Avoidence Strategies for Fractional Order Systems with Caputo Derivative

1 Ambroziak L, Lewon D, Pawluszewicz E. The use of fractional order operators in modeling of RC-electrical systems. Control & Cybernetics 2016; 45(3):275—288. Search in Google Scholar

2 Balachandran K, Govindaraj K, Rodriguez-Germa M, Trujillo JJ. Stabilizability of fractional dynamical system, Fractional & Applied Analisis. 2014; 17(2):511-521. Search in Google Scholar

3 Bandyopadhyay B, Kamal S. Stabilization and control of fractional order systems: a sliding mode approach, Lecture Notes in Electrical Engineering 317, Springer International Publishing, 2015:55-90. Search in Google Scholar

4 Bingi K, Prusty BR, Singh AP. A Review on Fractional-Order Modelling and Control of Robotic Manipulators, Fractal Fract. 2023; 7(1):77. Available from: https://doi.org/10.3390/fractalfract7010077. Search in Google Scholar

5 Bressan A, Piccoli B. Introduction to the Mathematical Theory of Control, AIMS Series on Applied Mathematics 2007. Search in Google Scholar

6 Burns TR, Roszkowska E, Corte U, Machado Des Johansson N. Linking Group Theory to Social Science Game Theory: Interaction Grammars, Group Subcultures and Games for Comparative Analysis, Social Sciences. 2017; 6(3):1-36. Available from: https://doi.org/10.3390/socsci6030107. Search in Google Scholar

7 Chen D, Zhang R, Liu X, Ma X. Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks, Commun. Nonlinear Sci. Numer. Simulat. 2014; 19(2014):4105-4121. Search in Google Scholar

8 Corless L, Leitmann G. Controller design for uncertain systems via Lyapunov functions. IEEE Proc. of 1988 American Control Conference 1988:2019–2025. Search in Google Scholar

9 Das S. Functonal Fractional Calculus for System Identyfication and Controls, Springer 2008. Search in Google Scholar

10 Djennoune S, Bettayeb M, Al-Saggaf UM. Synchronization of fractional-order discrete-time chaotic systems by exact state reconstructor: application to secure communication, Int. J. App. Math. Comput. Sci. 2018;29(1):179-194. Search in Google Scholar

11 Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations, Elsevier Science B. V. 2006. Search in Google Scholar

12 Koszewnik A, Pawluszewicz E, Ostaszewski M. Experimaental studies of the fractional PID and TID controllers for industrial process, International Journal of Control, Automation and Systems 2021; 19(5): 1847-1862. Search in Google Scholar

13 Kozlowska M, Kutner R. Dynamics of the Warsaw Stock Exchange index as analysed by the nonhomogeneous fractional relaxation equation, Acta Physica Polonica, Series B 2006; 37(11): 3027-3028. Search in Google Scholar

14 Leitmann G, Skowronski J. Avoidance Control, Journal of Optimization Theory and Applications 1977; 23(4): 581–591. Search in Google Scholar

15 Liu Y., Chen H., Zou Q., Du X., Wang Y., Yu J. Automatic Navigation of Microswarms for Dynamic Obstacle Avoidance, IEEE Transaction on Robotics 2023. DOI: 10.1109/TRO.2023.3263773. Search in Google Scholar

16 Marden JR, Shamma JS. Game Theory and Distributed Control, in: Handbook of Game Theory with Economic Applications 2015; 4:861-899. Search in Google Scholar

17 Mozyrska D, Girejko E, Wyrwas M. Fractional nonlinear systems with sequential operators, Cent. Eur. J. Phys. 2013: 11(10):1295-1303. Search in Google Scholar

18 Némcová J, Petreczky M, van Schuppen JH. Towards a system theory of rational systems. in: Bart, H., Horst, S., Ran, A., Woerdeman, H. (eds) Operator Theory, Analysis and the State Space Approach. Operator Theory: Advances and Applications 271. Birkhäuser, Cham 2018:327–359 Search in Google Scholar

19 Nguyen HD, Kim D, Son YS, Han K. Linear Time-Varying MPC-based Autonomous Emergency Steering Control for Collision Avoidance, IEEE Transaction on Vehicular Technology 2023; 1109/TVT.2023.3269787 Search in Google Scholar

20 Oprzędkiewicz K, Mitkowski W, Rosół M. Fractional order, state space model of the temperature field in the PCB plate, Acta Mechanica et Automatica 2023;17(2):180—187. Search in Google Scholar

21 Pawluszewicz E, Koszewnik A, Burzynski P. On Grünwald-Letnikov fractional order operator with measureble order on continuous-discrete time scale, Acta Mechanica et Automatica 2020;14(3): 161-165. Search in Google Scholar

22 Pawluszewicz E, Torres DMF. Avoidance Control on Time Scales, Journal of Optimization Theory and Applications 2010; 145(3): 527 – 542. Search in Google Scholar

23 Rana KPS, Kumar V, Mittra N, Pramanik N. Implementation of fractional order integrator/differentiator on field programmable gate array, Alexandria Engineering Journal 2016; 55:1765—1773. Search in Google Scholar

24 Rodríguez-Seda EJ, Stipanovič DM. Cooperative Avoidance Control With Velocity-Based Detection Regions, IEEE Control Systems Letters 2020: 4(2):432 – 437. Search in Google Scholar

25 Samuelson L. Game Theory in Economics and Beyond, Journal of Economic Perspectives 2016; 30(4):107–-130. Search in Google Scholar

26 Sierociuk D, Dzieliński A, Sarwas G, Petras I, Podlubny I., Skovranek T. Modelling heat transfer in heterogenous media using fractional calculus, Phylosophical Transaction of the Royal Society 2013;371(1990). Search in Google Scholar

27 Stipanovič DM, Hokayem P, Spong M, Šiljak, D. Cooperative avoidance control for multiagent systems, J. Dyn. Syst. Measur. Control 2007; 129( 5): 699—707. Search in Google Scholar

28 Ungureanu V. Pareto-Nash-Stackelberg Game and Control Theory, Springer 2018. Search in Google Scholar

29 Zhang W, Rodríguez-Seda EJ, Deka SA, Amrouche M, Zhou D, Stipanovič DM., Leitmann G. Avoidance Control with Relative Velocity Information for Lagrangian Dynamics, Journal of Intelligent & Robotic Systems 2020; 99:229–244. Available from: https://doi.org/10.1007/s10846-019-01122-x Search in Google Scholar