Dynamic Analysis And Control Of Timescale-Type Networked System

Timescale-type dynamic equation is the integration and extension of differential equa-tion and difference equation and it reveals the intrinsic differences of them.Dynamic behav-ior analytics and control of networked systems have received extensive attention in recent years.More specifically,the special timescale type-R(continuous-time)and-Z(discrete-time)neural and complex dynamical networks have been applied in various fields such as associative memory,information science,combinatorial optimization,secure communica-tion,and formation control.The analytical and control results for timescale-type networked system not only hold for type-R and type-Z networked system,but also hold for the sys-tems involved on more complex time domains,yielding more general potential applications Based on several analytical tools such as the theory of time scales,linear matrix inequal-ity,differential inclusion,and the generalized matrix-measure,together with intermittent control,pinning control,and adaptive control method,various dynamics of timescale-type neural networks like global exponential stability have been analyzed,and cooperative con-trol of timescale-type complex networks have been discussed as wellPassivity of a class of timescale type-R inertial neural dynamical networks is discussed Firstly,by an appropriate linear transformation,the original second-order system is trans-formed into a first-order equivalent system.Secondly,based on non-smooth analysis and linear matrix inequality techniques,we obtain the sufficient conditions ensuring the passiv-ity of the considered system.Thirdly,using matrix analysis yields the optimized passivity condition,in which only five inequalities involved and thus avoids solving 23n2 inequali-ties.Fourthly,robust passivity with parameter uncertainties is discussed.Finally,numerical examples validate the effectiveness of the obtained resultsGlobal exponential stability of a class of timescale type-rZ inertial neural dynami-cal networks is analyzed.A generalized matrix measure concept is defined and based on variable transformation,time scale theory,and timescale-type Halanay inequality,we get the sufficient criterion for its reduced-order system.Then by constructing appropriate V-function and scaling techniques,we acquire the conclusion directly for the original system The obtained two sufficient criteria complement each other.In the end,the theoretical results are validated in image encryption and decryptionSynchronization control for a class of timescale type-T complex dynamical networks is studied.Based on the designed timescale-type time-interval intermittent pinning con-trol protocol,combined with the analytical techniques and time scale theory,we obtain the sufficient condition for synchronization tracking problem,and prove that the pinning node set avoids the infinitely fast switching.By a selection algorithm,the pinning node set is updated online.When T is designated as the real set R,the criterion holds for the corre-sponding continuous-time system.If T is designated as the integer set Z,the criterion holds for the corresponding discrete-time system.Numerical examples demonstrate the validity and superiority of the obtained resultsContainment control for a class of timescale type-T complex dynamical networks is discussed.In the first scenario,the control gain on successive portion of time intervals is zero,that is,the common intermittent control scheme.Based on induction and adaptive control method,we get some sufficient conditions for containment control.In the second scenario,it is set to be the corresponding final velocity in the last time interval.Employing time scale theory,the original intermittent control system is converted to a timescale-type dynamical system.Using matrix analysis and output regulation scheme,we obtain the sufficient conditions for containment control of the system.Numerical examples show the effectiveness of the results.