Singular controls in optimal collision avoidance for participants with unequal linear speeds

This article studies optimal collision avoidance strategies for participants with unequal linear speeds in a planar close proximity encounter. It is known that bang-bang collision avoidance strategies are optimal for encounters of participants with equal linear speeds. However, as shown recently, bang-bang collision avoidance strategies are not necessarily optimal when the linear speeds of the participants are not equal. We study the structure of optimal singular controls for collision avoidance of participants with unequal linear speeds, but equal turn capabilities. We prove that both controls cannot be singular simultaneously, and that the only possible singular control is a zero control. We use several optimization techniques compute optimal state, control and adjoint variables. Numerical simulations suggest that a zero control strategy only exists for a slower participant and that, at most, one switching from a bang-bang to a singular control occurs. Different types of structural changes of the controls with change in the initial conditions are identified via the numerical simulations. References U. Ledzewicz, H. Maurer, and H. Schattler, Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy, Mathematical Biosciences and Engineering, 8, 2011, 307--328. doi:10.3934/mbe.2011.8.307 U. Ledzewicz, H. Maurer, H. Schattler, On optimal delivery of combination therapy for tumors, Mathematical Biosciences, 22, 2009, 13--26. doi:10.1016/j.mbs.2009.08.004 H. Maurer, C. Buskens, J.-H. R. Kim, Y. Kaya, Optimization methods for the verification of second-order sufficient conditions for bang-bang controls. Optimal Control Applications and Methods, 26, 2005, 129--156. doi:10.1002/oca.756 A. W. Merz, Optimal aircraft collision avoidance. Proceedings of the Joint Automatic Control Conf., Paper 15-3, pages 449--454, 1973. A. W. Merz, Optimal evasive manoeuvres in maritime collision avoidance. Navigation, 20(2), 1973, 144--152. T. Tarnopolskaya, and N. L. Fulton, Optimal cooperative collision avoidance strategy for coplanar encounter: Merz's solution revisited, J. Optim. Theory Appl., 140 (2), 2009, 355--375. doi:10.1007/s10957-008-9452-9 T. Tarnopolskaya, and N. L. Fulton, Parametric behavior of the optimal control solution for collision avoidance in a close proximity encounter, In R. S. Andersson et al., editors, 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, pages 425--431, 2009. http://www.mssanz.org.au/modsim09/A7/tarnopolskaya_A7.pdf T. Tarnopolskaya, and N. L. Fulton, Synthesis of optimal control for cooperative collision avoidance for aircraft (ships) with unequal turn capabilities, J. Optim. Theory Appl., 144 (2), 2010, 367--390. doi:10.1007/s10957-009-9597-1 T. Tarnopolskaya, and N. L. Fulton, Dispersal Curves for Optimal Collision Avoidance in a Close Proximity Encounter: a Case of Participants with Unequal Turn Rates, Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2010, WCE 2010, pages 1789--1794. IAENG, 2010. http://www.iaeng.org/publication/WCE2010/WCE2010_pp1789-1794.pdf T. Tarnopolskaya, and N. L. Fulton, Non-unique Optimal Collision Avoidance Strategies for Coplanar Encounter of Participants with Unequal Turn Capabilities, IAENG International Journal of Applied Mathematics, 40 (4), 2010, 289--296. http://www.iaeng.org/IJAM/issues_v40/issue_4/IJAM_40_4_10.pdf T. Tarnopolskaya, and N. L. Fulton, Synthesis of Optimal Control for Cooperative Collision Avoidance in a Close Proximity Encounter: Special Cases, Proceedings of the 18th World Congress of the International Federation of Automatic Control (IFAC), Milan (Italy), August 28--September 2, 2011, 18(1), 9775--9781. T. Tarnopolskaya, N. L. Fulton, and H. Maurer, Synthesis of optimal bang-bang control for cooperative collision avoidance for aircraft (ships) with unequal linear speeds. J. Optim. Theory Appl., to appear, 2012

Proceedings of the NASA Conference on Space Telerobotics, volume 3

The theme of the Conference was man-machine collaboration in space. The Conference provided a forum for researchers and engineers to exchange ideas on the research and development required for application of telerobotics technology to the space systems planned for the 1990s and beyond. The Conference: (1) provided a view of current NASA telerobotic research and development; (2) stimulated technical exchange on man-machine systems, manipulator control, machine sensing, machine intelligence, concurrent computation, and system architectures; and (3) identified important unsolved problems of current interest which can be dealt with by future research

The influence of mood and cognitive load on driver performance: using multiple measures to assess safety

Emotions and moods are an inevitable part of human life. Previous research suggests that positive and negative moods affect human performance in many aspects: decision making, perception, reasoning and memory. The influence of mood on drivers’ behaviour has been studied to a less extent and mainly with respect to negative emotions. The studies reported in this thesis are based on psychological theories regarding the differences in the effects of positive and negative moods on information processing and mind wandering. The thesis describes two studies: a desktop study and a driving simulator study, which measure drivers’ responses to the actions of other traffic, their observational patterns and driving behaviours in a variety of scenarios. The effects of neutral, happy, sad and angry moods were studied. The simulator study also investigated possible ways to disconnect drivers’ minds from mood induced mind wandering by using different types of cognitive load. The results suggest that mood valence and arousal have different effects on driving safety, with negative moods resulting in the most dangerous driving. In order to draw conclusions about the effect of mood, a combination of multiple measures (e.g. glance patterns, driving performance and drivers’ physiological measures) should be analysed. The results also suggest that some amount of cognitive load, applied while driving, can have a positive effect on drivers’ attention. Further research is needed to establish the amount and type of the cognitive load necessary to improve drivers’ ability to maintain their attention on the driving task. Studies with a larger number of participants and field studies are needed to validate the findings. It is suggested that the findings are used to improve in-car assistance systems able to both detect the harmful effects of a driver’s emotional state and re-direct their attention to the primary task of driving

Aeronautical engineering: A continuing bibliography (supplement 152)

The bibliography lists 338 reports, articles and other documents introduced into the NASA scientific and technical information system in August 1982

Nineteenth Annual Conference on Manual Control

No abstract availabl

Applicable Solutions in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare

Joint University Program for Air Transportation Research, 1989-1990

Research conducted during the academic year 1989-90 under the NASA/FAA sponsored Joint University Program for Air Transportation research is discussed. Completed works, status reports and annotated bibliographies are presented for research topics, which include navigation, guidance and control theory and practice, aircraft performance, human factors, and expert systems concepts applied to airport operations. An overview of the year's activities for each university is also presented

Aeronautical engineering. A continuing bibliography with indexes, supplement 114

This bibliography lists 394 reports, articles, and other documents introduced into the NASA scientific and technical information system in September 1979