Conic optimization for control,energy systems,and machine learning: Applications and algorithms

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems.     

A tutorial on linear and bilinear matrix inequalities

This is a tutorial on the mathematical theory and process control applications of linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Many convex inequalities common in process control applications are shown to be LMIs. Proofs are included to familiarize the reader with the mathematics of LMIs and BMIs. LMIs and BMIs are applied to several important process control applications including control structure selection, robust controller analysis and design, and optimal design of experiments. Software for solving LMI and BMI problems is reviewed.     

Game theory for cognitive radio networks: An overview

Cognitive radio technology, a revolutionary communication paradigm that can utilize the existing wireless spectrum resources more efficiently, has been receiving a growing attention in recent years. As network users need to adapt their operating parameters to the dynamic environment, who may pursue different goals, traditional spectrum sharing approaches based on a fully cooperative, static, and centralized network environment are no longer applicable. Instead, game theory has been recognized as an important tool in studying, modeling, and analyzing the cognitive interaction process. In this tutorial survey, we introduce the most fundamental concepts of game theory, and explain in detail how these concepts can be leveraged in designing spectrum sharing protocols, with an emphasis on state-of-the-art research contributions in cognitive radio networking. Research challenges and future directions in game theoretic modeling approaches are also outlined. This tutorial survey provides a comprehensive treatment of game theory with important applications in cognitive radio networks, and will aid the design of efficient, self-enforcing, and distributed spectrum sharing schemes in future wireless networks.     

Review of rational (total) nonlinear dynamic system modelling,identification, and control

This paper is a summary of the research development in the rational (total) nonlinear dynamic modelling over the last two decades. Total nonlinear dynamic systems are defined as those where the model parameters and input (controller outputs) are subject to nonlinear to the output. Previously, this class of models has been known as rational models, which is a model that can be considered to belong to the nonlinear autoregressive moving average with exogenous input (NARMAX) model subset and is an extension of the well-known polynomial NARMAX model. The justification for using the rational model is that it provides a very concise and parsimonious representation for highly complex nonlinear dynamic systems and has excellent interpolatory and extrapolatory properties. However, model identification and controller design are much more challenging compared to the polynomial models. This has been a new and fascinating research trend in the area of mathematical modelling, control, and applications, but still within a limited research community. This paper brings several representative algorithms together, developed by the authors and their colleagues, to form an easily referenced archive for promotion of the awareness, tutorial, applications, and even further research expansion.     

A Tutorial On Mean-Field-Type Games and Risk-Aware Controllers

This paper presents a tutorial of the role that mean-field-type games play in the design of risk-aware controllers. The tutorial is presented in an easy-to-follow manner for beginners, engineers and early career scientists. It starts by introducing a basic stochastic mean-field-free control design problem and progressively adds more complexity to the problem setup navigating through the risk-aware control design, stochastic differential games, mean-field games, and concluding with mean-field-type games. All the problems are solved in a semi-explicit way by means of the direct method and some engineering applications, such as water distribution system and consensus under uncertainties, illustrate the performance of the presented risk-awareness framework.     

A stochastic games framework for verification and control of discrete time stochastic hybrid systems

We describe a framework for analyzing probabilistic reachability and safety problems for discrete time stochastic hybrid systems within a dynamic games setting. In particular, we consider finite horizon zero-sum stochastic games in which a control has the objective of reaching a target set while avoiding an unsafe set in the hybrid state space, and a rational adversary has the opposing objective. We derive an algorithm for computing the maximal probability of achieving the control objective, subject to the worst-case adversary behavior. From this algorithm, sufficient conditions of optimality are also derived for the synthesis of optimal control policies and worst-case disturbance strategies. These results are then specialized to the safety problem, in which the control objective is to remain within a safe set. We illustrate our modeling framework and computational approach using both a tutorial example with jump Markov dynamics and a practical application in the domain of air traffic management.     

An exploratory classification of applications in the realm of collaborative modeling and design

The high complexity and diversity of today’s design projects demands the participation of multiple experts. The participating experts can influence the design process by sharing their perspective, expertise and resources. The involvement of various experts is often known as collaborative modeling and design. A collaborative modeling environment can encompass various geographical or organizational boundaries. In this paper, we provide a classification to study various aspects of this important issue through the exploration of the existing models, methods and applications in this area. The paper further addresses both model-oriented and artifact-neutral collaboration approaches and enumerates their features. The paper introduces the features of and classifies several relevant applications. The classification can serve as a guideline for customizing a suitable setting for a collaborative modeling process based on given requirements, needs and demands. Several suggestions for future work are also provided.     

