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This tutorial guide introduces online nonstochastic control, an emerging paradigm in control of dynamical systems and differentiable reinforcement learning that applies techniques from online convex optimization and convex relaxations to obtain new methods with provable guarantees for classical settings in optimal and robust control. In optimal control, robust control, and other control methodologies that assume stochastic noise, the goal is to perform comparably to an offline optimal strategy. In online control, both cost functions and perturbations from the assumed dynamical model are chosen by an adversary. Thus, the optimal policy is not defined a priori and the goal is to attain low regret against the best policy in hindsight from a benchmark class of policies. The resulting methods are based on iterative mathematical optimization algorithms and are accompanied by finite-time regret and computational complexity guarantees. This book is ideal for graduate students and researchers interested in bridging classical control theory and modern machine learning.
With an emphasis on timeless essential mathematical background for optimization, this textbook provides a comprehensive and accessible introduction to convex optimization for students in applied mathematics, computer science, and engineering. Authored by two influential researchers, the book covers both convex analysis basics and modern topics such as conic programming, conic representations of convex sets, and cone-constrained convex problems, providing readers with a solid, up-to-date understanding of the field. By excluding modeling and algorithms, the authors are able to discuss the theoretical aspects in greater depth. Over 170 in-depth exercises provide hands-on experience with the theory, while more than 30 'Facts' and their accompanying proofs enhance approachability. Instructors will appreciate the appendices that cover all necessary background and the instructors-only solutions manual provided online. By the end of the book, readers will be well equipped to engage with state-of-the-art developments in optimization and its applications in decision-making and engineering.
Providing a succinct overview of Lindenmayer system (L-system) topology optimization, this book focuses on the methods and theory underlying this novel bioinspired approach. Starting from basic principles, the book outlines how topology optimization can be utilized at the conceptual design stage and shows how it offers straightforward applicability to multi-objective and/or multi-physical industrial problems. Design strategies are clearly demonstrated using a host of case studies and real-world examples, and their potential challenges and solutions are discussed. Written from an optimization and design perspective, the authors both summarize the latest advances in this field and suggest potential avenues of research and development for future work. This will be the ideal resource for engineering practitioners, researchers, and students wanting to gain a new perspective on using topology optimization to improve product design.
This practical guide to optimization combines mathematical theory with hands-on coding examples to explore how Python can be used to model problems and obtain the best possible solutions. Presenting a balance of theory and practical applications, it is the ideal resource for upper-undergraduate and graduate students in applied mathematics, data science, business, industrial engineering and operations research, as well as practitioners in related fields. Beginning with an introduction to the concept of optimization, this text presents the key ingredients of an optimization problem and the choices one needs to make when modeling a real-life problem mathematically. Topics covered range from linear and network optimization to convex optimization and optimizations under uncertainty. The book's Python code snippets, alongside more than 50 Jupyter notebooks on the author's GitHub, allow students to put the theory into practice and solve problems inspired by real-life challenges, while numerous exercises sharpen students' understanding of the methods discussed.
Primal heuristics guarantee that feasible, high-quality solutions are provided at an early stage of the solving process, and thus are essential to the success of mixed-integer programming (MIP). By helping prove optimality faster, they allow MIP technology to extend to a wide variety of applications in discrete optimization. This first comprehensive guide to the development and use of primal heuristics within MIP technology and solvers is ideal for computational mathematics graduate students and industry practitioners. Through a unified viewpoint, it gives a unique perspective on how state-of-the-art results are integrated within the branch-and-bound approach at the core of the MIP technology. It accomplishes this by highlighting all the required knowledge needed to push the heuristic side of MIP solvers to their limit and pointing out what is left to do to improve them, thus presenting heuristic approaches for MIP as part of the MIP solving process.
Using a pedagogical, unified approach, this book presents both the analytic and combinatorial aspects of convexity and its applications in optimization. On the structural side, this is done via an exposition of classical convex analysis and geometry, along with polyhedral theory and geometry of numbers. On the algorithmic/optimization side, this is done by the first ever exposition of the theory of general mixed-integer convex optimization in a textbook setting. Classical continuous convex optimization and pure integer convex optimization are presented as special cases, without compromising on the depth of either of these areas. For this purpose, several new developments from the past decade are presented for the first time outside technical research articles: discrete Helly numbers, new insights into sublinear functions, and best known bounds on the information and algorithmic complexity of mixed-integer convex optimization. Pedagogical explanations and more than 300 exercises make this book ideal for students and researchers.
