Chaos control and chaos synchronization using the state-dependent Riccati equation techniques

In this paper, the problems of chaos control and chaos synchronization are solved using the state-dependent Riccati equation methods. In the former problem, a nonlinear suboptimal control law is found, which leads to a stable closed-loop system. In the latter, an optimal infinite-time horizon tracking problem is defined and solved using the state-dependent Riccati equation technique. It is shown that the synchronization error between the slave and the master systems converges asymptotically to zero under some mild conditions. Three numerical simulations are provided to demonstrate the design procedure and the flexibility of the methods.

[1]  J. Wen,et al.  Adaptive fuzzy control for a class of chaotic systems with nonaffine inputs , 2011 .

[2]  M. Tadi,et al.  Synchronization of chaotic systems based on SDRE method , 2006 .

[3]  Gangquan Si,et al.  Finite-time synchronization and identification of complex delayed networks with Markovian jumping parameters and stochastic perturbations , 2016 .

[4]  Nader Meskin,et al.  Nonlinear Suboptimal Tracking Controller Design Using State-Dependent Riccati Equation Technique , 2017, IEEE Transactions on Control Systems Technology.

[5]  Junji Ohtsubo,et al.  Chaos Control and Applications , 2013 .

[6]  Y. Batmani,et al.  On the Design of Observer for Nonlinear Time‐Delay Systems , 2014 .

[7]  Hamid Khaloozadeh,et al.  On the design of suboptimal sliding manifold for a class of nonlinear uncertain time-delay systems , 2016, Int. J. Syst. Sci..

[8]  Hai-Peng Ren,et al.  A chaotic spread spectrum system for underwater acoustic communication , 2015, 2015 IEEE International Wireless Symposium (IWS 2015).

[9]  Jun-Juh Yan,et al.  Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller , 2009 .

[10]  Ming-Chang Pai,et al.  Adaptive sliding mode observer‐based synchronization for uncertain chaotic systems , 2012 .

[11]  Nader Meskin,et al.  On design of suboptimal tracking controller for a class of nonlinear systems , 2016, 2016 American Control Conference (ACC).

[12]  Mohammad Shahrokhi,et al.  Adaptive observer-based synchronization of two non-identical chaotic systems with unknown parameters , 2017 .

[13]  Tayfun Çimen,et al.  Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method , 2010, Annu. Rev. Control..

[14]  Mahmoud Shahi,et al.  Adaptive sliding mode control approach , 2017 .

[15]  Qigui Yang,et al.  A hyperchaotic system from the Rabinovich system , 2010, J. Comput. Appl. Math..

[16]  M. P. Aghababa,et al.  Design of a sliding mode controller for synchronizing chaotic systems with parameter and model uncertainties and external disturbances , 2012 .

[17]  Abdesselem Boulkroune,et al.  A generalized function projective synchronization scheme for uncertain chaotic systems subject to input nonlinearities , 2016, Int. J. Gen. Syst..

[18]  Zhiyong Ye,et al.  Adaptive synchronization to a general non-autonomous chaotic system and its applications ☆ , 2012 .

[19]  Zhidong Teng,et al.  General impulsive control of chaotic systems based on a TS fuzzy model , 2011, Fuzzy Sets Syst..

[20]  Konrad Reif,et al.  Nonlinear state observation using H∞-filtering Riccati design , 1999, IEEE Trans. Autom. Control..

[21]  Tayfun Çimen,et al.  Survey of State-Dependent Riccati Equation in Nonlinear Optimal Feedback Control Synthesis , 2012 .

[22]  Y. Batmani.  Blood glucose concentration control for type 1 diabetic patients: a non-linear suboptimal approach. , 2017, IET systems biology.

[23]  Eckehard Schöll,et al.  Handbook of Chaos Control , 2007 .

[24]  Abdesselem Boulkroune,et al.  Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems , 2016, Neurocomputing.

[25]  Ling Lü,et al.  A new synchronization tracking technique for uncertain discrete network with spatiotemporal chaos behaviors , 2016 .

[26]  Hua Wang,et al.  Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication , 2018, Trans. Inst. Meas. Control.

[27]  Ned J. Corron,et al.  A new approach to communications using chaotic signals , 1997 .

[28]  Yong Wu,et al.  Robust adaptive finite-time synchronization of nonlinear resource management system , 2016, Neurocomputing.

[29]  Sohrab Khanmohammadi,et al.  Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller , 2011 .

[30]  Zuolei Wang.  Chaos synchronization of an energy resource system based on linear control , 2010 .

[31]  Sahjendra N. Singh,et al.  State-dependent Riccati equation-based robust dive plane control of AUV with control constraints , 2007 .

[32]  M. Yahyazadeh,et al.  Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control. , 2011, ISA transactions.

[33]  Ju H. Park.  Synchronization of Genesio chaotic system via backstepping approach , 2006 .

[34]  P. Manimaran,et al.  Multifractal detrended cross-correlation analysis of coding and non-coding DNA sequences through chaos-game representation , 2015 .

[35]  Shih-Yu Li,et al.  Chaos generalized synchronization of new Mathieu-Van der Pol systems with new Duffing-Van der Pol systems as functional system by GYC partial region stability theory , 2011 .