Toward Global Complex Systems Control The Autonomous Intelligence Challenge

Journal: Journal of Autonomous Intelligence DOI: 10.32629/jai.v2i1.38

Michel Cotsaftis

Director of Undergraduate Scientific Research Program ECE Paris


Complex systems are the emerging new scientific frontier with modern technology advance and new parametric domains study in natural systems. An important challenge is, contrary to classical systems studied so far, the great difficulty in predicting their future behaviour from initial time because, by their very structure, interactions strength between system components is shielding completely their specific individual features. Independent of clear existence of strict laws complex systems are obeying like classical systems, it is however possible today to develop methods allowing to handle dynamical properties of such systems and to master their evolution. So the methods should be imperatively adapted to representing system self organization when becoming complex. This rests upon the new paradigm of passing from classical trajectory space to more abstract trajectory manifolds associated to natural system invariants characterizing complex system dynamics. The methods are basically of qualitative nature, independent of system state space dimension and, because of its generic impreciseness, privileging robustness to compensate for not well known system parameters and functional variations. This points toward the importance of control approach for complex system study in adequate function spaces, the more as for industrial applications there is now evidence that transforming a complicated man made system into a complex one is extremely beneficial for overall performance improvement. But this last step requires larger intelligence delegation to the system requiring more autonomy for exploiting its full potential. A well defined, meaningful and explicit control law should be set by using equivalence classes within which system dynamics are forced to stay, so that a complex system described in very general terms can behave in a prescribed way for fixed system parameters value. Along the line traced by Nature for living creatures, the delegation is expressed at lower level by a change from regular trajectory space control to task space control following system reassessment into its complex stage imposed by the high level of interactions between system constitutive components. Aspects of this situation with coordinated action on both power and information fluxes are handled in a new and explicit control structure derived from application of Fixed Point Theorem which turns out to better perform than (also explicit) extension of Popov criterion to more general nonlinear monotonically upper bounded potentials bounding system dynamics discussed here. An interesting observation is that when correctly amended as proposed here, complex systems are not as commonly believed a counterexample to reductionism so strongly influential in Science with Cartesian method supposedly only valid for complicated systems.


[1] W. Bolton : Mechatronics, 2nd ed., Addison-Wesley, UK, 1999
[2] J. Secher : Paradigm Shift in Robot Based Automation through Industrial IT, Proc. 32nd ISR, Vol.II, p.705, Seoul, Korea, 2001
[3] T.B. Sheridan : Telerobotics, Automation and Human Supervisory Control, The MIT Press, 1992.
[4] B.B Kadomtsev : Self Organization and Transport in Tokamak Plasma, Plasma Phys. and Nucl. Fus., Vol.34(13), pp.1931-1938, 1992; P. Bautay, I.M. Janosi : Self Organization and Anomalous Diffusion, Physica A, Vol.185(1-4), p.11-18,1992; S.Camazine, J.L. Deneubourg, N.R. Franks, J. Sneyd, G. Theraulaz, E. Bonabeau : Self organization in Biological Systems, Princeton Univ. Press, Princeton, New-Jersey, 2002
[5] R.C. Hilborn : Chaos and Nonlinear Dynamics, Oxford Univ. Press, Oxford, UK, 1994; T. Kapitaniak : Chaos for Engineers : Theory, Applications and Control, Springer, Berlin, 1998; I. Prigogine : Les Lois du Chaos, Nouvelle Bibliothèque Scientifique, Flammarion, Paris, 1993; Yu.L. Klimontovitch : Criteria for Self Organization, Chaos, Solitons & Fractals, Vol.5(10), pp.1985-1995, 2002
[6] A. Goriely : Integrability and Nonintegrability of Dynamical Systems, World Scientific Publ., 2001; M. Tabor : Chaos and Integrability in Nonlinear Dynamics, an Introduction, Wiley and Sons, New-York, 1989
[7] P.J. Antsaklis, K.M. Passino : An Introduction to Intelligent and Autonomous Control, Kluwer Acad. Publ., Norwell, MA, 1993; L.X. Wang : Adaptive Fuzzy Systems and Control : Design and Stability Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1994; B. Kosko :, Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence. Englewood Cliffs, NJ: Prentice-Hall, 1991; D.A. White, D.A. Sofge, eds : Handbook of Intelligent Control : Neural, Fuzzy and Adaptive Approaches, Van Nostrand-Reinhold, New-York, 1992; D. Fogel : Evolutionary Computation : Toward a New Philosophy of Machine Intelligence, IEEE Press, Wiley Interscience, New York, 1995; 3rd edition, 2006; M. Brown, C. Harris : Neuro Fuzzy Adaptive Modeling and Control, Prentice Hall, Englewood Cliffs, NJ, 1994
[8] B. Kosko : Global Stability of Generalized Additive Fuzzy Systems, IEEE Trans. on Systems, Man, and Cybernetics, Part C, Vol.28(3), p.441, 1998
[9] M. Cotsaftis : Recent Advances in Control of Complex Systems, Survey Lecture, Proceedings ESDA'96, Montpellier, France, ASME, Vol.I, p.1, 1996
[10] M. Cotsaftis : Vision Limitation for Robot Deformation Control, Proc. 5th Intern. Conf. on Mechatronics and Machine Vision in Practice (M2VIP), Nanjing, China, p.393, 1998; M. Cotsaftis : Application of Energy Conservation to Control of Deformable Systems, Proceedings 3rd Workshop on Systems Science and its Application, Beidaihe, China, p.42, 1998
[11] 11-H.C. von Baeyer : Maxwell’s Demon, Random House, 1998
[12] H.L. Trentelman, A.A. Stoorvogel, M. Hautus : Control Theory of Linear Systems, Lecture Notes at Eindhoven Univ.,; E.D. Sontag, Mathematical Control Theory Deterministic Finite Dimensional Systems, 2nd ed., Springer, New York, 1998; J. Doyle, B. Francis, A. Tannenbaum : Feedback Control Theory, McMillan, 1990; G.F. Franklin, D. Powell : Feedback Control of Dynamic Systems, 3rd ed., Addison-Wesley, 1994; B. Ross Barmish : New Tools for Robustness in Linear Systems, Macmillan, 1994; A.L.Fradkov, I.V. Miroshnik, V.O. Nikiforov : Nonlinear and Adaptive Control of Complex Systems, Kluwer Acad. Publ., Dordrecht, the Netherlands, 1999; S. Arimoto : Control Theory of Nonlinear Mechanical Systems : a Passivity Based and Circuit Theoretic Approach, Oxford Univ. Press, Oxford, UK, 1996; K.J. Astrom : Control of Complex Systems, Springer, Berlin, 2000
[13] S. Nolfi, D. Floreano : Evolutionary Robotics : the Biology, Intelligence and Technology of Self-Organizing Machines, The MIT Press, Cambridge, Mass., 2000; Y. Kondratoff, R.S. Michalski : Machine Learning : An Artificial Intelligence Approach, Morgan Kaufman Publ., CA, 1990
[14] M. Cotsaftis : On the Definition of Task Oriented Intelligent Control, Proceedings ISIC’02 Conf., Vancouver, Oct. 27-30, 2002
