A joint state and parameter estimation scheme for nonlinear dynamical systems

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger models.

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen: (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes. (C) 2011 Elsevier B.V. All rights reserved.

Agent-Based Hybrid Intelligent Systems: An Agent-Based Framework for Complex Problem Solving

Pt. I. Fundamentals of hybrid intelligent systems and agents -- 1. Introduction -- 2. Basics of hybrid intelligent systems -- 3. Basics of agents and multi-agent systems -- Pt. II. Methodology and framework -- 4. Agent-oriented methodologies -- 5. Agent-based framework for hybrid intelligent systems --6. Matchmaking in middle agents -- Pt. III. Application systems -- 7. Agent-based hybrid intelligent system for financial investment
planning -- 8. Agent-based hybrid intelligent system for data mining -- Pt. IV. Concluding remarks -- 9. The less the more -- App. Sample source codes of the agent-based financial planning system

Building agent-based hybrid intelligent systems : a case study

Many complex problems (e.g., financial investment planning, foreign exchange trading, data mining from large/multiple databases) require hybrid intelligent systems that integrate many intelligent techniques (e.g., fuzzy logic, neural networks, and genetic algorithms). However, hybrid intelligent systems are difficult to develop because they have a large number of parts or components that have many interactions. On the other hand, agents offer a new and often more appropriate route to the development of complex systems, especially in open and dynamic environments. Thus, this paper discusses the development of an agent-based hybrid intelligent system for financial investment planning, in which a great number of heterogeneous computing techniques/packages are easily integrated into a unifying agent framework. This shows that agent technology can indeed facilitate the development of hybrid intelligent systems.

Stability theory and numerical analysis of non-autonomous dynamical systems

The development and use of cocycles for analysis of non-autonomous behaviour is a technique that has been known for several years. Initially developed as an extension to semi-group theory for studying rion-autonornous behaviour, it was extensively used in analysing random dynamical systems [2, 9, 10, 12]. Many of the results regarding asymptotic behaviour developed for random dynamical systems, including the concept of cocycle attractors were successfully transferred and reinterpreted for deterministic non-autonomous systems primarily by P. Kloeden and B. Schmalfuss [20, 21, 28, 29]. The theory concerning cocycle attractors was later developed in various contexts specific to particular classes of dynamical systems [6, 7, 13], although a comprehensive understanding of cocycle attractors (redefined as pullback attractors within this thesis) and their role in the stability of non-autonomous dynamical systems was still at this stage incomplete. It was this purpose that motivated Chapters 1-3 to define and formalise the concept of stability within non-autonomous dynamical systems. The approach taken incorporates the elements of classical asymptotic theory, and refines the notion of pullback attraction with further development towards a study of pull-back stability arid pullback asymptotic stability. In a comprehensive manner, it clearly establishes both pullback and forward (classical) stability theory as fundamentally unique and essential components of non-autonomous stability. Many of the introductory theorems and examples highlight the key properties arid differences between pullback and forward stability. The theory also cohesively retains all the properties of classical asymptotic stability theory in an autonomous environment. These chapters are intended as a fundamental framework from which further research in the various fields of non-autonomous dynamical systems may be extended. A preliminary version of a Lyapunov-like theory that characterises pullback attraction is created as a tool for examining non-autonomous behaviour in Chapter 5. The nature of its usefulness however is at this stage restricted to the converse theorem of asymptotic stability. Chapter 7 introduces the theory of Loci Dynamics. A transformation is made to an alternative dynamical system where forward asymptotic (classical asymptotic) behaviour characterises pullback attraction to a particular point in the original dynamical system. This has the advantage in that certain conventional techniques for a forward analysis may be applied. The remainder of the thesis, Chapters 4, 6 and Section 7.3, investigates the effects of perturbations and discretisations on non-autonomous dynamical systems known to possess structures that exhibit some form of stability or attraction. Chapter 4 investigates autonomous systems with semi-group attractors, that have been non-autonomously perturbed, whilst Chapter 6 observes the effects of discretisation on non-autonomous dynamical systems that exhibit properties of forward asymptotic stability. Chapter 7 explores the same problem of discretisation, but for pullback asymptotically stable systems. The theory of Loci Dynamics is used to analyse the nature of the discretisation, but establishment of results directly analogous to those discovered in Chapter 6 is shown to be unachievable. Instead a case by case analysis is provided for specific classes of dynamical systems, for which the results generate a numerical approximation of the pullback attraction in the original continuous dynamical system. The nature of the results regarding discretisation provide a non-autonomous extension to the work initiated by A. Stuart and J. Humphries [34, 35] for the numerical approximation of semi-group attractors within autonomous systems. . Of particular importance is the effect on the system's asymptotic behaviour over non-finite intervals of discretisation.

