Abstract
This chapter discusses problems dealing with cooperative control of multiple agents moving in a region. An appropriate search strategy for the whole system can be embodied: hierarchical, coordinated, or cooperative. Geometrical and computational aspects of many-target search problems are considered. Nonlinear and bilinear processes of search for moving objects are proposed. Search problems of ecological danger objects and detection of biological and chemical agents using multi-spectral information are also considered.
Multiagent coordination problems are studied in detail. This problem is addressed for a class of targets for which control Lyapunov functions can be derived. We describe such a multiagent system by a hierarchical structure, which can be simplified using a fiber bundle. Then, using geometrical techniques, we study controllability, observability, and optimality problems. In addition, we also consider a cooperative problem when the agents motions must satisfy a separation constraint throughout the encounter to be conflict-free. A classification of maneuvers based on different commutative diagrams is introduced using their fiber bundle representation. In the case of two agents, these optimality conditions allow us to construct optimal maneuvers geometrically.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cressman, R.: Evolutionary Dynamics and Extensive Form Games. MIT Press, Cambridge (2003)
Kalman, R., Falb, S., Arbib, M.: Topics in Mathematical System Theory. McGraw-Hill, New York (1969)
Yatsenko, V.: Control systems and fiber bundles. Avtomatika 5, 25–28 (1985)
Butkovskiy, A., Samoilenko, Y.: Control of Quantum-Mechanical Processes and Systems. Kluwer Academic Publishers, Dordrecht (1990)
Chikrii, A.: Differential games with multiple pursuers. of the Banach International Mathematical Centre 14, 81–107 (1985)
Chikrii, A.: Conflict-Controlled Processes. Kluwer Academic Publishers, Dordrecht (1997)
Gall, S.: Search Games. Academic Press, London (1980)
Larrie, F.: Ships and Science: The Birth of Naval Architecture in the Scientific Revolution, pp. 1600–1800. MIT Press, Cambridge (2007)
Krasovskii, A., Subbotin, A.: Game-theoretical control problems. Springer, Heidelberg (1988)
Imado, F.: The features of optimal avoidance in two dimensional pursuit-evasion dynamic games. Technical report, Information, Technology, and Management (ITEM) (2002)
Albus, J., Meystel, A., Chikrii, A., Belousov, A.: Analytic method for solution of the game problem of soft landing for moving objects. Cybernetics and Systems Analysis 37(1), 75–91 (2001)
Mizutani, A., Chahl, J., Srinivasan, M.: Insect behavior: Motion camouflage in dragonflies. Nature 423(6940), 604 (2003)
Matichin, A., Chikriy, A.: Motion camouflage in differential games of pursuit. Journal of Automation and Information Science 37(3), 1–5 (2003)
Matichin, I., Chikriy, A.: Motion camouflage in differential games of pursuit ((in Russian)). Journal of Automation and Information Science 37(3), 1–5 (2005)
Koopman, B.: The theory of search. Operations Research 4, 324–346 (1956)
Stone, L.: Theory of optimal search. Academic Press, London (1975)
Hellman, O.: Optimization of search for an object drifting in outer space. Journal of Spacecraft and Rockets 7(7), 886–889 (1970)
Hellman, O.: On the optimal search for a randomly moving target. SIAM Journal on Applied Mathematics 22(4), 545–552 (1972)
Pardalos, P., Yatsenko, V., Grundel, D.: Nonlinear dynamics of sea clutter and detection of small targets. In: Pardalos, P., Murphey, R., Butenko, S. (eds.) Recent Developments in Cooperative Control and Optimization, pp. 407–426. Kluwer Academic Publishers, Dordrecht (2004)
Van der Shaft, A.: Controllability and observability for affine nonlinear hamiltonian systems. IEEE Transactions on Automatic Control 27, 490–494 (1982)
Van der Shaft, A.: Equations of motion for Hamiltonian systems with constraints. Journal of Physics A 11, 3271–3277 (1987)
Arnold, V.: Mathematical Methods of Classical Methods. Springer, Heidelberg (1983)
Samoilenko, Y.: Reduction to the elementary cell of the linear system with discrete symmetry. Cybernetics and Computer Techniques 3, 48–53 (1970)
Krener, A.: On the equivalence of control systems and the linearization of nonlinear systems. SIAM Journal of Control 11, 670–676 (1973)
Griffiths, P., Coates, J., Helgason, S.: Exterior Differential Systems and the Calculus of Variations. Birkhäuser, Basel (1983)
Marcus, L.: General theory of global dynamics. In: Mayne, D., Brockett, R.W. (eds.) Geometric Methods in System Theory, pp. 150–158 (1973)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yatsenko, V.A., Hirsch, M.J., Pardalos, P.M. (2007). Cooperative Control of Multiple Agents and Search Strategy. In: Pardalos, P.M., Murphey, R., Grundel, D., Hirsch, M.J. (eds) Advances in Cooperative Control and Optimization. Lecture Notes in Control and Information Sciences, vol 369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74356-9_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-74356-9_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74354-5
Online ISBN: 978-3-540-74356-9
eBook Packages: EngineeringEngineering (R0)