{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T23:18:09Z","timestamp":1725664689965},"publisher-location":"Berlin, Heidelberg","reference-count":75,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540604723"},{"type":"electronic","value":"9783540475194"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1995]]},"DOI":"10.1007\/3-540-60472-3_15","type":"book-chapter","created":{"date-parts":[[2012,2,26]],"date-time":"2012-02-26T20:40:27Z","timestamp":1330288827000},"page":"294-321","source":"Crossref","is-referenced-by-count":21,"title":["Hybrid systems as Finsler manifolds: Finite state control as approximation to connections"],"prefix":"10.1007","author":[{"given":"Wolf","family":"Kohn","sequence":"first","affiliation":[]},{"given":"Anil","family":"Nerode","sequence":"additional","affiliation":[]},{"given":"Jeffrey B.","family":"Remmel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2005,5,31]]},"reference":[{"key":"15_CR1","unstructured":"Akhiezer, N. I.: The calculus of variations. Blaisdell. (1962)"},{"key":"15_CR2","unstructured":"Bejancu, A.: Finsler geometry and applications. Harwood. (1990)"},{"key":"15_CR3","doi-asserted-by":"crossref","unstructured":"Berger M., Gostiaux, B.: Differential geometry: manifolds, curves, surfaces. Springer Verlag. (1988)","DOI":"10.1007\/978-1-4612-1033-7"},{"key":"15_CR4","doi-asserted-by":"crossref","unstructured":"Bluman, G. W., Kumei, S.: Symmetries and differential equations. Springer-Verlag. (1989)","DOI":"10.1007\/978-1-4757-4307-4"},{"key":"15_CR5","unstructured":"Brockett, R., Millman, R. S., Sussman, H. J. (eds): Differential geometric control theory. Birkh\u00e4user. (1983)"},{"key":"15_CR6","unstructured":"Burke, W.: Applied differential geometry. Cambridge University Press. (1987)"},{"key":"15_CR7","unstructured":"Caratheodory, C.: Uber die discontinuierlichen L\u00f6sungen in der Variationsrechnung, Diss., G\u00f6ttingen, 71pp. (1904)"},{"key":"15_CR8","volume-title":"Variationsrechnung und Partialle Differentialgleichenngenerster Ordnung","author":"C. Caratheodory","year":"1935","unstructured":"Caratheodory, C.: Variationsrechnung und Partialle Differentialgleichenngenerster Ordnung. Teubner, Berlin. (1935) (Dover 2nd English edition, 1982)","edition":"Dover 2nd Engli"},{"key":"15_CR9","unstructured":"Cartan, E.: Les Espaces de Finsler. Actualities scientifiques et industrielle 79, Exposes de geometrie II (1934)"},{"key":"15_CR10","doi-asserted-by":"crossref","unstructured":"Crampin, M., Pirini, F.A.E.: Applicable Differential geometry. Cambridge University Press. (1986)","DOI":"10.1017\/CBO9780511623905"},{"key":"15_CR11","unstructured":"Ekeland, I.: Infinite dimensional optimization and convexity. University of Chicago Press. (1983)"},{"key":"15_CR12","doi-asserted-by":"crossref","unstructured":"Ekeland, I.: Convexity methods in Hamiltonian mechanics. Springer-Verlag. (1990)","DOI":"10.1007\/978-3-642-74331-3"},{"key":"15_CR13","unstructured":"Ekeland, I., Temam, R.: Convex analysis and variational problems. North-Holland. (1976)"},{"key":"15_CR14","doi-asserted-by":"crossref","unstructured":"Finsler, P.: \u00fcber Kurven und Fl\u00e4chen in allegmeinen R\u00e4umen. Diss. G\u00f6ttingen (1918) (republished by Verlag Birkh\u00e4user Basel, 1951)","DOI":"10.1007\/978-3-0348-4144-3"},{"key":"15_CR15","doi-asserted-by":"crossref","unstructured":"Friedman, A.: Stochastic Differential Equations I, II. Academic Press. (1975)","DOI":"10.1016\/B978-0-12-268201-8.50010-4"},{"key":"15_CR16","unstructured":"Cummings, B., James, J., Kohn, W., Nerode, A., Remmel, J.B., Shell, K.: Distributed MAHCA Cost-Benefit Analysis. MSI Tech. Report, Cornell University. (1995)"},{"key":"15_CR17","unstructured":"Ge, X., Kohn, W., Nerode, A., Remmel, J.B.: Algorithms for Chattering Approximations to Relaxed Optimal Control. MSI Tech. Report 95-1, Cornell University. (1995)"},{"key":"15_CR18","unstructured":"Gelfand, I. M., Fomin, S. V.: Calculus of variations. Prentice-Hall. 1963."