Dive into the foundations of intelligent systems, machine learning, and control with this hands-on, project-based introductory textbook. Precise, clear introductions to core topics in fuzzy logic, neural networks, optimization, deep learning, and machine learning, avoid the use of complex mathematical proofs, and are supported by over 70 examples. Modular chapters built around a consistent learning framework enable tailored course offerings to suit different learning paths. Over 180 open-ended review questions support self-review and class discussion, over 120 end-of-chapter problems cement student understanding, and over 20 hands-on Arduino assignments connect theory to practice, supported by downloadable Matlab and Simulink code. Comprehensive appendices review the fundamentals of modern control, and contain practical information on implementing hands-on assignments using Matlab, Simulink, and Arduino. Accompanied by solutions for instructors, this is the ideal guide for senior undergraduate and graduate engineering students, and professional engineers, looking for an engaging and practical introduction to the field.
Using a step-by-step approach, this textbook provides a modern treatment of the fundamental concepts, analytical techniques, and software tools used to perform multi-domain modeling, system analysis and simulation, linear control system design and implementation, and advanced control engineering. Chapters follow a progressive structure, which builds from modeling fundamentals to analysis and advanced control while showing the interconnections between topics, and solved problems and examples are included throughout. Students can easily recall key topics and test understanding using Review Note and Concept Quiz boxes, and over 200 end-of-chapter homework exercises with accompanying Concept Keys are included. Focusing on practical understanding, students will gain hands-on experience of many modern MATLAB® tools, including Simulink® and physical modeling in Simscape™. With a solutions manual, MATLAB® code, and Simulink®/Simscape™ files available online, this is ideal for senior undergraduates taking courses on modeling, analysis and control of dynamic systems, as well as graduates studying control engineering.
Presenting students with a comprehensive and efficient approach to the modelling, simulation, and analysis of dynamic systems, this textbook addresses mechanical, electrical, thermal and fluid systems, feedback control systems, and their combinations. It features a robust introduction to fundamental mathematical prerequisites, suitable for students from a range of backgrounds; clearly established three-key procedures – fundamental principles, basic elements, and ways of analysis – for students to build on in confidence as they explore new topics; over 300 end-of-chapter problems, with solutions available for instructors, to solidify a hands-on understanding; and clear and uncomplicated examples using MATLAB®/Simulink® and Mathematica®, to introduce students to computational approaches. With a capstone chapter focused on the application of these techniques to real-world engineering problems, this is an ideal resource for a single-semester course in dynamic systems for students in mechanical, aerospace and civil engineering.
Most systems involved in a chemical process plant are interactive multivariable systems, to control which, the transfer function matrix model is required. This lucid book considers the identification and control of such systems. It discusses open loop and closed loop identification methods, as well as the design of multivariable controllers based on steady state gain matrix. Simple methods for designing controllers based on transfer function matrix model have been reviewed. The design of controllers for non-square systems, and closed loop identification of multivariable unstable systems by the optimization method are also covered. Several simulation examples and exercise problems at the end of each chapter further help the reader consolidate the knowledge gained. This book will be useful to any engineering student, researcher or practitioner who works with interactive, multivariable control systems.
Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering a broad overview of the growing intersection of data-driven methods, machine learning, applied optimization, and classical fields of engineering mathematics and mathematical physics. With a focus on integrating dynamical systems modeling and control with modern methods in applied machine learning, this text includes methods that were chosen for their relevance, simplicity, and generality. Topics range from introductory to research-level material, making it accessible to advanced undergraduate and beginning graduate students from the engineering and physical sciences. The second edition features new chapters on reinforcement learning and physics-informed machine learning, significant new sections throughout, and chapter exercises. Online supplementary material – including lecture videos per section, homeworks, data, and code in MATLAB®, Python, Julia, and R – available on databookuw.com.
