Robustness Verification And Optimization Of Nonlinear Systems PDF Download
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| Author | : Dongchan Lee |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2022 |
| Genre | : |
| ISBN | : |
Download Robustness Verification and Optimization of Nonlinear Systems Book in PDF, ePub and Kindle
Nonlinear systems allow us to describe and analyze physical and virtual systems, including dynamical systems, power grids, robots, and neural networks. The problems involving nonlinearity pose challenges in providing safety guarantees and robustness in the presence of uncertainty. This thesis provides methods to exploit knowledge on upper and lower bounds on the nonlinearity and solves problems related to robustness verification and optimization subject to uncertain parameters. The first half of the thesis develops the convex restriction of a non-convex feasibility set defined by a set of nonlinear equality and inequality constraints. Convex restrictions provide a closed-form convex quadratic condition that is sufficient for solving a system of nonlinear equations. By replacing the original constraints with the proposed conditions, a non-convex optimization problem can be solved as a sequence of convex optimization problems, with feasibility and robustness guarantees. We demonstrate its applications in Model Predictive Control (MPC), robustness verification of neural networks, robust Optimal Power Flow (OPF) problem, and motion planning in robotics. The second part of the thesis focuses on nonlinear dynamical systems and develops reachability analysis and constrained-input constrained-output analysis for verification problems. We provide an optimization-based method for computing reachable sets around a nominal trajectory. The proposed methods use contraction metrics to find templates for reachable sets. Additionally, we developed constrained-input constrained-output analysis to characterize the relationship between peak magnitudes of input and output signals. Numerical experiments were conducted to demonstrate their applicability to a broad class of nonlinear systems.
| Author | : Bhawna Tandon |
| Publisher | : |
| Total Pages | : 176 |
| Release | : 2019-07-24 |
| Genre | : |
| ISBN | : 9783346038661 |
Download How Can Robust Control of Nonlinear Systems be Achieved? Examining Optimization Techniques Book in PDF, ePub and Kindle
Doctoral Thesis / Dissertation from the year 2019 in the subject Engineering - General, Basics, grade: A.00, language: English, abstract: The following text examines the questions, how nonlinear system can better be controlled by new optimisation techniques such as feedback linearization. Due to the inevitable nonlinearities in real systems, several nonlinear control methods like feedback linearization, sliding mode control, backstepping approach and further modes are described in detail in the literature. Due to limitations in application of well known classical methods, researchers have struggled for decades to realize robust and practical solutions for nonlinear systems by proposing different approaches or improving classical control methods. The feedback linearization approach is a control method which employs feedback to stabilize systems containing nonlinearities. In order to accomplish this, it assumes perfect knowledge of the system model to linearize the input-output relationship. In the absence of perfect system knowledge, modelling errors inevitably affect the performanceof the feedback controller. Many researchers have come up with a new form of feedback linearization, called robust feedback. This method gives a linearizing control law that transforms the nonlinear system into its linear approximation around an operating point. Thus, it causes only a small transformation in the natural behavior of the system, which is desired in order to obtain robustness. The controllers are required to provide various time domain and frequency domain performances while maintaining sufficient stability robustness. In this regard, the evolutionary optimization techniques provide better option as these are probabilistic search procedures and facilitate inclusion of wide variety of time and frequency domain performance functionals in the objective functions. A significant scope of work remains to be done which provides motivation for the research in the design of rob
| Author | : Stephen Prajna |
| Publisher | : |
| Total Pages | : 204 |
| Release | : 2005 |
| Genre | : Electronic dissertations |
| ISBN | : |
Download Optimization-based Methods for Nonlinear and Hybrid Systems Verification Book in PDF, ePub and Kindle
| Author | : A.J. Fossard |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 250 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 1461311934 |
Download Nonlinear Systems Book in PDF, ePub and Kindle
Nonlinear Systems is divided into three volumes. The first deals with modeling and estimation, the second with stability and stabilization and the third with control. This three-volume set provides the most comprehensive and detailed reference available on nonlinear systems. Written by a group of leading experts in the field, drawn from industry, government and academic institutions, it provides a solid theoretical basis on nonlinear control methods as well as practical examples and advice for engineers, teachers and researchers working with nonlinear systems. Each book focuses on the applicability of the concepts introduced and keeps the level of mathematics to a minimum. Simulations and industrial examples drawn from aerospace as well as mechanical, electrical and chemical engineering are given throughout.