},{"key":"15_CR19","doi-asserted-by":"crossref","unstructured":"Griffiths, P. A.: Exterior differential systems and the calculus of variations. Birkh\u00e4user. (1983)","DOI":"10.1007\/978-1-4615-8166-6"},{"key":"15_CR20","unstructured":"Grossman, R.L.: Managing persistent object stores of predicates. Oak Park Research Technical Report, Number 92-R1, May, 1992. (1992)"},{"key":"15_CR21","series-title":"Springer Lecture Notes in Computer Science","volume-title":"Hybrid Systems","year":"1993","unstructured":"Grossman, R.L., Nerode, A., Ravn, A., Rischel, H. (eds.): Hybrid Systems. Springer Lecture Notes in Computer Science, Springer-Verlag, Bonn. (1993)"},{"key":"15_CR22","doi-asserted-by":"crossref","unstructured":"Grossman, R.L., Valsamis, D., Qin, X.: Persistent stores and hybrid systems. Proceedings of the 32st IEEE Conference on Decision and Control, IEEE Press. (1993) 2298\u20132302","DOI":"10.1109\/CDC.1993.325607"},{"key":"15_CR23","doi-asserted-by":"crossref","unstructured":"Grossman, R.L., Larson, R.G.: An algebraic approach to hybrid systems. Journal of Theoretical Computer Science. (to appear)","DOI":"10.1016\/0304-3975(94)00146-A"},{"key":"15_CR24","unstructured":"Grossman, R.L., Nerode, A.: Quantum automata and hybrid systems. (in preparation)"},{"key":"15_CR25","volume-title":"Le\u00c7ons sur le calcul des variations","author":"J. Hadamard","year":"1910","unstructured":"Hadamard, J., Le\u00c7ons sur le calcul des variations. Hermann et Fils, Paris. (1910)"},{"key":"15_CR26","unstructured":"Hermann, R.: Geometry, Physics, and Systems. Marcel Dekker. (1973)"},{"key":"15_CR27","volume-title":"Ricci-Levi Civita's paper on Tensor Analysis","author":"R. Hermann","year":"1975","unstructured":"Hermann, R.: Ricci-Levi Civita's paper on Tensor Analysis. Math. Sciences Press, Brookline, Mass. (1975)"},{"key":"15_CR28","unstructured":"Hermann, R.: Differential geometry and the calculus of variations. Math. Sci. Press. (1977)"},{"key":"15_CR29","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1515\/crll.1905.129.63","volume":"129","author":"D. Hilbert","year":"1905","unstructured":"Hilbert, D.: \u00fcber das Dirichletsche Prinzip, J. reine angew. Math. Bd. 129 (1905) 63\u201367","journal-title":"J. reine angew. Math."},{"key":"15_CR30","unstructured":"Kinderlehrer, D., Stampacchia, G.: An introduction to variational inequalities. Academic Press. (1983)"},{"key":"15_CR31","first-page":"131","volume":"1","author":"W. Kohn","year":"1988","unstructured":"Kohn, W.: A declarative theory for rational controllers. Proceedings of the 27th IEEE CDC, Vol. 1. (1988) 131\u2013136.","journal-title":"Proceedings of the 27th IEEE CDC"},{"key":"15_CR32","unstructured":"Kohn, W.: Declarative hierarchical controllers. Proc. of the Workshop on Software Tools for Distributed Intelligent Control Systems, Pacifica, CA, July 17\u201319 (1990) 141\u2013163."},{"key":"15_CR33","unstructured":"Kohn, W.: Multiple agent inference in equational domains via Infinitesimal operators. Proc. of Application Specific Symbolic Techniques in High Performance Computing Environments, The Fields Institute, Oct. 17\u201320 (1993)"},{"key":"15_CR34","unstructured":"Kohn, W., Nerode, A.: An autonomous control theory: an overview. IEEE Symposium on Computer Aided Control System Design (March 17\u201319, 1992, Napa Valley, CA) (1992) 204\u2013210"},{"key":"15_CR35","series-title":"Springer Lecture Notes in Computer Science","volume-title":"Hybrid Systems","author":"W. Kohn","year":"1993","unstructured":"Kohn, W., Nerode, A.: Models for hybrid systems: automata, topologies, controllability and observability. in [GNRR93]. (1993)"},{"key":"15_CR36","unstructured":"Kohn, W., Nerode, A.: Multiple agent autonomous control. Proceedings of the 31st IEEE CDC. (1993) 2956\u20132966"},{"key":"15_CR37","doi-asserted-by":"crossref","unstructured":"Kohn, W., Nerode, A.: Multiple agent autonomous hybrid control systems. Logical Methods (Crossley,J., Remmel, J.B., Shore, R., Sweeder, M. eds.), Birkhauser. (1993)","DOI":"10.1007\/978-1-4612-0325-4_20"},{"key":"15_CR38","unstructured":"Kohn, W., Nerode, A., Remmel, J.B.: Agents in hybrid control. MSI Technical Report 93-101, Cornell University. (1993)"},{"key":"15_CR39","unstructured":"Kohn, W., Nerode, A., Remmel, J.B., Ge, X.: Multiple agent hybrid control: carrier manifolds and chattering approximations to optimal control. CDC94 (1994)"},{"key":"15_CR40","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0304-3975(94)00150-H","volume":"138","author":"W. Kohn","year":"1995","unstructured":"Kohn, W., Nerode, A., Remmel, J.B., Yakhnis, A.: Viability in hybrid systems. J. Theoretical Computer Science. 