Compositional Security Analysis of Dynamic Component-based Systems

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Mean privacy: A metric for security of computer systems

Dynamic neural networks are considered as specific class of nonlinear dynamic systems with neural controller in the control contour. It is explained that classical methods of analysis of nonlinear control systems are applicable for the class of systems under consideration. Specific features of application of statistical linearization method for analysis and parametrical synthesis of dynamic neural systems are considered. Analysis of system is interpreted as determination of second statistical moments of various coordinates, for example, of error signal. Synthesis is interpreted as determination of optimal parameters of neural controller, in terms of minimization of root-mean-square error.

Compositional security analysis of dynamic component-based systems

Suppose you are a bicycle messenger in the busy business district of a large city. Here is what your day looks like: You are to deliver incoming mail to building i, and you are to pick up outgoing mail destined only for building i + 1. All in all you are responsible for m buildings. Your bike, however, is not of the highest quality: It can accommodate only mail for a single delivery. Riding from building i to building j requires tij minutes. Once you arrive at a building, you need d minutes to get off your bike, run into the building, and get onto your bike again. Moreover, once incoming mail has arrived at building i, it takes pi minutes for the outgoing mail to be ready (if this is too long, you may want to make another delivery and pickup in the meantime). You are to visit each building k times. Question: In which order should you visit the buildings so that you finish your work as fast as possible? The above description is a simplified version of the problem discussed in the paper by Milind W. Dawande, H. Neil Geismar, and Suresh P. Sethi. There the messenger is a robot, the buildings are machines, and the mail represents parts to be processed by the machines. The authors show that there exists a cyclic schedule that maximizes long-term throughput. Cyclic schedules are preferred in industrial environments, because they are easy to implement and control. Since the literature on robotic cell scheduling is full of different models for different kinds of industrial applications, it is important to know that all optimal schedules can be reduced to cyclic schedules. The authors end their paper by describing several challenging open problems. The paper by Miguel Torres-Torriti and Hannah Michalska describes a software package (LTP), implemented in Maple, for the symbolic manipulation of expressions that occur in the context of Lie algebra theory. This theory has found applications in classical and quantum mechanics, analysis of dynamical systems, construction of nonlinear filters, and the design of feedback control laws for nonlinear systems. Since the symbolic computations are often complex and tedious, the development of software for applications of Lie algebra theory is crucial. The LTP software package is targeted at applications such as solution of differential equations evolving on Lie groups, and structure analysis of general dynamical systems.

In this paper a general method for the analysis of multidimensional second-order dynamic systems with periodically varying parameters is presented. The state vector and the periodic matrices appearing in the equations are expanded in Chebyshev polynomials over the principal period and the original differential problem is reduced to a set of linear algebraic equations. The technique is suitable for constructing either numerical or approximate analytical solutions. As an illustrative example, approximate analytical expressions for the Floquet characteristic exponents of Mathieu’s equation are obtained. Stability charts are drawn to compare the results the proposed method with those obtained by Runge-Kutta and perturbation methods. Numerical solutions for the flap-lag motion of a three blade helicopter rotor are constructed in the next example. The numerical accuracy and efficiency of the proposed technique is compared with standard numerical codes based on Runge-Kutta, Adams-Moulton and Gear algorithms. The results obtained in the both examples indicate that the suggested approach extremely accurate and is by far the most efficient one.

Decomposition multi-step non-iterative method for the numerical integration of short-term and long-term dynamics of power systems

Probabilistic Risk Assessment (PRA) is the primary tool used to risk-inform nuclear power regulatory and licensing activities. Risk-informed regulations are intended to reduce inherent conservatism in regulatory metrics (e.g., allowable operating conditions and technical specifications) which are built into the regulatory framework by quantifying both the total risk profile as well as the change in the risk profile caused by an event or action (e.g., in-service inspection procedures or power uprates). Dynamical Systems (DS) analysis has been used to understand unintended time-dependent feedbacks in both industrial and organizational settings. In dynamical systems analysis, feedback loops can be characterized and studied as a function of time to describe the changes to the reliability of plant Structures, Systems and Components (SSCs). While DS has been used in many subject areas, some even within the PRA community, it has not been applied toward creating long-time horizon, dynamic PRAs (with time scales ranging between days and decades depending upon the analysis). Understanding slowly developing dynamic effects, such as wear-out, on SSC reliabilities may be instrumental in ensuring a safely and reliably operating nuclear fleet. Improving the estimation of a plant's continuously changing risk profile will allow for more meaningful risk insights, greater stakeholder confidence more » in risk insights, and increased operational flexibility. « less