This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.
A high school student can create deep Q-learning code to control her robot, without any understanding of the meaning of 'deep' or 'Q', or why the code sometimes fails. This book is designed to explain the science behind reinforcement learning and optimal control in a way that is accessible to students with a background in calculus and matrix algebra. A unique focus is algorithm design to obtain the fastest possible speed of convergence for learning algorithms, along with insight into why reinforcement learning sometimes fails. Advanced stochastic process theory is avoided at the start by substituting random exploration with more intuitive deterministic probing for learning. Once these ideas are understood, it is not difficult to master techniques rooted in stochastic control. These topics are covered in the second part of the book, starting with Markov chain theory and ending with a fresh look at actor-critic methods for reinforcement learning.
The authors explain in this work a new approach to observing and controlling linear systems whose inputs and outputs are not fixed in advance. They cover a class of linear time-invariant state/signal system that is general enough to include most of the standard classes of linear time-invariant dynamical systems, but simple enough that it is easy to understand the fundamental principles. They begin by explaining the basic theory of finite-dimensional and bounded systems in a way suitable for graduate courses in systems theory and control. They then proceed to the more advanced infinite-dimensional setting, opening up new ways for researchers to study distributed parameter systems, including linear port-Hamiltonian systems and boundary triplets. They include the general non-passive part of the theory in continuous and discrete time, and provide a short introduction to the passive situation. Numerous examples from circuit theory are used to illustrate the theory.
This comprehensive text provides an excellent introduction to the state of the art in the identification of network-connected systems. It covers models and methods in detail, includes a case study showing how many of these methods are applied in adaptive optics and addresses open research questions. Specific models covered include generic modelling for MIMO LTI systems, signal flow models of dynamic networks and models of networks of local LTI systems. A variety of different identification methods are discussed, including identification of signal flow dynamics networks, subspace-like identification of multi-dimensional systems and subspace identification of local systems in an NDS. Researchers working in system identification and/or networked systems will appreciate the comprehensive overview provided, and the emphasis on algorithm design will interest those wishing to test the theory on real-life applications. This is the ideal text for researchers and graduate students interested in system identification for networked systems.
Discover a comprehensive set of tools and techniques for analyzing the impact of uncertainty on large-scale engineered systems. Providing accessible yet rigorous coverage, it showcases the theory through detailed case studies drawn from electric power application problems, including the impact of integration of renewable-based power generation in bulk power systems, the impact of corrupted measurement and communication devices in microgrid closed-loop controls, and the impact of components failures on the reliability of power supply systems. The case studies also serve as a guide on how to tackle similar problems that appear in other engineering application domains, including automotive and aerospace engineering. This is essential reading for academic researchers and graduate students in power systems engineering, and dynamic systems and control engineering.
Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.
Infrastructures are complex networks dominated by tight interdependencies between technologies and institutions. These networks supply services crucial to modern societies, services that can be provided only if several critical functions are fulfilled. This book proposes a theoretical framework with a set of concepts to analyse rigorously how these critical functions require coordination within the technological dimension as well as within the institutional dimension. It also shows how fundamental the alignment between these two dimensions is. It argues that this alignment operates along different layers characterized successively by the structure, governance and transactions that connect technologies and institutions. These issues of coordination and alignment, at the core of the book, are substantiated through in-depth case studies of networks from the energy, water and wastewater, and transportation sectors.
Presenting a fresh look at process control, this new text demonstrates state-space approach shown in parallel with the traditional approach to explain the strategies used in industry today. Modern time-domain and traditional transform-domain methods are integrated throughout and explain the advantages and limitations of each approach; the fundamental theoretical concepts and methods of process control are applied to practical problems. To ensure understanding of the mathematical calculations involved, MATLAB® is included for numeric calculations and MAPLE for symbolic calculations, with the math behind every method carefully explained so that students develop a clear understanding of how and why the software tools work. Written for a one-semester course with optional advanced-level material, features include solved examples, cases that include a number of chemical reactor examples, chapter summaries, key terms, and concepts, as well as over 240 end-of-chapter problems, focused computational exercises and solutions for instructors.