138 (1995) 141\u2013168","journal-title":"J. Theoretical Computer Science"},{"key":"15_CR41","unstructured":"Kohn, W., Nerode, A., Subrhamanian, V.S.: Constraint logic programming: hybrid control and logic as linear programming. MSI Technical Report 93-80, Cornell University. (1993) (to appear in CLP93 1995)"},{"key":"15_CR42","unstructured":"Levi-Civita, T.: Rendiconti del Circolo Matematico di Palermo, fascicolo XLII. (1917)"},{"key":"15_CR43","unstructured":"Levi-Civita, T.: The Absolute Differential Calculus. Blackie and Sons. (1926) (Dover Reprint. 1977)"},{"key":"15_CR44","unstructured":"Lu, J., Nerode, A., Remmel, J.B., Subrahmanian, V.S.: Toward a theory of hybrid knowledge bases. MSI Technical Report 93-14, Cornell University. (1993)"},{"key":"15_CR45","unstructured":"Lu, J., Ge, X., Kohn, W., Nerode, A., Coleman, N.: A Semi-autonomous multiagent decision model for a battlefield environment. MSI Technical Report, Oct. 1994, Cornell University. (1994)"},{"key":"15_CR46","volume-title":"Some Remarks on Geometric Mechanics. Report","author":"J. E. Marsden","year":"1993","unstructured":"Marsden, J. E.: Some Remarks on Geometric Mechanics. Report, Department of Mathematics, the University of California, Berkeley. (1993)"},{"issue":"no.1","key":"15_CR47","first-page":"4","volume":"1","author":"J. E. Marsden","year":"1991","unstructured":"Marsden, J. E., O'Reilly, O.M., Wicklin, F.J., Zombro, B.W.: Symmetry, Stability, Geometric Phases, and Mechanical Integrators. Part I: Non-Linear Science Today, Vol. 1, no. 1, (1991) 4\u201311: Part II: Non-Linear Science Today, Vol. 1, no. 2, (1991) 14\u201321","journal-title":"Part I: Non-Linear Science Today"},{"key":"15_CR48","volume-title":"Foundations of Finsler geometry and special Finsler spaces","author":"M. Matsumoto","year":"1986","unstructured":"Matsumoto, M.: Foundations of Finsler geometry and special Finsler spaces. Kaiseisha Press, Shigkan. (1986)"},{"key":"15_CR49","unstructured":"Nelson, E.: Tensor Analysis Princeton University Press. (1967)"},{"key":"15_CR50","volume-title":"Intermetrics Report","author":"A. Nerode","year":"1992","unstructured":"Nerode, A., James, J., Kohn, W.: Multiple agent declarative control architecture: A knowledge based system for reactive planning, scheduling and control in manufacturing systems. Intermetrics Report, Intermetrics, Bellevue, Wash., Nov. (1992)"},{"key":"15_CR51","volume-title":"Intermetrics Report","author":"A. Nerode","year":"1994","unstructured":"Nerode, A., James, J., Kohn, W.: Multiple Agent Hybrid Control Architecture: A \u03b5neric open architecture for incremental construction of reactive planning and scheduling. Intermetrics Report, Intermetrics, Bellevue, Wash., June (1994)"},{"key":"15_CR52","unstructured":"Nerode, A., James, J., Kohn, W.: Multiple agent reactive control of distributed interactive simulations. Proc. Army Workshop on Hybrid Systems and Distributed Simulation, Feb. 28\u2013March 1, (1994)"},{"key":"15_CR53","volume-title":"Intermetrics Report","author":"A. Nerode","year":"1994","unstructured":"Nerode, A., James, J., Kohn, W.: Multiple agent reactive control of wireless distributed multimedia communications networks for the digital battlefield. Intermetrics Report, Intermetrics, Bellevue, Wash., June (1994)"},{"key":"15_CR54","unstructured":"Nerode, A., James, J., Kohn, W., DeClaris, N.: Intelligent integration of medical models. Proc. IEEE Conference on Systems, Man, and Cybernetics, San Antonio, 1\u20136 Oct. (1994)"},{"key":"15_CR55","unstructured":"Nerode, A., James, J., Kohn, W., DeClaris, N.: Medical information systems via high performance computing and communications. Proc. IEEE