| Author | : Erin M. Aylward |
| Publisher | : |
| Total Pages | : 110 |
| Release | : 2006 |
| Genre | : |
| ISBN | : |
Download Robust Stability and Contraction Analysis of Nonlinear Systems Via Semidefinite Optimization Book in PDF, ePub and Kindle
A wide variety of stability and performance problems for linear and certain classes of nonlinear dynamical systems can be formulated as convex optimization problems involving linear matrix inequalities (LMIs). These formulations can be solved numerically with computationally-effcient interior-point methods. Many of the first LMI-based stability formulations applied to linear systems and the class of nonlinear systems representable as an interconnection of a linear system with bounded uncertainty blocks. Recently, stability and performance analyses of more general nonlinear deterministic systems, namely those with polynomial or rational dynamics, have been converted into an LMI framework using sum of squares (SOS) programming. SOS programming combines elements of computational algebra and convex optimization to provide e±cient convex relaxations for various computationally-hard problems. In this thesis we extend the class of systems that can be analyzed with LMI-based methods.
| Author | : Oliver Nelles |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 785 |
| Release | : 2013-03-09 |
| Genre | : Technology & Engineering |
| ISBN | : 3662043238 |
Download Nonlinear System Identification Book in PDF, ePub and Kindle
Written from an engineering point of view, this book covers the most common and important approaches for the identification of nonlinear static and dynamic systems. The book also provides the reader with the necessary background on optimization techniques, making it fully self-contained. The new edition includes exercises.
| Author | : Lucas Matthew Tecot |
| Publisher | : |
| Total Pages | : 40 |
| Release | : 2021 |
| Genre | : |
| ISBN | : |
Download Robustness Verification with Non-Uniform Randomized Smoothing Book in PDF, ePub and Kindle
Formal verification via randomized smoothing has become an effective method for verifying the robustness of machine learning models to adversarial attacks. In this work, I extend randomized smoothing by allowing noises with independent variances on each input element of a smoothed classifier, enabling the flexibility of using non-uniform perturbations rather than the standard l-p norm perturbations. Furthermore, I provide practical optimization methods to find the optimal variance matrix through gradient descent. I evaluate my method on MNIST, Fashion-MNIST, CIFAR-10, ImageNet, and KITTI datasets and show that my optimized non-uniform smoothing noises can certify a region with guaranteed robustness magnitudes larger in volume than previous works. Additionally, my method can be used to evaluate the sensitivity of input features and identify non-robust and robust features.
| Author | : Tevfik Bultan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 545 |
| Release | : 2011-09-21 |
| Genre | : Computers |
| ISBN | : 3642243711 |
Download Automated Technology for Verification and Analysis Book in PDF, ePub and Kindle
This book constitutes the refereed proceedings of the 9th International Symposium on Automated Technology for Verification and Analysis, ATVA 2011, held in Taipei, Taiwan, in October 2011. The 23 revised regular papers presented together with 5 invited papers, 11 short papers, and 2 tool papers, were carefully reviewed and selected from 75 submissions. The papers address all theoretical and practical aspects of automated analysis, verification and synthesis; thus providing a forum for interaction between the regional and the international research communities and industry in the field.
| Author | : |
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| Total Pages | : 0 |
| Release | : 1997 |
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Download Robustness Analysis and Synthesis for Essentially Nonlinear Systems Book in PDF, ePub and Kindle
The research was concentrated on developing an advanced theory of stability and performance analysis of nonlinear dynamical systems. The ultimate goal is to provide algorithms and software for analytical validation of flight control algorithms involving gain scheduling, actuator saturation logical switching, etc., thus reducing the current dependence on extensive simulations in feedback control design. A number of new results were obtained. A study of dynamic behaviour of rate limiters allowed for the first time to develope methods of absolute stability analysis that are capable of discriminating between systems with quasiconcave nonlinearities (such as the saturation) and quasiconvex nonlinearities (such as the deadzone). A software package for rigorous analysis of stability and performance of nonlinear/time-varying/uncertain systems was developed based on the concept of Integral Quadratic Constraints. A new method of gain scheduling for linear feedback design under the condition of control saturation has been developed, with guaranteed stability margins rigorously proven. A unique technique for rigorous analysis of global and semiglobal stability of self-oscillations in higher order relay feedback systems has been developed.
| Author | : Alexandra Silva |
| Publisher | : Springer Nature |
| Total Pages | : 922 |
| Release | : 2021-07-17 |
| Genre | : Computers |
| ISBN | : 3030816850 |
Download Computer Aided Verification Book in PDF, ePub and Kindle
This open access two-volume set LNCS 12759 and 12760 constitutes the refereed proceedings of the 33rd International Conference on Computer Aided Verification, CAV 2021, held virtually in July 2021. The 63 full papers presented together with 16 tool papers and 5 invited papers were carefully reviewed and selected from 290 submissions. The papers were organized in the following topical sections: Part I: invited papers; AI verification; concurrency and blockchain; hybrid and cyber-physical systems; security; and synthesis. Part II: complexity and termination; decision procedures and solvers; hardware and model checking; logical foundations; and software verification. This is an open access book.
