Generic finite-size enhancement of pairing in mesoscopic Fermi systems

The finite-size-dependent enhancement of pairing in mesoscopic Fermi systems is studied under the assumption that the BCS approach is valid and that the two-body force is size independent. Different systems are investigated such as superconducting metallic grains and films as well as atomic nuclei. It is shown that the finite size enhancement of pairing in these systems is in part due to the presence of a surface which accounts quite well for the data of nuclei and explains a good fraction of the enhancement in Al grains.

Stochastic processes and their applications semi-markov analysis of some inventory and queuing problems

This thesis analyses certain problems in Inventories and Queues. There are many situations in real-life where we encounter models as described in this thesis. It analyses in depth various models which can be applied to production, storag¢, telephone traffic, road traffic, economics, business administration, serving of customers, operations of particle counters and others. Certain models described here is not a complete representation of the true situation in all its complexity, but a simplified version amenable to analysis. While discussing the models, we show how a dependence structure can be suitably introduced in some problems of Inventories and Queues. Continuous review, single commodity inventory systems with Markov dependence structure introduced in the demand quantities, replenishment quantities and reordering levels are considered separately. Lead time is assumed to be zero in these models. An inventory model involving random lead time is also considered (Chapter-4). Further finite capacity single server queueing systems with single/bulk arrival, single/bulk services are also discussed. In some models the server is assumed to go on vacation (Chapters 7 and 8). In chapters 5 and 6 a sort of dependence is introduced in the service pattern in some queuing models.

Robust finite-time consensus tracking algorithm for multirobot systems

This paper studies the finite-time consensus tracking control for multirobot systems. We prove that finite-time consensus tracking of multiagent systems can be achieved on the terminal sliding-mode surface. Also, we show that the proposed error function can be modified to achieve relative state deviation between agents. These results are then applied to the finite-time consensus tracking control of multirobot systems with input disturbances. Simulation results are presented to validate the analysis.

Adaptive fast finite time control of a class of uncertain nonlinear systems

This paper concerns the adaptive fast finite time control of a class of nonlinear uncertain systems of which the upper bounds of the system uncertainties are unknown. By using the fast non-smooth control Lyapunov function and the method of so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided, which guarantees the fast finite time stability of the closed-loop system. It is proved that the control input is bounded, and a simulation example is given to illustrate the effectiveness of the theoretical results.

Fast finite-time consensus of a class of high-order uncertain nonlinear systems

This paper poses and solves a new problem of consensus control where the task is to make the fixed-topology multi-agent network, with each agent described by an uncertain nonlinear system in chained form, to reach consensus in a fast finite time. Our development starts with a set of new sliding mode surfaces. It is proven that, on these sliding mode surfaces, consensus can be achieved if the communication graph has the proposed directed spanning tree. Next, we introduce the multi-surface sliding mode control to drive the sliding variables to the sliding mode surfaces in a fast finite time. The control Lyapunov function for fast finite time stability, motivated by the fast terminal sliding mode control, is used to prove the reachability of the sliding mode surface. A recursive design procedure is provided, which guarantees the boundedness of the control input.

Comments on "finite-time stability theorem of stochastic nonlinear systems" [Automatica 46 (2010) 2105-2108]

In this comment, we will point out some errors existing in Chen and Jiao (2010) from definitions to the proof of the main result, where the authors discussed the finite-time stability of stochastic nonlinear systems and proved a Lyapunov theorem on the finitetime stability.

A finite-time stability theorem of stochastic nonlinear systems and stabilization designs

This paper focuses on the finite-time stability and stabilization designs of stochastic nonlinear systems. We first present and discuss a definition on the finite-time stability in probability of stochastic nonlinear systems, then we introduce a stochastic Lyapunov theorem on the finite-time stability, which has been established by Yin et al. We also employ this theorem to design a continuous state feedback controller that makes a class of stochastic nonlinear systems to be stable in finite time. An example and a simulation are given to illustrate the theoretical analysis.

Robust finite-horizon Kalman filtering for uncertain discrete-time systems

In this note, we propose a design for a robust finite-horizon Kalman filtering for discrete-time systems suffering from uncertainties in the modeling parameters and uncertainties in the observations process (missing measurements). The system parameter uncertainties are expected in the state, output and white noise covariance matrices. We find the upper-bound on the estimation error covariance and we minimize the proposed upper-bound.

Adaptive fast finite-time multiple-surface sliding control for a class of uncertain non-linear systems

This paper concerns the adaptive fast finite-time multiple-surface sliding control (AFFTMSSC) problem for a class of high-order uncertain non-linear systems of which the upper bounds of the system uncertainties are unknown. By using the fast control Lyapunov function and the method of so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided, which guarantees the fast finite-time stability of the closed-loop system. Further, it is proved that the control input is bounded.

Continuous finite-time state feedback stabilizers for some nonlinear stochastic systems

This paper is concerned with the problem of finite-time stabilization for some nonlinear stochastic systems. Based on the stochastic Lyapunov theorem on finite-time stability that has been established by the authors in the paper, it is proven that Euler-type stochastic nonlinear systems can be finite-time stabilized via a family of continuous feedback controllers. Using the technique of adding a power integrator, a continuous, global state feedback controller is constructed to stabilize in finite time a large class of two-dimensional lower-triangular stochastic nonlinear systems. Also, for a class of three-dimensional lower-triangular stochastic nonlinear systems, a recursive design scheme of finite-time stabilization is given by developing the technique of adding a power integrator and constructing a continuous feedback controller. Finally, a simulation example is given to illustrate the theoretical results. © 2014 John Wiley & Sons, Ltd.

Global finite-time stabilisation for a class of stochastic nonlinear systems by output feedback

In this paper, the problem of global finite-time stabilisation by output feedback is considered for a class of stochastic nonlinear systems. First, based on homogeneous systems theory and the adding a power integrator technique, a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system. Then, the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms; it is shown that the proposed output-feedback control law can guarantee that the closed-loop system is global finite-time stable in probability. Finally, simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme.