This Letter considers the robust adaptive tracking control problem of a class of uncertain chaotic systems with time-varying unknown but bounded parameters. A novel controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic systems globally asymptotically track the desired bounded trajectories. Simulation results verify the effectiveness of the proposed controller.

基于混沌现象普遍存在于各类非线性系统中这一事实，针对工业过程中的混沌运动行为，给出了混沌稳态的数学定义，证明了具有非线性机制的工业过程混沌稳态的存在性定理，并对一个化工过程的混沌稳态进行了仿真计算。

The controllability of both continuous and discrete periodic systems are evaluated. The controllability for continuous periodic systems is extended to unit period control, and these results are then directly extended to discrete periodic systems. An assessment is made on retaining periodic system controllability during discretisation, resulting in the conclusion that there is no loss in the controllability of linear periodic systems during discretisation when using a nonequidistant sampling pattern.

Track initiation and termination is an important function in multi-target tracking (MTT), it is a decision part for establishing the records of the new targets and terminating the unwanted records of the inexistent targets when they leave the surveillance region. But in the heavy cluttered environment, there exists so called "incomplete data problem", due to the unknown state of the target and the sequence of measurements which originate from the target. Because the EM algorithm is an efficient means to solve the "incomplete data problem", a fast track initiation and termination approach applicable to engineering is presented, which combines the sequential probabilistic ratio test (SPRT) with recursive expectation maximization (EM). Here, track initiation and termination is modeled as a hypothesis testing problem. And aiming at the computational difficulty of the likelihood function due to the unknown target state and the sequence of measurements which originate from the target, the recursive EM-based formula of likelihood function is introduced. It gives an efficient solution to track initiation and termination by processing the measurement data sequentially, and its recursive form can meet the real-time demand. The simulation results indicate that the proposed method performs well for track initiation and termination, especially in heavy cluttered environment.

Active control is an effective method for making two identical Rossler and Chen systems be synchronized. However, this method works only for a certain class of chaotic systems with known parameters both in drive systems and response systems. Modification based on Lyapunov stability theory is proposed in order to overcome this limitation. An adaptive synchronization controller, which can make the states of two identical Rossler and Chen systems globally asymptotically synchronized in the presence of system's unknown constant parameters, is derived. Especially, when some unknown parameters are positive, we can make the controller more simple, besides, the controller is independent of those positive uncertain parameters. At last, when the condition that arbitrary unknown parameters in two systems are identical constants is cancelled, we demonstrate that it is possible to synchronize two chaotic systems. All results are proved using a well-known Lyapunov stability theorem. Numerical simulations are given to validate the proposed synchronization approach.