimal control problem that involves nonlinear transformations of the expectation operator can be quickly instantiated using an unscented transform. These nonlinear transformations are particularly useful in managing trajectory dispersions be it associated with path constraints or targeted values of final-time conditions. This paper also presents a systematic and rapid process for formulating and computing the most desirable tychastic trajectory using an unscented transform. Numerical examples are used to illustrate how unscented trajectory optimization may be used for risk reduction and mission recovery caused by uncertainties and failures. © 2024, CC BY-NC-ND.

关键词： Trajectories

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Scaling and balancing for high-performance computation of optimal controls

arXiv

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arXiv 2018年

作者： Ross, I.M. Gong, Q. Karpenko, M. Proulx, R.J. Department of Mechanical and Aerospace Engineering Naval Postgraduate School MontereyCA93943 United States Department of Applied Mathematics University of California Santa CruzCA95064 United States Control and Optimization Laboratories Space Systems Academic Group

It is well-known that proper scaling can increase the efficiency of computational problems. In this paper we define and show that a balancing technique can substantially improve the computational efficiency of optimal control algorithms. We also show that non-canonical scaling and balancing procedures may be used quite effectively to reduce the computational difficulty of some hard problems. These results have been used successfully for several flight and field operations at NASA and DoD. A surprising aspect of our analysis shows that it may be inadvisable to use auto-scaling procedures employed in some software packages. The new results are agnostic to the specifics of the computational method;hence, they can be used to enhance the utility of any existing algorithm or software. Copyright © 2018, The Authors. All rights reserved.

关键词： NASA

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Unscented optimization

Unscented optimization

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AAS/AIAA Astrodynamics Specialist Conference, ASC 2015

作者： Ross, I. Michael Proulx, Ronald J. Karpenko, Mark Control and Optimization Laboratories Naval Postgraduate School 700 Dyer Road MontereyCA93943-5100 United States

ISBN: (纸本)9780877036296

Unscented optimization combines the concept of the unscented transform with standard optimization to produce a simple technique for mitigating the effect of uncertainties. This new approach addresses some long-standing challenges in practical probabilistic programming by trading some well-known theoretical and computational difficulties to an a posteriori estimation of risk and reliability. Every practical optimization problem can be unscented;hence, the concepts introduced in this paper can be applied to a wide range of problems in astrodynamics. If unscented optimization techniques are used during the early phases of a mission design, it holds the potential to provide program managers quick estimates on risk, reliability and associated costs so that "optimal missions" do not suffer from cost overruns due to requirements creep. Using numerical examples, we demonstrate how it is possible to reduce risk from 50% all the way down to 1%.

关键词： Cost benefit analysis

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Fuel-optimal design of Moon-Earth trajectories using Legendre pseudospectral method

Fuel-optimal design of Moon-Earth trajectories using Legendr...

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作者： Park, Chandeok Gong, Qi Ross, I. Michael Sekhavat, Pooya Naval Postgraduate School Monterey CA 93943 United States University of California Santa Cruz CA 95064 United States Control and Optimization Laboratories Watkins Hall 208 United States Applied Mathematics and Statistics Department United States Mechanical and Astronautical Engineering Watkins Hall 306 United States

ISBN: (纸本)9781563479458

A fuel-optimal trans-Earth trajectory design for manned lunar missions is presented. The gravitational effects of the Moon, Earth, and Sun constitute a 4-body problem. Imposing maximum thrust, fuel budget, and flight time as design constraints, we formulate a nonlinear constrained fuel-optimal control problem to obtain an optimal trajectory from a low lunar parking orbit to an Earth interface condition. The resulting optimal control problem is solved using Legendre pseudospectral method. An anti-aliasing method based on Bellman's principle of optimality is employed to test and improve the accuracy of the solution. All results are developedn and obtained using the software package DIDO ©. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc.

关键词： Budget control

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Integrated sliding mode autopilot-guidance for dual control missiles

Integrated sliding mode autopilot-guidance for dual control ...

