Motives with exceptional Galois groups and the inverse Galois problem

We construct motivic $\ell$-adic representations of \GQ into exceptional groups of type $E_7,E_8$ and $G_2$ whose image is Zariski dense. This answers a question of Serre. The construction is uniform for these groups and uses the Langlands correspondence for function fields. As an application, we solve new cases of the inverse Galois problem: the finite simple groups E_{8}(\FF_{\ell}) are Galois groups over \QQ for large enough primes $\ell$.Comment: 40 page

On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

This paper divides into two parts. Let $(X,\omega)$ be a compact Hermitian manifold. Firstly, if the Hermitian metric $\omega$ satisfies the assumption that $\partial\overline{\partial}\omega^k=0$ for all $k$, we generalize the volume of the cohomology class in the K\"{a}hler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle $K^{-1}_X$ is nef, then for any $\varepsilon>0$, there is a smooth function $\phi_\varepsilon$ on $X$ such that $\omega_\varepsilon:=\omega+i\partial\overline{\partial}\phi_\varepsilon>0$ and Ricci$(\omega_\varepsilon)\geq-\varepsilon\omega_\varepsilon$. Furthermore, if $\omega$ satisfies the assumption as above, we prove that for a Harder-Narasimhan filtration of $T_X$ with respect to $\omega$, the slopes $\mu_\omega(\mathcal{F}_i/\mathcal{F}_{i-1})\geq 0$ for all $i$, which generalizes a result of Cao which plays a very important role in his studying of the structures of K\"{a}hler manifolds

Editorial for modelling, monitoring and fault-tolerant control for complex systems

This is the editorial for the special issue entitled ``Modelling, Monitoring and Fault-Tolerant Control for Complex Systems'' published in the Open Automation and Control Systems Journal

Fault estimation and fault-tolerant control for discrete-time dynamic systems

In this paper, a novel discrete-time estimator is proposed, which is employed for simultaneous estimation of system states, and actuator/sensor faults in a discrete-time dynamic system. The existence of the discrete-time simultaneous estimator is proven mathematically. The systematic design procedure for the derivative and proportional observer gains is addressed, enabling the estimation error dynamics to be internally proper and stable, and robust against the effects from the process disturbances, measurement noise, and faults. Based on the estimated fault signals and system states, a discrete-time fault-tolerant design approach is addressed, by which the system may recover the system performance when actuator/sensor faults occur. Finally, the proposed integrated discrete-time fault estimation and fault-tolerant control technique is applied to the vehicle lateral dynamics, which demonstrates the effectiveness of the developed techniques