Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

Two-dimensional viscoelastic discrete triangular system with negative-stiffness components

Potential applications of high-damping and high-stiffness composites have motivated extensive research on the effects of negative-stiffness inclusions on the overall properties of composites. Recent theoretical advances have been based on the Hashin-Shtrikman composite models, one-dimensional discrete viscoelastic systems and a two-dimensional nested triangular viscoelastic network. In this paper, we further analyze the two-dimensional triangular structure containing pre-selected negative-stiffness components to study its underlying deformation mechanisms and stability. Major new findings are structure-deformation evolution with respect to the magnitude of negative stiffness under shear loading and the phenomena related to dissipation-induced destabilization and inertia-induced stabilization, according to Lyapunov stability analysis. The evolution shows strong correlations between stiffness anomalies and deformation modes. Our stability results reveal that stable damping peaks, i.e. stably extreme effective damping properties, are achievable under hydrostatic loading when the inertia is greater than a critical value. Moreover, destabilization induced by elemental damping is observed with the critical inertia. Regardless of elemental damping, when the inertia is less than the critical value, a weaker system instability is identified.

Anomalies in stiffness and damping of a 2D discrete viscoelastic system due to negative stiffness components

The recent development of using negative stiffness inclusions to achieve extreme overall stiffness and mechanical damping of composite materials reveals a new avenue for constructing high performance materials. One of the negative stiffness sources can be obtained from phase transforming materials in the vicinity of their phase transition, as suggested by the Landau theory. To understand the underlying mechanism from a microscopic viewpoint, we theoretically analyze a 2D, nested triangular lattice cell with pre-chosen elements containing negative stiffness to demonstrate anomalies in overall stiffness and damping. Combining with current knowledge from continuum models, based on the composite theory, such as the Voigt, Reuss, and Hashin-Shtrikman model, we further explore the stability of the system with Lyapunov's indirect stability theorem. The evolution of the microstructure in terms of the discrete system is discussed. A potential application of the results presented here is to develop special thin films with unusual in-plane mechanical properties. © 2006 Elsevier B.V. All rights reserved.

Relative Compactness for Hyperspaces

The present paper contains results characterizing relatively compact subsets of the space of the closed subsets of a metrizable space, equipped with various hypertopologies. We investigate the hyperspace topologies that admit a representation as weak topologies generated by families of gap functionals defined on closed sets, as well as hit-and-miss topologies and proximal-hit and-miss topologies.

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

* This work was supported by the CNR while the author was visiting the University of Milan.

Perturbations of Critical Values in Nonsmooth Critical Point Theory

* Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993). ** Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).

Branching Processes with Immigration and Integer-valued Time Series

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes to stationary Ginar(d) and get consistency and asymptotic normality for the corresponding estimators. The technique covers autoregressive moving average time series as well.

A New Approach for Eliminating the Spurious States in Recurrent Neural Networks

As is well known, the Convergence Theorem for the Recurrent Neural Networks, is based in Lyapunov ́s second method, which states that associated to any one given net state, there always exist a real number, in other words an element of the one dimensional Euclidean Space R, in such a way that when the state of the net changes then its associated real number decreases. In this paper we will introduce the two dimensional Euclidean space R2, as the space associated to the net, and we will define a pair of real numbers ( x, y ) , associated to any one given state of the net. We will prove that when the net change its state, then the product x ⋅ y will decrease. All the states whose projection over the energy field are placed on the same hyperbolic surface, will be considered as points with the same energy level. On the other hand we will prove that if the states are classified attended to their distances to the zero vector, only one pattern in each one of the different classes may be at the same energy level. The retrieving procedure is analyzed trough the projection of the states on that plane. The geometrical properties of the synaptic matrix W may be used for classifying the n-dimensional state- vector space in n classes. A pattern to be recognized is seen as a point belonging to one of these classes, and depending on the class the pattern to be retrieved belongs, different weight parameters are used. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented.

A multi-modular second life hybrid battery energy storage system for utility grid applications

