Abstract
Most of the real modern systems are complex, nonlinear, and large-scale. A natural approach for reducing the complexity of large scale systems places a hierarchical structure on the system architecture. In hierarchical control models, the notion of consistency is much important, as it ensures the implementation of high-level objectives by the lower level systems. In this work, we present a model for synthesis of hierarchically consistent control systems for complex nonlinear multidimensional and multicoupled dynamical systems, using invariant manifold theory.
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References
Mesarovic, M.D.: Theory of Hierarchical, Multilevel, Systems. In: Mathematics in Science and Engineering, vol. 68. Academic Press, New York (1970)
Girard, A., Lafferriere, G., Sastry, S.: Hierarchically Consistent Control Systems. IEEE Trans. Automatic Control 45, 1144–1160 (2000)
Lollini, P., Bondavalli, A., Di Giandomenico, F.: A Modeling Methodology for Hierarchical Control System and its Application. J. Braz. Comp. Soc. 10, 57–69 (2005)
Bagdasaryan, A.: Discrete Dynamic Simulation Models and Technique for Complex Control Systems. Simulation Modelling Practice and Theory 19, 1061–1087 (2011)
Bagdasaryan, A., Kim, T.-H.: Dynamic Simulation and Synthesis Technique for Complex Control Systems. In: Ślęzak, D., Kim, T.-h., Stoica, A., Kang, B.-H. (eds.) CA 2009. CCIS, vol. 65, pp. 15–27. Springer, Heidelberg (2009)
Bagdasaryan, A.G.: Mathematical and Computer Tools of Discrete Dynamic Modeling and Analysis of Complex Systems in Control Loop. Int. J. Math. Models Methods Appl. Sci. 2, 82–95 (2008)
Mahmoud, M.S.: Multilevel Systems Control and Applications: A Survey. IEEE Transactions on System, Man, and Cybernetics 7(3), 125–143 (1978)
Park, J., Obeysekera, J., VanZee, R.: Multilayer Control Hierarchy for Water Management Decisions in Integrated Hydrologic Simulation Model. Journal of Water Resources Planning and Management 133(2), 117–125 (2007)
Singh, M.G., Hindi, K.: A Multilevel Multilayer Framework for Manufacturing Control. Journal of Intelligent and Robotic Systems 4, 75–93 (1991)
Tatjewski, P.: Advanced Control and On-line Process Optimization in Multilayer Structures. Annual Reviews in Control 32, 71–85 (2008)
Boskovic, J.D., Prasanth, R., Mehra, R.K.: A Multilayer Control Architecture for Unmanned Aerial Vehicles. In: Proc. of the American Control Conference, vol. 3, pp. 1825–1830 (2002)
Josić, K.: Invariant Manifolds and Synchronization of Coupled Dynamical Systems. Phys. Rev. Lett. 80, 3053–3056 (1998)
Kwong, C.P., Zheng, Y.-K.: Aggregation on Manifolds. Int. J. Systems Sci. 17(4), 581–589 (1986)
Liu, Y.: The Invariant Manifold Method and the Controllability of Nonlinear Control System. Appl. Math. Mech. 11(21), 1320–1330 (2010)
Karagiannis, D., Astolfi, A.: Non-linear and Adaptive Flight Control of Autonomous Aircraft Using Invariant Manifolds. J. Aerospace Engineering 224(4), 403–415 (2010)
Yu, X., Chen, G., Xia, Y., Song, Y., Cao, Z.: An Invariant-Manifold-Based Method for Chaos Control. IEEE Trans. Circuits and Systems 48(8), 930–937 (2001)
Tian, Y.-P., Yu, X.: Adaptive Control of Chaotic Dynamical Systems Using Invariant Manifold Approach. IEEE Trans. Circuits and Systems 47(10), 1537–1542 (2000)
Astolfi, A., Ortega, R.: Invariant Manifolds, Asymptotic Immersion and the (Adaptive) Stabilization of Nonlinear Systems. In: Zinober, A., Owens, D. (eds.) Nonlinear and Adaptive Control. LNCIS, vol. 281, pp. 1–20. Springer, Heidelberg (2003)
Zhong, H., Wonham, W.M.: On the Consistency of Hierarchical Supervision in Discrete-Event Systems. IEEE Trans. Automatic Control 35, 1125–1134 (1990)
Nijmeijer, H., van der Schaft, A.: Nonlinear Dynamical Control Systems. Springer, New York (1990)
Jurdjevic, V.: Geometric Control Theory. Cambridge University Press (1997)
Dubrovin, B.A., Fomenko, A.T., Novikov, S.P.: Modern Geometry. Springer, New York (1985)
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Bagdasaryan, A.G., Kim, Th. (2011). A Model of Hierarchically Consistent Control of Nonlinear Dynamical Systems. In: Kim, Th., Adeli, H., Stoica, A., Kang, BH. (eds) Control and Automation, and Energy System Engineering. CES3 CA 2011 2011. Communications in Computer and Information Science, vol 256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-26010-0_7
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DOI: https://doi.org/10.1007/978-3-642-26010-0_7
Publisher Name: Springer, Berlin, Heidelberg
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