Biomedical Engineering Symposium, Baltimore, MD, Nov. (1994)"},{"key":"15_CR56","unstructured":"Nerode, A., James, J., Kohn, W., Harbison, K., Agrawala, A.: A hybrid systems approach to computer aided control system design. Proc. Joint Symposium on Computer Aided Control System Design. Tucson AZ 7\u20139 March (1994)"},{"key":"15_CR57","unstructured":"Nerode, A., Lu, J., Subrahmanian, V.S.: Hybrid knowledge bases. IEEE Trans. on Knowledge and Data Engineering. (to appear)"},{"key":"15_CR58","unstructured":"Nerode, A., Remmel, J.B., Yakhnis, A.: Hybrid system games: Extraction of control automata and small topologies. MSI Technical Report 93-102, Cornell University. (1993)"},{"key":"15_CR59","unstructured":"Nerode, A., Remmel, J.B., Yakhnis, A.: Hybrid systems and continuous Sensing Games. 9th IEEE Conference on Intelligent Control, August 25\u201327, (1993)"},{"key":"15_CR60","unstructured":"Nerode, A.,Ge, X.: Effective Content of Relaxed Calculus of Variations: Semicontinuity, MSI Tech. Report, Feb. 1995, Cornell University. (1995)"},{"key":"15_CR61","unstructured":"Nerode, A., Yakhnis, A.: Modelling hybrid systems as games. CDC92. (1992) 2947\u20132952"},{"key":"15_CR62","unstructured":"Nerode, A., Yakhnis, A.: Control automata and fixed points of set-valued operators for discrete sensing hybrid systems. MSI Technical Report 93-105, Cornell University. (1993)"},{"key":"15_CR63","unstructured":"Nerode, A., Yakhnis, A.: An example of extraction of a finite control automaton and A. Nerode's AD-converter for a discrete sensing hybrid system. MSI Technical Report 93-104, Cornell University. (1993)"},{"key":"15_CR64","unstructured":"Nerode, A., Yakhnis, A.: Hybrid games and hybrid systems. MSI Technical Report 93-77, Cornell University. (1993)"},{"key":"15_CR65","doi-asserted-by":"crossref","unstructured":"Olver, P. J.: Applications of Lie groups to differential equations. Springer-Verlag. (1986)","DOI":"10.1007\/978-1-4684-0274-2"},{"key":"15_CR66","doi-asserted-by":"crossref","unstructured":"O'Neill, Barrett: Elementary Differential Geometry. Academic Press. (1966)","DOI":"10.1016\/B978-1-4832-3170-9.50011-7"},{"key":"15_CR67","unstructured":"Riemann, B.: \u00fcber die Hypothesen, welche der Geometriezugrunde liegen. (1854)"},{"key":"15_CR68","doi-asserted-by":"crossref","unstructured":"Rund, H.: The Differential Geometry of Finsler Spaces. Springer. (1959)","DOI":"10.1007\/978-3-642-51610-8"},{"key":"15_CR69","unstructured":"Rund, H.: The Hamilton Jacobi Theory. Van Nostrand. (1966)"},{"key":"15_CR70","unstructured":"Spivak, M.: Calculus on Manifolds. Benjamin. (1965)"},{"key":"15_CR71","unstructured":"Stokes, E.C.: Applications of the Covariant Derivative of Cartan in the Calculus of Variations. in Contributions to the Calculus of Variations, 1938\u20131941 (G A Bliss, L M Graves, M. R. Hestenes, W. T. Reid, eds.). The University of Chicago Press. (1942)"},{"key":"15_CR72","unstructured":"Torretti, R.: Relativity and Geometry. Pergamon. (1983)"},{"key":"15_CR73","doi-asserted-by":"crossref","unstructured":"Warga, J.: Optimal Control of Differential and Functional Equations. Academic Press. (1972)","DOI":"10.1016\/B978-0-12-735150-6.50011-7"},{"key":"15_CR74","unstructured":"Wren, F.L.: A New Theory of Parametric Problems in the Calculus of Variations. in Contributions to the Calculus of Variations. The University of Chicago Press. (1930)"},{"key":"15_CR75","volume-title":"Optimal Control Theory","author":"L.C. Young","year":"1980","unstructured":"Young, L.C.: Optimal Control Theory. Chelsea Pub. Co. N.Y. (1980)"}],"container-title":["Lecture Notes in Computer Science","Hybrid Systems II"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-60472-3_15.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T01:25:33Z","timestamp":1619573133000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-60472-3_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995]]},"ISBN":["9783540604723","9783540475194"],"references-count":75,"URL":"https:\/\/doi.org\/10.1007\/3-540-60472-3_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1995]]}}}