The modern grid system or the smart grid is likely to be populated with multiple distributed energy sources, e.g. wind power, PV power, Plug-in Electric Vehicle (PEV). It will also include a variety of linear and nonlinear loads. The intermittent nature of renewable energies like PV, wind turbine and increased penetration of Electric Vehicle (EV) makes the stable operation of utility grid system challenging. In order to ensure a stable operation of the utility grid system and to support smart grid functionalities such as, fault ride-through, frequency response, reactive power support, and mitigation of power quality issues, an energy storage system (ESS) could play an important role. A fast acting bidirectional energy storage system which can rapidly provide and absorb power and/or VARs for a sufficient time is a potentially valuable tool to support this functionality. Battery energy storage systems (BESS) are one of a range suitable energy storage system because it can provide and absorb power for sufficient time as well as able to respond reasonably fast. Conventional BESS already exist on the grid system are made up primarily of new batteries. The cost of these batteries can be high which makes most BESS an expensive solution. In order to assist moving towards a low carbon economy and to reduce battery cost this work aims to research the opportunities for the re-use of batteries after their primary use in low and ultra-low carbon vehicles (EV/HEV) on the electricity grid system. This research aims to develop a new generation of second life battery energy storage systems (SLBESS) which could interface to the low/medium voltage network to provide necessary grid support in a reliable and in cost-effective manner. The reliability/performance of these batteries is not clear, but is almost certainly worse than a new battery. Manufacturers indicate that a mixture of gradual degradation and sudden failure are both possible and failure mechanisms are likely to be related to how hard the batteries were driven inside the vehicle. There are several figures from a number of sources including the DECC (Department of Energy and Climate Control) and Arup and Cenex reports indicate anything from 70,000 to 2.6 million electric and hybrid vehicles on the road by 2020. Once the vehicle battery has degraded to around 70-80% of its capacity it is considered to be at the end of its first life application. This leaves capacity available for a second life at a much cheaper cost than a new BESS Assuming a battery capability of around 5-18kWhr (MHEV 5kWh - BEV 18kWh battery) and approximate 10 year life span, this equates to a projection of battery storage capability available for second life of >1GWhrs by 2025. Moreover, each vehicle manufacturer has different specifications for battery chemistry, number and arrangement of battery cells, capacity, voltage, size etc. To enable research and investment in this area and to maximize the remaining life of these batteries, one of the design challenges is to combine these hybrid batteries into a grid-tie converter where their different performance characteristics, and parameter variation can be catered for and a hot swapping mechanism is available so that as a battery ends it second life, it can be replaced without affecting the overall system operation. This integration of either single types of batteries with vastly different performance capability or a hybrid battery system to a grid-tie 3 energy storage system is different to currently existing work on battery energy storage systems (BESS) which deals with a single type of battery with common characteristics. This thesis addresses and solves the power electronic design challenges in integrating second life hybrid batteries into a grid-tie energy storage unit for the first time. This study details a suitable multi-modular power electronic converter and its various switching strategies which can integrate widely different batteries to a grid-tie inverter irrespective of their characteristics, voltage levels and reliability. The proposed converter provides a high efficiency, enhanced control flexibility and has the capability to operate in different operational modes from the input to output. Designing an appropriate control system for this kind of hybrid battery storage system is also important because of the variation of battery types, differences in characteristics and different levels of degradations. This thesis proposes a generalised distributed power sharing strategy based on weighting function aims to optimally use a set of hybrid batteries according to their relative characteristics while providing the necessary grid support by distributing the power between the batteries. The strategy is adaptive in nature and varies as the individual battery characteristics change in real time as a result of degradation for example. A suitable bidirectional distributed control strategy or a module independent control technique has been developed corresponding to each mode of operation of the proposed modular converter. Stability is an important consideration in control of all power converters and as such this thesis investigates the control stability of the multi-modular converter in detailed. Many controllers use PI/PID based techniques with fixed control parameters. However, this is not found to be suitable from a stability point-of-view. Issues of control stability using this controller type under one of the operating modes has led to the development of an alternative adaptive and nonlinear Lyapunov based control for the modular power converter. Finally, a detailed simulation and experimental validation of the proposed power converter operation, power sharing strategy, proposed control structures and control stability issue have been undertaken using a grid connected laboratory based multi-modular hybrid battery energy storage system prototype. The experimental validation has demonstrated the feasibility of this new energy storage system operation for use in future grid applications.

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

2000 Mathematics Subject Classification: 60J80.

CO adsorption over Pd nanoparticles:a general framework for IR simulations on nanoparticles

CO vibrational spectra over catalytic nanoparticles under high coverages/pressures are discussed from a DFT perspective. Hybrid B3LYP and PBE DFT calculations of CO chemisorbed over Pd4 and Pd13 nanoclusters, and a 1.1 nm Pd38 nanoparticle, have been performed in order to simulate the corresponding coverage dependent infrared (IR) absorption spectra, and hence provide a quantitative foundation for the interpretation of experimental IR spectra of CO over Pd nanocatalysts. B3LYP simulated IR intensities are used to quantify site occupation numbers through comparison with experimental DRIFTS spectra, allowing an atomistic model of CO surface coverage to be created. DFT adsorption energetics for low CO coverage (θ → 0) suggest the CO binding strength follows the order hollow > bridge > linear, even for dispersion-corrected functionals for sub-nanometre Pd nanoclusters. For a Pd38 nanoparticle, hollow and bridge-bound are energetically similar (hollow ≈ bridge > atop). It is well known that this ordering has not been found at the high coverages used experimentally, wherein atop CO has a much higher population than observed over Pd(111), confirmed by our DRIFTS spectra for Pd nanoparticles supported on a KIT-6 silica, and hence site populations were calculated through a comparison of DFT and spectroscopic data. At high CO coverage (θ = 1), all three adsorbed CO species co-exist on Pd38, and their interdiffusion is thermally feasible at STP. Under such high surface coverages, DFT predicts that bridge-bound CO chains are thermodynamically stable and isoenergetic to an entirely hollow bound Pd/CO system. The Pd38 nanoparticle undergoes a linear (3.5%), isotropic expansion with increasing CO coverage, accompanied by 63 and 30 cm− 1 blue-shifts of hollow and linear bound CO respectively.