[15] C.A. Desoer, M. Vidyasagar : Feedback Systems : Input-Output Properties, Acad. Press, New-York, 1975; R. Dorf : Modern Control Theory, 7th ed., Addison-Wesley, 1997; F.W. Fairman : Linear Control Theory, Wiley, New York, 1998; J.R. Leigh : Functional Analysis and Linear Control Theory, Dover, New York, 2007; L. Schimansky-Geier, B. Fiedler, J. Kurths, E. Scholl : Analysis and Control of Complex Nonlinear Processes in Physics, Chemistry and Biology, Worldscience Publ;, Singapore, 2010; S.P. Banks : State Space and Frequency Domain Methods in the Control of Distributed Parameter Systems, Peter Peregrinus Ltd., London, 1983; R.C. Dorf, R.H. Bishop : Modern Control Systems, Addison-Wesley, Reading, Mass, 1995; B. Friedland : Advanced Control System Design, Prentice Hall, Englewodd Cliffs, N.J., 1996; T. Glad, L. Ljung : Control Theory : Multi-variable and Nonlinear Methods, Taylor and Francis, London, 2000; J.W. Helton, M.R. James : Extending H1 Control to Nonlinear Systems, SIAM, Frontiers in Appl. Sci., 1999
[16] W. Ebeling : Entropy and Information in Processes of Self Organization : Uncertainty and Predictability, Physica A, Vol.194(1-4), pp.563-575, 1993; S. Kauffman : At Home in the Universe : the Search for Laws of Self organization and Complexity, Oxford Univ. Press, New-York, 1993; G. Nicolis, I. Prigogine : Self Organization in Non Equilibrium Systems, Wiley, New-York, 1977; Yu.L. Klimontovich : Entropy, Information, and Criteria of Order in Open Systems, Nonlinear Phenomena in Complex Systems, Vol.2(4), pp.1-25, 1999; R. Badii and A. Politi : Complexity: Hierarchical structures and scaling in physics, Cambridge University Press, Cambridge, Mass., 1997; B. Goodwin : How the Leopard Changed Its Spots: The Evolution of Complexity, Weidenfield and Nicholson, London, 1994; S. Johnson : Emergence, Penguin, New-York, 2001; S. Wolfram : Cellular Automata and Complexity, Collected Papers, Addison-Wesley, 1994; F.E. Yates, ed : Self-Organizing Systems: The Emergence of Order, Plenum Press, 1987; R.K. Standish : On Complexity and Emergence, Complexity International, Vol.9, pp.1-6, 2004; B. Cohen, W.T. Hartwood, M.I. Jackson : The Specification of Complex Systems, Addison-Wesley, Reading, Mass, 1986
[17] D. Kondepudi, I. Prigogine : Modern Thermodynamics : from Heat Engines to Dissipative Structures, J. Wiley and Sons, NY, 1997; S. Oyama : The Ontogeny of Information: Developmental Systems and Evolution, Cambridge Univ. Press, Cambridge, Mass., 1986; I. Prigogine, I. Stengers : The End of Certainty, Time, Chaos, the New Laws of Nature, Free Press, 1997.
[18] S.Y. Anyang : Foundations of Complex System Theories in Economics, Evolutionnary Biology and Statistical Physics, Cambridge Univ. Press, Cambridge, Mass., 1998; G. Nicolis, I. Prigogine : Exploring Complexity : an Introduction, W.H. Freeman and Co, NY, 1989; R. Serra, M. Andretta, M. Compiani, G. Zanarini : Introduction to the Physics of Complex Systems (the Mesoscopic Approach to Fluctuations, Nonlinearity and Self-Organization), Pergamon Press, 1986; R. Feistel, W. Ebeling : Evolution of Complex Systems, Kluver, Dordrecht, 1989; H. Haken : Information and Self-Organization, Springer, Berlin, 1988; M. Gell-Mann : The Quark and the Jaguar - Adventures in the simple and the complex, Little, Brown & Company, New-York, 1994; G. Nicolis, I. Prigogine : A la Rencontre du Complexe, PUF, Paris, 1992; P. Erdi : Complexity Explained, Springer, Berlin, 2007; G. Parisi : Complex Systems : a Physicist’s Viewpoint, Internet arxiv:cond-mat/0205297; C.R. Shalizi : Methods and Techniques of Complex Systems Science : an Overview, Internet arxiv:nlin.AO/0307015; M. Cotsaftis : Understanding Complex Systems – A Survey of Phenomenological, Physical and Structural Approaches, Proc. ICCSA Conf. (International Conference on Complex Systems and Applications), Le Havre, June 29-July 03, 2009