Using MATLAB and Simulink to perform symbolic, graphical, numerical, and simulation tasks, Modeling and Analysis of Dynamic Systems provides a thorough understanding of the mathematical modeling and analysis of dynamic systems. It meticulously covers techniques for modeling dynamic systems, methods of response analysis, and vibration and control sy

bal: A library for the brute-force analysis of dynamical systems

Introduction: This article is the result of the research “Analysis of the dynamic systems component of the engineering programs in control and automation and technology in industrial electronics,” developed at the Francisco José de Caldas District University in the years 2022-2023. Problem: The document addresses the lack of a clear and comprehensive structure in the analysis of linear dynamic systems, as well as the absence of an innovative approach to addressing these topics in traditional courses, which hinders their understanding and application in different disciplines. Objective: The objective is to present a novel approach to analyzing linear dynamic systems, providing a complete framework of concepts, relationships, and important tools in this analysis, as well as a literature review based on over seventeen years of experience in courses and studies of this kind. Methodology: A journey of concepts is proposed from signals and systems, through modeling with methods such as black box, white box, gray box, to linear analysis based on examples with calculation of differential equations, state representation, transfer function, and block diagrams. Results: The document aggregates and articulates all the concepts of dynamic systems, along with the relationships and tools used, offering a more practical and intuitive approach to understanding the material. Conclusion: The document provides a comprehensive and articulated view of key concepts in the analysis of linear dynamic systems, highlighting an innovative approach that facilitates their understanding. Its main contribution is to aggregate and articulate these concepts, along with the tools and relationships used, to offer a more practical and clear approach for their study. Originality: The originality lies in proposing a novel and structured approach to analyzing linear dynamic systems, addressing the lack of clarity and completeness in traditional approaches. Limitations: Although the document proposes a novel approach, it does not delve into specific aspects of some topics covered, which could limit the detailed understanding of certain concepts. Deepening: The document could delve into the practical application of the proposed concepts and tools in real cases of dynamic systems, as well as into the comparison with traditional approaches to highlight the differences and advantages of the proposed new approach.

The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with a wide range of applications have been proposed. However, popular implementations of DMD suffer from observation noise on random dynamical systems and generate inaccurate estimation of the spectra of the stochastic Koopman operator. In this paper, we propose subspace DMD as an algorithm for the Koopman analysis of random dynamical systems with observation noise. Subspace DMD first computes the orthogonal projection of future snapshots to the space of past snapshots and then estimates the spectra of a linear model, and its output converges to the spectra of the stochastic Koopman operator under standard assumptions. We investigate the empirical performance of subspace DMD with several dynamical systems and show its utility for the Koopman analysis of random dynamical systems.

This paper outlines a computational theory of linguistic dynamic systems for computing with words by fusing procedures and concepts from several different areas: Kosko’s geometric interpretation of fuzzy sets, Hsu’s cell-to-cell mappings in nonlinear analysis, equi-distribution lattices in number theory, and dynamic programming in optimalcontrol theory. The proposed framework enables us to conduct a global dynamic analysis, system design and synthesis for linguistic dynamic systems that use words or linguistic terms in computation, based on concepts and methods well developed for conventional dynamic systems. This theory has significant potential for modeling and analysis of systems where model, goal, control and feedback are primarily specified in words or linguistic terms.

In this chapter, we will develop the basic relationships to solve the motion control problem for dynamic systems using analog and digital proportional-integralderivative (PID) controllers as well as state-space control algorithms It should be emphasized that the PID control laws use the tracking errore(t)whereas the state-space controllers use the tracking errore(t)and the state variablesx (t).Proportional-integral-derivative and state-space control algorithms are widely used in dynamic systems to stabilize systems, attain tracking and disturbance attenuation, guarantee robustness and accuracy, and so forth. This chapter provides the introduction to nonlinear control and feedback tracking, and single-input/singleoutput as well as multi-input/multi-output systems are studied. We model the dynamic systems in thes-and z-domains using transfer functionsG sys (s)and Gsys(z) to synthesize the PID-type controllers. The state-space models are used to design control algorithms applying the Hamilton—Jacobi and Lyapunov theories for multi-input/multi-output systems. The theoretical foundations in analysis and design of dynamic systems modeled using linear differential equations are needed to be covered to fully understand the basic concepts in control of nonlinear systems. It should be emphasized that analysis of linear continuous-and discrete-time closed-loop systems with control constraints will be accomplished. As mathematical models are found in the form of differential or difference equations, system parameters (coefficients of differential or difference equations) are defined, and the analysis can be performed to study stability and stability margins, time response, accuracy, and so on. The system characteristics and performance can be improved and “shaped” using PID-type and state-space stabilizing and tracking controllers studied in this chapter. The general problem approached is the design of PID-type and state-space controllers to ensure the specifications imposed on the desired performance of closed-loop dynamic systems. The synthesis of analog and digital control laws involve the design of controller structures as well as adjusting feedback coefficients to attain certain desired criteria and characteristics. These performance specifications relate stability, robustness, dynamics, accuracy, tracking, disturbance attenuation, as well as other criteria needed to be achieved through the use of control algorithms. The tradeoff between stability and accuracy, robustness and system response, and complexity and implementability is well known. The design procedures are reported to find the structures and feedback coefficients of control laws.

This paper introduces an information granularity reduction principle in connection with the analysis of the component of uncertainty associated with data. This overall study is illustrated utilizing simple numerical studies dealing with dynamical systems with first order dynamics. Classical and fuzzy Petri models are introduced in the analysis of dynamical systems. The overall study is illustrated utilizing simple numeric studies. The agenda involves a number of essential development issues: (i) providing a constructive way to build Petri nets out of numerical experimental data from dynamical systems, (ii) analyzing the component of uncertainty associated with data and elaborating on its minimization via an optimal quantization of the variables involved in the model of construction, (iii) considering the role of set-theoretic and fuzzy set frameworks in the transformation of numeric quantities into their qualitative (symbolic) counterparts, and (iv) identifying the role of Petri nets in the analysis of dynamical systems.