Agent-based hybrid framework for decision making on complex problems

Electronic commerce and the Internet have created demand for automated systems that can make complex decisions utilizing information from multiple sources. Because the information is uncertain, dynamic, distributed, and heterogeneous in nature, these systems require a great diversity of intelligent techniques including expert systems, fuzzy logic, neural networks, and genetic algorithms. However, in complex decision making, many different components or sub-tasks are involved, each of which requires different types of processing. Thus multiple such techniques are required resulting in systems called hybrid intelligent systems. That is, hybrid solutions are crucial for complex problem solving and decision making. There is a growing demand for these systems in many areas including financial investment planning, engineering design, medical diagnosis, and cognitive simulation. However, the design and development of these systems is difficult because they have a large number of parts or components that have many interactions. From a multi-agent perspective, agents in multi-agent systems (MAS) are autonomous and can engage in flexible, high-level interactions. MASs are good at complex, dynamic interactions. Thus a multi-agent perspective is suitable for modeling, design, and construction of hybrid intelligent systems. The aim of this thesis is to develop an agent-based framework for constructing hybrid intelligent systems which are mainly used for complex problem solving and decision making. Existing software development techniques (typically, object-oriented) are inadequate for modeling agent-based hybrid intelligent systems. There is a fundamental mismatch between the concepts used by object-oriented developers and the agent-oriented view. Although there are some agent-oriented methodologies such as the Gaia methodology, there is still no specifically tailored methodology available for analyzing and designing agent-based hybrid intelligent systems. To this end, a methodology is proposed, which is specifically tailored to the analysis and design of agent-based hybrid intelligent systems. The methodology consists of six models - role model, interaction model, agent model, skill model, knowledge model, and organizational model. This methodology differs from other agent-oriented methodologies in its skill and knowledge models. As good decisions and problem solutions are mainly based on adequate information, rich knowledge, and appropriate skills to use knowledge and information, these two models are of paramount importance in modeling complex problem solving and decision making. Follow the methodology, an agent-based framework for hybrid intelligent system construction used in complex problem solving and decision making was developed. The framework has several crucial characteristics that differentiate this research from others. Four important issues relating to the framework are also investigated. These cover the building of an ontology for financial investment, matchmaking in middle agents, reasoning in problem solving and decision making, and decision aggregation in MASs. The thesis demonstrates how to build a domain-specific ontology and how to access it in a MAS by building a financial ontology. It is argued that the practical performance of service provider agents has a significant impact on the matchmaking outcomes of middle agents. It is proposed to consider service provider agents' track records in matchmaking. A way to provide initial values for the track records of service provider agents is also suggested. The concept of ‘reasoning with multimedia information’ is introduced, and reasoning with still image information using symbolic projection theory is proposed. How to choose suitable aggregation operations is demonstrated through financial investment application and three approaches are proposed - the stationary agent approach, the token-passing approach, and the mobile agent approach to implementing decision aggregation in MASs. Based on the framework, a prototype was built and applied to financial investment planning. This prototype consists of one serving agent, one interface agent, one decision aggregation agent, one planning agent, four decision making agents, and five service provider agents. Experiments were conducted on the prototype. The experimental results show the framework is flexible, robust, and fully workable. All agents derived from the methodology exhibit their behaviors correctly as specified.

An empirical investigation of hybrid corporate governance systems in large firms: Evidence from India

The heightened pace of corporate governance reforms has focused attention on country-specific
governance models. Considerable debate has ensured as to whether the outsider Anglo-Saxon system
or the insider Continental system is most applicable to India. This paper reports the results of a study
of Indian governance which used a primary qualitative approach of twelve interviews of key executives
of five large firms in 2008 as well as publicly available documents. A literature review establishes six
key characteristics that distinguish the two major systems. The governance characteristics of the
Indian firms are classified in terms of the two systems with a view to assessing the extent and nature of
hybridization. The findings endorse the hybrid corporate governance system of India, clearly
identifying similarities and differences to the two major governance models. In drawing on rich
interview data, the paper delves into the national characteristics of India that have influenced the
hybrid model such as stewardship, corporate social responsibility and partnerships between the
corporate and community sectors. The evolution of the governance practices and the rationale for their
existence are also examined. The paper demonstrates that the hybrid governance system has emanated
from country-specific culture including values and ideologies, and political orientation of socialism.
The scope of this study was limited to large listed companies and business groups. Future research
should use a larger and more diverse sample including private and unaffiliated firms for outcomes that
can be generalized.