[19] M. Cotsaftis : An Emergence Principle for Complex Systems, Lecture Notes of the Inst. for Computer Sci. Social Informatics and Telecom. Engin., Part I, Vol.4, pp.1105-1117, Complex Sci. Ser., Springer, Berlin, 2009
[20] M. Cotsaftis : Complexity, Emergence and Irreversibility, Survey Lecture at EPNADS 2011, Vienna, Sept.12-16, 2011
[21] G. Nicolis : Dynamics of Hierarchical Systems, Springer, Berlin, 1986; K. Kelly : Out of Control: The New Biology of Machines, Social Systems and the Economic World, Addision-Wesley, 1994
[22] S. Chandrasekhar : Stochastic Problems in Physics and Astronomy, Rev. Mod. Phys., Vol.15(1), pp.1-89, 1943
[23] M. Cotsaftis : Comportement et Contrôle des Systèmes Complexes, Diderot, Paris, 1997 
[24] Recall that the simplest trajectory functional is the potential (the Lagrangian in conservative case) from which trajectories are defined as zeros of its functional derivative. It directly represents the system invariant when, in fully complex case, there remains only one invariant, as shown by elementary example of temperature in Thermodynamics; E. Cartan : Leçons sur les Invariants Intégraux, Hermann, Paris, 1958; A.N. Gorban, I.V. Karlin : Invariant Manifolds for Physical and Chemical Kinetics, Lecture Notes in Physics, Vol.660, Springer, Berlin/Heidelberg, 2005
[25] D.R. Smart : Fixed Point Theorems, Cambridge Univ. Press, Mass., 1980; W. Takahashi : Nonlinear Functional Analysis - Fixed Point Theory and its Applications, Yokohama Publ., Japan, 2000; T.H. Jiang : Fixed-Point Theory, Springer-Verlag, New-York, 1985; J. Dugundji, A. Granas : Fixed-Point Theory, Vol.I, Polish Scientific Publ., Warsaw, 1982; K. Deimling : Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985
[26] H. Poincaré : Les Méthodes Nouvelles de la Mécanique Céleste, 3 Vol., Gauthier-Villars, Paris, 1892-1899 ; A.M. Lyapounov : Le Problème Général de la Stabilité du Mouvement, Ann. Fac. Sciences Toulouse, 1907; J.P. La Salle, S. Lefschetz : Stability by Lyapounov Direct Method with Applications, Acad. Press, New-York, 1961; V.I. Zubov : Methods of A.M. Lyapounov and their Applications, Noordhoff, Groningen, Holland, 1964
[27] G.A. Leonov, I.V. Ponomarenko, V.B. Smirnova : Frequency Domain Methods for Nonlinear Analysis : Theory and Applications, World Scientific Publ., Singapore, 1996; V.M. Popov : Hyperstability of Automatic Control Systems, Springer-Verlag, New-York, 1973
[28] M. Cotsaftis : Popov Criterion Revisited for Other Nonlinear Systems, Proc. ISIC 03 (Intern. Symp. on Intelligent Control), Oct 5-8, Houston, 2003; M. Cotsaftis : Extended Popov Criterion vs. Fixed Point Theorem for Complex Non Linear Systems, Proc. SIAM Conf. on Mathematics for Industry, Detroit, MI, 22-24 Oct., 2005
[29] M. Buss, H. Hashimoto : Information and Power Flows during Skill Acquisition for the Intelligent Assisting System, Proc. 1993 IEEE/RSJ Intern. Conf. on Intelligent Robots and Systems, Yokohama, Japan, Vol.1, p.25, 1993; H. Kazerooni : Human Robot Interaction via the Transfer of Power and Information Signals, IEEE Trans. on SMC, Vol20(2), pp.450-463, 1990
[30] K. Zhou, J.C. Doyle, K. Glover : Robust and Optimal Control, Prentice-Hall, Englewood Cliffs, NJ, 1996; G.E. Dullerud, F. Paganini : A Course in Robust Control Theory : a Convex Approach, Springer-Verlag, New-York, 2000; A. Feintuch : Robust Control Theory in Hilbert Space, Springer-Verlag, New-York, 1988; R.S. Sanchez-Pena, M. Sznaier : Robust Systems, Theory and Applications, Wiley, New-York, 1998