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AIAA Guidance, Navigation, and control Conference 2005

作者： Idan, Moshe Shima, Tal Golan, Oded M. Technion - Israel Institute of Technology Haifa 32000 Israel RAFAEL Haifa 31021 Israel Faculty of Aerospace Engineering Israel AIAA United States Air Force Research Laboratories Control and Optimization Branch Air Vehicles Directorate Wright-Patterson AFB OH 45433 United States Department 35 P.O.B. 2250 Israel

ISBN: (纸本)1563477378

An integrated autopilot and guidance algorithm is developed, using the sliding mode control approach, for a missile with forward and aft control surfaces. Based on guidance considerations, the zero effort miss (ZEM), encountered in differential games guidance solutions, is used as one of the sliding variables in the proposed control scheme. The dual control configuration provides an additional degree of freedom in the integrated design. This degree of freedom is exploited by introducing a second sliding surface, selected based on autopilot design considerations. Restraining the system to the ZEM surface guarantees zero miss distance, while remaining on the second surface provides a damped response. The performance of the integrated dual controller is evaluated using a two-dimensional nonlinear simulation of the missile lateral dynamics and relative kinematics, assuming first order dynamics for the target evasive maneuvers. The simulation results validate the design approach of using ZEM and the flight-control based sliding surfaces to attain high accuracy interceptions.

关键词： Sliding mode control

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NETWORK PLANNING BASED ON VIRTUAL PATH BANDWIDTH MANAGEMENT

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INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS 1995年第2期8卷 143-153页

作者： LOGOTHETIS, M KOKKINAKIS, G Wire Communications Lab. Electrical Engineering Dept. University of Patras 261 10 Patras Greece Michael D. Logothetis was born in Andros Greece in 1959. He received the Dipl.-Eng. and Ph.D. degrees in electrical engineering both from the University of Patras PatradGreece in 1981 and 1990 respectively. From 1982 to 1990 he was a Teaching and Research Assistant at the laboratory of Wire Communications University of Patras and participated in many national research programmes and three EEC projects (ESPRIT LRE) dealing with telecommunication networks as well as with natural language processing. From 1991 to 1992 he was Research Associate in NTT's Telecommunication Networks Laboratories. Since 1992 he has been a Lecturer in the Department of Electrical Engineering University of Patras Greece. His research interests include traffic control network management simulation and performance optimization of telecommunication networks. He is a member of the IEEE (Commun. Society-CNOM) IEICE and the Technical Chamber of Greece (TEE). George K. Kokkinakis was born in Chios Greece in 1937. He received the Diploma in Electrical Engineering (Dipl.-Ing.) in 1961 the Doctor's Degree in Engineering (Dr.-Ing) in 1966 and the Diploma in Engineering Economics (Dipl. Wjrt.-Ing) in 1967 all from the Technical University of Munich Germany. Since 1969 he has been with the Department of Electrical Engineering at the University of Patras where he has organGed and directing the Wire Communications Laboratory (WCL). His current activity in research and development which coincides with the activity of WCL includes the design and optimization of telecommunication networks and the analysis synthesis recognition and linguistic processing of the Greek language. He has published several books and over 100 technical papers articles and reports on Telecommunications Electrotechnology and Speech Technology. Prof. Kokkinakis is a senior member of IEEE and a member of the Technical Chamber of Greece (TEE) the VDE (Vere

Periodical performance evaluation and adaptive resource assignment, already proposed as performance-oriented management, seems to be the most suitable strategy for network planning under demand uncertainty. In this paper, we exploit the inherent capability of ATM networks to rearrange dynamically the already installed resources, and propose performance-oriented management combined with virtual path bandwidth (VPB) control for the planning of the extensions of bandwidth capacities of virtual paths (VPs) and transmission links of the network. We define a large network optimization problem and solve it by a rigorous, analytical procedure. The optimization model comprises specific requirements of the network-planning problem and a bandwidth distribution scheme ensuring network reliability. We reveal the efficiency of the proposed scheme by applying it on a model network, considering two realistic case-studies of network-traffic evolution. We show that in the presence of VPB control: (a) the initial distribution of the total bandwidth to VPs is of no importance, since it can be adaptively rearranged according to the offered traffic, (b) the network is well used and bandwidth investment could be saved, and (c) whenever additional bandwidth must be installed in VPs which have an unanticipated bad grade-of-service, time savings result. We present the network performance in detail, in figures, and compare this with the performance of the network in the absence of VPB control.

