Some Control and Observation Issues in Cellular Automata

This review article focuses on studying problems of observability and controllability of cellular automata (CAs) considered in the context of control theory, an important feature of which is the adoption of a state-space model. Our work first consists in generalizing the obtained results to systems described by CAs considered as the discrete counterpart of partial differential equations, and in exploring possible approaches to prove controllability and observability. After having introduced the notion of control and observation in cellular automata models, in a similar way to the case of discrete-time distributed parameter systems, we investigate these key concepts of control theory in the case of complex systems. For the controllability issue, the Boolean class is particularly studied and applied to the regional case, while the observability is approached in the general case and related to the reconstructibility problem for linear or nonlinear CAs.

[1]  Rekha Jain,et al.  Wireless Sensor Network -A Survey , 2013 .

[2]  D. Russell.  Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions , 1978 .

[3]  I. Kaarer.  Weak Controllability and the New Choice of Actuators , 2018 .

[4]  Ashraf Elnagar,et al.  On optimal constrained trajectory planning in 3D environments , 2000, Robotics Auton. Syst..

[5]  Stuart A. Kauffman,et al.  The global dynamics of cellular automata, by Andrew Wuensche and Mike Lesser , 2000, Complex.

[6]  Ulrich Eggers,et al.  Introduction To Infinite Dimensional Linear Systems Theory , 2016 .

[7]  Michael A. Demetriou,et al.  Guidance of Mobile Actuator-Plus-Sensor Networks for Improved Control and Estimation of Distributed Parameter Systems , 2010, IEEE Transactions on Automatic Control.

[8]  Ali Boutoulout,et al.  Actuators and regional boundary controllability of parabolic systems , 2000, Int. J. Syst. Sci..

[9]  Gérard Y. Vichniac,et al.  Boolean derivatives on cellular automata , 1991 .

[10]  Kyongsu Yi,et al.  Obstacle avoidance of autonomous vehicles based on model predictive control , 2009 .

[11]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[12]  A. El Jai,et al.  On the relations between actuator structures and final-constraint minimum-energy problem , 1992 .

[13]  G B Ermentrout,et al.  Cellular automata approaches to biological modeling. , 1993, Journal of theoretical biology.

[14]  Andreas Deutsch,et al.  Cellular automaton modeling of biological pattern formation , 2009 .

[15]  R. Kálmán.  Mathematical description of linear dynamical systems , 1963 .

[16]  Samira El Yacoubi,et al.  Toward a boundary regional control problem for Boolean cellular automata , 2017, Natural Computing.

[17]  Lijun Zhang,et al.  A Weighted Pair Graph Representation for Reconstructibility of Boolean Control Networks , 2015, SIAM J. Control. Optim..

[18]  Samira El Yacoubi,et al.  A graph theory approach for regional controllability of Boolean cellular automata , 2020, Int. J. Parallel Emergent Distributed Syst..

[19]  Michael A. Demetriou,et al.  Estimation of Spatially Distributed Processes Using Mobile Spatially Distributed Sensor Network , 2009, SIAM J. Control. Optim..

[20]  S. El Yacoubi,et al.  A mathematical method for control problems on cellular automata models , 2008, Int. J. Syst. Sci..

[21]  Observability of Affine Cellular Automaton Through Mobile Sensors , 2020, ACRI.

[22]  J. L. Lions,et al.  Controlabilite Exacte des Systemes Distribues: Remarques sur la Theorie Generale et les Applications , 1986 .

[23]  Dusan M. Stipanovic,et al.  Effective Coverage Control for Mobile Sensor Networks With Guaranteed Collision Avoidance , 2007, IEEE Transactions on Control Systems Technology.

[24]  S. Kauffman,et al.  Cell-cell interaction and diversity of emergent behaviours. , 2011, IET systems biology.

[25]  S. Kauffman.  Homeostasis and Differentiation in Random Genetic Control Networks , 1969, Nature.

[26]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems , 1999, Encyclopedia of Complexity and Systems Science.

[27]  K.-C. Chou,et al.  Using cellular automata to generate image representation for biological sequences , 2005, Amino Acids.

[28]  Samira El Yacoubi,et al.  Boundary Regional Controllability of Linear Boolean Cellular Automata Using Markov Chain , 2020 .

[29]  Stephen Wolfram,et al.  Cellular Automata And Complexity , 1994 .

[30]  Samira El Yacoubi,et al.  Markov Chains Approach for Regional Controllability of Deterministic Cellular Automata, via Boundary Actions , 2019, J. Cell. Autom..

[31]  Samira El Yacoubi,et al.  Regional Controllability with Cellular Automata Models , 2002, ACRI.

[32]  Roman Garnett,et al.  Bayesian optimization for sensor set selection , 2010, IPSN '10.

[33]  A. El Jai.  Distributed systems analysis via sensors and actuators , 1991 .

[34]  Ettore Fornasini,et al.  Observability, Reconstructibility and State Observers of Boolean Control Networks , 2013, IEEE Transactions on Automatic Control.

[35]  M. Amouroux,et al.  Sensors and observers in distributed parameter systems , 1988 .

[36]  R. Kálmán.  On the general theory of control systems , 1959 .

[37]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Autonomous Robot Vehicles.