[31] T. Sakaki, Y. Inoue, S. Tachi : “Tele-existence Virtual Dynamic Display Using Impedance Scaling with Physical Similarity”, Proc. 1993 JSME Intern. Conf. on Advanced Mechatronics, Tokyo, Japan, p.127, 1994
[32] M. Cotsaftis : On Definition of Task Oriented System Intelligence, Proc. PerMIS’00 Workshop, Aug. 14-16, NIST, Washington DC, 2000
[33] E. Zeidler : Nonlinear Functional Analysis and its Applications, Vol.I, Springer-Verlag, New-York, 1986
[34] M. Cotsaftis : Exponentially Stable and Robust Control for Dynamical Systems, Proceedings 1999 IEEE Hong-Kong Symposium on Robotics and Control, Vol.II, p.623, 1999
[35] M. Cotsaftis : Robust Asymptotically Stable Control for Unknown Robotic Systems, Proceedings 1998 Symposium on ISSPR, Hong Kong, Vol.I, p.267, 1998
[36] M. Cotsaftis : From Trajectory Control to Task Control – Emergence of Self-organization in Complex Systems, Proc. EPNADS’05 Conf., 24-28 Sept. 2005, Springer-Verlag, 2006
[37] A.M.A. Youssef, H.A. Elmaraghy : Optimal Configuration Selection for Reconfigurable Manufacturing Systems, Intern. J. Flexible Manufacturing, Vol.19(2), pp.67-106, 2007; R.T. Marler, J.S. Aurora : Survey of Multi-Objective Optimization Methods for Engineering, Structural and Multidisciplinary Optimization, Vol.26(6), pp.369-395, 2004
[38] E. Saarinen, R.P. Hamalainen, eds : Essays on Systems Intelligence, Systems Analysis Lab. Report, Aalto Univ., 2010; N. Avgoustinov : Modeling in Mechanical Engineering and Mechatronics : Towards Autonomous Intelligent Software Models, Springer-Verlag, Berlin, 2007; J. H.E. Cartwright, A.L. Mackay : Beyond Crystals : the Dialectic of Materials and Information, : 1207.3997, submitted to J. Royal Soc.
[39] S. Martin, P. Minet, L. George : End-to-end response Time with Fixed Priority Scheduling : Trajectory Approach vs. Holistic Approach, International J. of Communication Systems, Wiley, Vol.18(1), p.1-95, 2005; M. Cotsaftis : High Precision Robust Dynamical Positioning Controller Design for Compliant System, Rept LTME/ECE, 1998
[40] M. Cotsaftis : A Further Step toward System Autonomy and Intelligence, Proc. 4th AISM (Asian Intern. Symp. On Mechatronics), Singapore, Dec. 15-18, 2010
[41] Globus Project.; Niek J. E. Wijngaards, B. J. Overeinder, M. van Steen, F.M.T. Brazier : Supporting Internet-Scale Multi-agent Systems. Data Knowledge Engineering, 41(2-3):229–245, 2002; I. Foster, C. Kesselman, S. Tuecke., The Anatomy of the Grid: Enabling Scalable Virtual Organizations, International J. Supercomputer Applications, 15(3), p.29, 2001; V. Bharadwaj, D. Ghose, V. Mani, T.G. Robertazzi : Scheduling Divisible Loads in Parallel and Distributed Systems, IEEE Computer Society Press, Los Alamitos CA, 09/1996;
[42] R. Albert, A-L Barabasi : Statistical Mechanics of Complex Networks, Rev. of Modern Phys., Vol.74, p.47, 2002; R.C. Arkin, T. Bulch : Cooperative Multi-agent Robotic Systems, 1997; D. Armbruster, K. Kaneko, A.S. Mikhailov : Networks of Interacting Machines, World Scientific Lecture Notes in Complex Systems, Vol.3, Singapore, 2005; A. Asama and Al., Eds., Distributed Autonomous Robotic Systems, Springer-Verlag, Part I, 1994, Part II, 1996; J. Yick, B. Mukherjee, D. Ghosal : Wireless Sensor Network Survey, Computer Networks: The International J.l of Computer and Telecom. Networking, Vol. 52(12), pp. 2292-2330, 2008
[43] M. Elhawary, Z. Haas : Energy-Efficient Protocol for Cooperative Networks, IEEE/ACM Trans. on Networking, Vol. 19(2), pp. 561-574, 2011; H. Sarma, A. Kar, R. Mall : Energy Efficient Communication Protocol for a Mobile Wireless Sensor Network System, International J. Computer Science and Network Security, Vol. 9(1), pp. 386-394, 2009; V. Rajendran, K. Obraczka, J. Aceves : Energy-Efficient, Collision-Free Medium Access Control for Wireless Sensor Networks, Proc. 1rst Intern. Conf. on Embedded Networked Sensor Systems, Los Angeles, 5-7 November 2003, pp. 419-438