Functional observers for dynamical systems

In control theory, a state observer is an auxiliary dynamical system that mirrors the behaviour of a physical system, and it is driven by input and output measurements of the physical system in order to provide an estimate of internal states of the physical system. The primary consideration in the design of an observer is that the estimate of the states should be close to the actual value of the system states. On the other hand, the functional observation problem centers on the construction of an auxiliary dynamical system, known as the functional observer or functional reconstructor, driven by the available system inputs and outputs in order to estimate a linear function or functions of the system states. Obviously, a functional observer is a general form of the state observer because when the linear functions are chosen as the individual states of the system then the problem of functional observation reduces to the problem of state observation.

Terminal sliding mode control strategy design for second-order nonlinear system

This study mainly focuses on the terminal sliding mode control (TSMC) strategy design, including an adaptive terminal sliding mode control (ATSMC) and an exact-estimator-based terminal sliding mode control (ETSMC) for second-order nonlinear dynamical systems. In the ATSMC system, an adaptive bound estimation for the lump uncertainty is proposed to ensure the system stability. On the other hand, an exact estimator is designed for exact estimating system uncertainties to solve the trouble of chattering phenomena caused by a sign function in ATSMC law in despite of the utilization of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes can be verified in numerical simulations.

Characteristics and applications of energy storage system to power network - A review

Maintaining reliability and stability of a power systems in transmission and distribution level becomes a big challenge in present scenario. Grid operators are always responsible to maintain equilibrium between available power generation and demand of end users. Maintaining grid balance is a bigger issue, in case of any unexpected generation shortage or grid disturbance or integration of any renewable energy sources like wind and solar power in the energy mix. In order to compensate such imbalance and to facilitate more renewable energy sources with the grid, energy storage system (ESS) started to be playing an important role with the advancement of the state of the art technology. ESS can also help to get reduction in greenhouse gas (GHG) emission by means of integrating more renewable energy sources to the grid. There are various types of Energy Storage (ES) technologies which are being used in power systems network from large scale (above 50MW) to small scale (up to 100KW). Based on the characteristics, each storage technology has their own merits and demerits. This paper carried out extensive review study and verifies merits and demerits of each storage technology and identifies the suitable technology for the future. This paper also has conducted feasibility study with the aid of E-SelectTM tool for various ES technologies in applications point of view at different grid locations. This review study helps to evaluate feasible ES technology for a particular electrical application and also helps to develop smart hybrid storage system for grid applications in efficient way.

Performance study of a wind-grid system in a semi- arid region and major integration issues

The phenomenal growth in economy experienced in developed countries throughout the 20th century has largely been driven by the availability of conventional energy sources for electricity generation. However, increased concern about fossil fuels and adverse effect of carbon dioxide emission in to atmosphere changed the conventional power system to a viable one by integrating renewable energy sources into the existing system. Among the Renewable Energy (RE) sources, wind energy is one of the fastest growing technologies in reducing the Green House Gas (GHG) emissions in to the atmosphere due to its continuous availability throughout a period. Hence, this paper discusses the performance of a wind-grid connected system in a semi-arid region by conducting a case study. Wilson promontory, one of the best locations for wind generation in Victoria is considered as a case study. Hybrid Optimization Model for Electric Renewable (HOMER) is used as a simulating tool for this analysis. This study also presents the influences of storage system in the proposed Hybrid Power System (HPS) allowing energy to be stored during higher generations or lower load demands. In addition this paper also discusses the major integration issues to facilitate the large scale wind energy into the grid for reliable power generation and distribution.

DYNAMICS AT INFINITY of A CUBIC CHUA'S SYSTEM

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

On an optimal control design for Rossler system

In this Letter, an optimal control strategy that directs the chaotic motion of the Rossler system to any desired fixed point is proposed. The chaos control problem is then formulated as being an infinite horizon optimal control nonlinear problem that was reduced to a solution of the associated Hamilton-Jacobi-Bellman equation. We obtained its solution among the correspondent Lyapunov functions of the considered dynamical system. (C) 2004 Elsevier B.V All rights reserved.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.