Formal Analysis of Linear Control Systems using Theorem Proving

Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation methods, however, both of these methods cannot provide accurate analysis due to their inherent limitations. Model checking has been widely used to analyze control systems but the continuous nature of their environment and physical components cannot be truly captured by a state-transition system in this technique. To overcome these limitations, we propose to use higher-order-logic theorem proving for analyzing linear control systems based on a formalized theory of the Laplace transform method. For this purpose, we have formalized the foundations of linear control system analysis in higher-order logic so that a linear control system can be readily modeled and analyzed. The paper presents a new formalization of the Laplace transform and the formal verification of its properties that are frequently used in the transfer function based analysis to judge the frequency response, gain margin and phase margin, and stability of a linear control system. We also formalize the active realizations of various controllers, like Proportional-Integral-Derivative (PID), Proportional-Integral (PI), Proportional-Derivative (PD), and various active and passive compensators, like lead, lag and lag-lead. For illustration, we present a formal analysis of an unmanned free-swimming submersible vehicle using the HOL Light theorem prover.Comment: International Conference on Formal Engineering Method

Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

Frequency Domain Analysis Reveals External Periodic Fluctuations Can Generate Sustained p53 Oscillation

p53 is a well-known tumor suppressor protein that regulates many pathways, such as ones involved in cell cycle and apoptosis. The p53 levels are known to oscillate without damping after DNA damage, which has been a focus of many recent studies. A negative feedback loop involving p53 and MDM2 has been reported to be responsible for this oscillatory behavior, but questions remain as how the dynamics of this loop alter in order to initiate and maintain the sustained or undamped p53 oscillation. Our frequency domain analysis suggests that the sustained p53 oscillation is not completely dictated by the negative feedback loop; instead, it is likely to be also modulated by periodic DNA repair-related fluctuations that are triggered by DNA damage. According to our analysis, the p53-MDM2 feedback mechanism exhibits adaptability in different cellular contexts. It normally filters noise and fluctuations exerted on p53, but upon DNA damage, it stops performing the filtering function so that DNA repair-related oscillatory signals can modulate the p53 oscillation. Furthermore, it is shown that the p53-MDM2 feedback loop increases its damping ratio allowing p53 to oscillate at a frequency more synchronized with the other cellular efforts to repair the damaged DNA, while suppressing its inherent oscillation-generating capability. Our analysis suggests that the overexpression of MDM2, observed in many types of cancer, can disrupt the operation of this adaptive mechanism by making it less responsive to the modulating signals after DNA damage occurs

Simplifying the Auto Regressive and Moving Average (ARMA) Model Representing the Dynamic Thermal Behaviour of iHouse Based on Theoretical Knowledge

Modelling and simulation is an alternative way of testing the dynamic behaviour of a real system – in some situation, testing the real system are expensive, time consuming, not comfortable, and dangerous. Mathematical model describing the dynamic behaviour of a system can be represented by using white, black, or grey box model. This study focuses on developing a simplified Auto Regressive Moving Average (ARMA) model (a type of linear black model) to represent the dynamic thermal behaviour of iHouse – simplification is done based on the theoretical knowledge of the building. The performance of the simplified ARMA model developed in this study is compared with the performance of the models developed in previous studies, which are: (1) House Thermal Simulator; (2) and ARMA model. Result shows that the simplified ARMA model developed in this study consists of simpler set of mathematical equations, but can still simulate the dynamic thermal behaviour of iHouse with the accuracy that is almost on par with the models developed in previous studies.Modeling, Design and Simulation of Systems. AsiaSim 2017