[44] H. Hashimoto, J.H. Lee : Intelligent Space – Its Concept and Content, Adv. Rob. J., Vol.16(4), 2002
[45] A.S. Besicovitch : Almost Periodic Functions, Cambridge Univ. Press, Cambridge, UK, 1932; C. Corduneanu : Almost Periodic Functions, Interscience Tracts in Pure and Applied Maths., Vol.22, Interscience Publ., New York, 1961
[46] D.S. Mitrinovic, J.E. Pecaric, A.M. Fink : Classical and New Inequalities in Analysis, Kluwer, Dordrecht, the Netherlands, 1993; D. Bainov, P. Simeonov : Integral Inequalities and Applications, Kluwer Acad. Press, Dordrecht, The Netherlands, 1992; B.G. Pachpatte : Inequalities for Differential and Integral Equations, Academic Press, New York, 1998, and Mathematical Inequalities, North-Holland Math. Library, Vol.67, Elsevier Science, 2005; D. Kinderlehrer, G. Stampacchia : An Introduction to Variational Inequalities and their Applications, SIAM, Philadelphia, 2000
[47] P. Viljamaa, J. Raitamaki, P. Neittaanmaki, H. N. Koivo : Basic Functions in Soft Computing – A Survey, Proc. WAC’96, Vol.4, p. 545, TSI Press, Albuquerque, N.M., 1996
[48] J. Appell, P.P. Zabrijko : Nonlinear Superposition Operators, Cambridge University Press, Mass., 1990
[49] V.G. Majda : Sobolev Spaces, Springer-Verlag, New-York, 1985; J.A. Dubinskij : Sobolev Spaces of Infinite Order and Differential Equations, Teubner, Leipzig, 1988
[50] P. Constantin, C. Foias, B. Nikolaenko, R. Temam : Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Springer, Berlin-Heidelberg-New-York, 1989; M. Taboada, Y.C. You : Invariant Manifolds for Retarded Semi-linear Wave Equations, J. Diff. Eqns., Vol.114, pp.337-369, 1994; J. Carr : The Centre Manifold Theorem and its Applications, Springer Verlag, Berlin, 1983; C. Foias, G.R. Sell, R. Temam : Inertial Manifolds for Nonlinear Evolutionary Equations, J. Diff. Eqns, Vol.73, pp.309-353, 1988; A. Degenhard, J. Rodrigues-Laguna : Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations, J. Stat. Phys., Vol.106(516), pp.1093–1119, 2002; K.A. Morris : Design of Finite-dimensional Controllers for Infinite-dimensional Systems by Approximation, J. Math. Syst., Estimation and Control, Vol.4(2), pp.1630, 1994; M.J. Balas : Exponentially Stabilizing Finite-dimensional Controllers for Linear Distributed Parameter Systems : Galerkin Approximation of Infinite Dimensional Controllers, J. Math. Anal. Appl., Vol.114, pp.358-384, 1986; J.T. Wen : Finite Dimensional Controller Design for Infinite Dimensional Systems : the Circle Criterion Approach, Syst. and Control Letters, Vol.13(5), pp.445-454, 1989
[51] J. Awrejcewicz, I.V. Adrianov, L.I. Manevitch : Asymptotic Approaches in Nonlinear Systems, New Trends and Applications, Springer, New York, 1998; N.A. Bobylev, Y.M. Burman, S.K.Korovin : Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, 1994
[52] M. Cotsaftis : Lecture on Advanced Dynamics, National Taiwan Univ., Taipeh, R.O.C., 1993
[53] J.C.S. Hsu, A.U. Meyer : Modern Control Principles and Applications, McGraw Hill, New-York, 1968; A.I. Luri’e : Some Nonlinear Problems in Automatic Control, Gozdekhizdat, Moscow, 1957; M.A. Aizerman, F.R. Gantmacher : Absolute Stability of Regulator Systems, Holden-Day, San Franscisco, 1964
[54] S. Lefschetz : Stability of Nonlinear Control Systems, Academic Press, NY, 1965; N. Minorsky : Theory of Nonlinear Control Systems, McGraw Hill, New-York, 1969

Copyright © 2019 Michel Cotsaftis

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License