Local Stabilization of the Navier–Stokes Equations with a Feedback Controller Localized in an Open Subset of the Domain

We study the local exponential stabilization, near a given steady-state flow, of solutions of the 2-D and 3-D Navier–Stokes equations in a bounded domain. The control is effectuated through a distributed control localized in an open subset of the domain. We apply a linear feedback controller, obtained by the solution of a control problem. Lyapunov functionals are given for a large class of cost functionals.     

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介绍了磁通环法测量等离子体位移的原理。通过计算由磁通环及其附近小磁探针得到的数据,给出了位移随时间变化的曲线。通过将所得到的等离子体位移的变化趋势与非对称探针和CCD相机的测量结果进行比较,验证了磁通环法测量的正确性。该测量方法已用于HL-2A等离子体位移反馈控制系统。     

Reduction of magnetic field fluctuations in powered magnets for NMR using inductive measurements and sampled-data feedback control

Resistive and hybrid (resistive/superconducting) magnets provide substantially higher magnetic fields than those available in low-temperature superconducting magnets, but their relatively low spatial homogeneity and temporal field fluctuations are unacceptable for high resolution NMR. While several techniques for reducing temporal fluctuations have demonstrated varying degrees of success, this paper restricts attention to methods that utilize inductive measurements and feedback control to actively cancel the temporal fluctuations. In comparison to earlier studies using analog proportional control, this paper shows that shaping the controller frequency response results in significantly higher reductions in temporal fluctuations. Measurements of temporal fluctuation spectra and the frequency response of the instrumentation that cancels the temporal fluctuations guide the controller design. In particular, we describe a sampled-data phase-lead-lag controller that utilizes the internal model principle to selectively attenuate magnetic field fluctuations caused by the power supply ripple. We present a quantitative comparison of the attenuation in temporal fluctuations afforded by the new design and a proportional control design. Metrics for comparison include measurements of the temporal fluctuations using Faraday induction and observations of the effect that the fluctuations have on nuclear resonance measurements.     

Null controllability and global blowup controllability of ordinary differential equations with feedback controls

This paper concerns the problem of feedback null controllability and blowup controllability with feedback controls for ordinary differential equations. First, we study the feedback null controllability on a time-varying ordinary differential system by unbounded feedback operators. Then, the global exact blowup controllability with feedback controls is derived on a time-invariant ordinary differential system. Finally, we obtain the approximate null controllability by bounded feedback operators, and get the approximate blowup controllability with feedback controls for ordinary differential equations.     

Using reservoir computer to predict and prevent extreme events

We show that a reservoir computer is an effective tool for model-free prediction of extreme events in deterministic chaotic systems. This prediction allows us to suppress unwanted extreme events, by applying weak control perturbations to the system at times preceding expected extreme events. The effectiveness of such a prediction and prevention strategy is demonstrated for a system of globally coupled FitzHugh-Nagumo neurons and for a system of two almost identical unidirectionally coupled chaotic oscillators.     

Linearity properties of binary FCSR sequences

Maximal length FCSR sequences, or l-sequences, are an important type of nonlinear sequences used for building stream ciphers. This paper studies the linearity properties of l-sequences. Although it is widely accepted that l-sequences have high linear complexities close to their half periods, it is shown that for most of the l-sequences, linear relations with large statistical advantage exist.      

A new fractional order hyperchaotic Rabinovich system and its dynamical behaviors

In the paper, the dynamical behaviors of a new fractional order hyperchaotic Rabinovich system are investigated, which include its local stability, hyperchaos, chaotic control and synchronization. Firstly, a new fractional order hyperchaotic Rabinovich system with Caputo derivative is proposed. Then, the hyperchaotic attractors of the commensurate and incommensurate fractional order hyperchaotic Rabinovich system are found. After that, four linear feedback controllers are designed to stabilize this fractional order system Finally, by using the active control method the synchronization is studied between the fractional order hyperchaotic and chaos controlled Rabinovich system In addition, the theoretical predictions are confirmed by numerical simulations.     

Control and adaptive modified function projective synchronization of Liu chaotic dynamical system

In this work, the feedback control method is proposed to control the behaviour of Liu chaotic dynamical system. The controlled system is stable under some conditions on the parameters of the system determined by Routh-Hurwitz criterion. This paper also presents the adaptive modified function projective synchronization (AMFPS) between two identical Liu chaotic dynamical systems. Based on the Lyapunov stability theorem, adaptive control laws are designed to achieving the AMFPS. Finally, some numerical simulations are obtained to validate the proposed methods.