关键词： NETWORK PLANNING NETWORK optimization BANDWIDTH control MATHEMATICAL PROGRAMMING VIRTUAL PATH CALL BLOCKING PROBABILITY ATM

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ACCURACY REQUIREMENTS FOR MEASUREMENT SYSTEMS WITH UNIFORM AND NORMAL ERRORS

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NAVAL ENGINEERS JOURNAL 1993年第1期105卷 66-69页

作者： SNOW, JM STUCKMAN, BE USHER, JS Jeffrey M. Snow:received his B.S. degree in mechanical engineering from the University of Washington in 1977. He has worked at Boeing Commercial Aircraft Company and Puget Sound Naval Shipyard. Since 1985 he has been at Naval Surface Warfare Center Crane Division (NSWCC). From 1987 to 1990 he was in charge of quality assurance configuration management and reliability for Aegis (SPY-1 and Mk-99) microwave tubes. He currently is in the Radar System Branch at NSWCC. He is a member of ASQC and ASME. His areas of interest include the use of statistics in process improvement efforts and objectively rating and rewarding suppliers for better quality. Bruce E. Stuckman:holds a Ph.D. degree in systems engineering from Oakland University where he also obtained M.S. and B.S. degrees in electrical and computer engineering. In 1992 Dr. Stuckman obtained his J.D. from the University of Louisville where he graduated cum laude. He is currently an associate in the patent and computer law department of Brooks & Kushman a law firm specializing in intellectual property and technology related causes. Prior to this he was an associate professor of both electrical engineering at the University of Louisville and a member of the Research Advisory Board of the South Central Bell Telecommunications Research Center. Dr. Stuckman is the author of over 75 published works in a variety of research areas including global optimization algorithms control systems communication and telecommunication systems and instrumentation electronics. He has served as a technical consultant to such organizations as Control Data Corporation General Electric General Motors Research Laboratories Gulf & Western AT&T Bell Laboratories ARCO Research and Technical Services and the U.S. Government and has been a frequent lecturer at national and international symposia. He is a senior member of IEEE and a member of ASNE Eta Kappa Nu Tau Beta Pi Sigma Xi and Phi Kappa Phi. John S. Usher Ph.D. P.E.:is an assistant professor of industrial engineering

Accuracy requirements are usually determined as a percentage of the specification range of the measured part or process. Setting accuracy requirements in this manner results in a wide and unpredictable range of false rejection and acceptance probabilities. This causes extra costs due to either: 1) over specification of measurement systems accuracy requirements;2) time, effort, retesting, and resolution of false rejections;or 3) system degradation caused by false acceptance of out-of-specification parts. Achieving a consistent and known risk of false acceptance is only possible by considering the measured process C(pk), the process's mean in relation to the center of the specification range, and the measurement system error distribution. This paper presents a method for calculating the probabilities of false rejection and false acceptance for a normal process which is measured with, alternately, uniform and normally distributed error. It is shown that under most conditions uniform error causes 20% to 30% higher false rejection and acceptance probabilities. Thus, knowledge of measurement error distribution could provide lower total production cost.

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MATERIALS AND THE ENVIRONMENT

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MRS BULLETIN 1992年第3期17卷 26-26页

作者： WEISSMAN, SH SEKUTOWSKI, JC Process Optimization and Control Division Sandia National Laboratories Albuquerque USA Environmental and Materials Technology Department AT&T Bell Labs Princeton USA

We co-organized the first MRS technical symposium dealing with the environment at the 1991 Spring Meeting in Anaheim, California. Entitled “Environmentally Conscious Materials Processing,” the symposium dealt with waste minimization, pollution prevention, alternative materials and processes, recovery and recycling, and chemical sensors for process stream monitoring. This symposium captured much interest among the press and the materials community. Because of the growing interest in the environment, the MRS Bulletin asked us to guest edit this special issue that deals with the interrelated areas of materials science and the *** recent years, environmental concern has heightened in the United States and around the world. Public concern was greatly raised by increased environmental awareness incidents such as the accident in Bhopal, India, and the oil spill in Alaska by the Exxon Valdez. As a result, U.S. companies are more concerned with public acceptance of their operations. In addition, manufacturers have been subject to increasingly stringent environmental legislation. Federal, state, and local legislation currently regulate air emissions, water discharges, occupational exposure, and treatment and disposal of various hazardous chemicals. In addition, the Montreal Protocol, an international agreement signed by the United States, regulates the production and use of halogenated organic compounds now known to deplete the Earth's ozone layer. Associated with these stringent environmental regulations are increasing waste-associated costs. Waste disposal costs are increasing at an annual rate of about 10%.

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