Parallelizing irregular and pointer-based computations automatically: Perspectives from logic and constraint programming

Irregular computations pose some of the most interesting and challenging problems in automatic parallelization. Irregularity appears in certain kinds of numerical problems and is pervasive in symbolic applications. Such computations often use dynamic data structures, which make heavy use of pointers. This complicates all the steps of a parallelizing compiler, from independence detection to task partitioning and placement. Starting in the mid 80s there has been significant progress in the development of parallelizing compilers for logic programming (and more recently, constraint programming) resulting in quite capable parallelizers. The typical applications of these paradigms frequently involve irregular computations, and make heavy use of dynamic data structures with pointers, since logical variables represent in practice a well-behaved form of pointers. This arguably makes the techniques used in these compilers potentially interesting. In this paper, we introduce in a tutorial way, some of the problems faced by parallelizing compilers for logic and constraint programs and provide pointers to some of the significant progress made in the area. In particular, this work has resulted in a series of achievements in the areas of inter-procedural pointer aliasing analysis for independence detection, cost models and cost analysis, cactus-stack memory management, techniques for managing speculative and irregular computations through task granularity control and dynamic task allocation (such as work-stealing schedulers), etc.     

Upwind-Difference Potentials Method for Patlak-Keller-Segel Chemotaxis Model

We develop a novel upwind-difference potentials method for the Patlak-Keller-Segel chemotaxis model that can be used to approximate problems in complex geometries. The chemotaxis model under consideration is described by a system of two nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction-diffusion equation for the chemoattractant concentration. Chemotaxis is an important process in many medical and biological applications, including bacteria/cell aggregation and pattern formation mechanisms, as well as tumor growth. Furthermore modeling of real biomedical problems often has to deal with the complex structure of computational domains. There is consequently a need for accurate, fast, and computationally efficient numerical methods for different chemotaxis models that can handle arbitrary geometries. The upwind-difference potentials method proposed here handles complex domains with the use of only Cartesian meshes, and can be easily combined with fast Poisson solvers. In the numerical tests presented below we demonstrate the robustness of the proposed scheme.     

The role and use of the stochastic linear-quadratic-Gaussian problem in control system design

The role of the linear-quadratic stochastic control problem in engineering design is reviewed in tutorial fashion. The design approach is motivated by considering the control of a non-linear uncertain plant about a desired input-output response. It is demonstrated how a design philosophy based on 1) deterministic perturbation control, 2) stochastic state estimation, and 3) linearized stochastic control leads to an overall closed-loop control system. The emphasis of the paper is on the philosophy of the design process, the modeling issue, and the formulation of the problem; the results are given for the sake of completeness, but no proofs are included. The systematic off-line nature of the design process is stressed throughout.     

Modeling of ferrofluid magnetic actuation with dynamic magnetic fields in small channels

One of the most important and promising research areas in biomedical and micropumping applications is magnetic actuation of ferrofluids with dynamic magnetic fields. For ensuring the use of ferrofluids in various applications in engineering fields, their flows generated by magnetic fields should be extensively investigated and simulated. In this study, simulations of ferrofluid actuation with dynamic magnetic fields were performed by modeling it using the COMSOL Multiphysics software, and iron oxide nanoparticle-based ferrofluids at different angles of rotating magnets were considered to provide insight into ferrofluid flow in small channels. Ferrofluid flows were modeled at different magnetic flux densities provided by rotating magnets, and velocity profiles inside the channel were analyzed. It was shown that ferrofluid actuation can be considered as a futuristic micropumping alternative, simulation results matched well with the experimental results of previous work, and the established model could serve as a tool to analyze ferrofluid flows generated by dynamic magnetic fields. The results of the model show that flow rates up to 100 µl/s can be reached at a rotation angle of 30° by using dynamic magnetic fields. Various applications including biomedical applications might be envisaged.     

A tutorial – game theory-based extended H infinity filtering approach to nonlinear problems in signal processing

In this paper, we provide a tutorial for the applications of “game-theory-based extended H infinity filtering (EHIF)” approach to various problems in disciplines of signal processing. The algorithm of this filtering approach is similar to that of the extended Kalman filtering (EKF). Since its invention, the Kalman filtering approach has been successfully and widely employed for many problems in scientific and engineering fields, e.g. target tracking, satellite systems, control, communications, etc. Therefore, the H infinity filtering approach also can be applied to all these problems. One big difference of EHIF from the EKF approach is that we apply it with unknown noise statistics of the state and measurement. In this tutorial, we introduce this non-well-known approach in spite of its practical usefulness, by providing the step by step algorithm with example problems of a number of signal processing disciplines. We also show that EHIF can outperform other approaches including the EKF that need to know the noise statistics in their applications, in some scenarios. By the contribution of this tutorial, we look forward to easy, and disseminative applications of EHIF to problems where, particularly, the EKF or particle filter could have been applied if noise statistics were known.     

Computer algebra tailored to matrix inequalities in control

A major advance in linear systems theory over the last decade has been a formalism for converting systems problems to matrix inequalities. In this tutorial paper we describe computer algebra algorithms, methodology, and implementation which allows users to convert many systems problems to linear matrix inequalities (LMIs). We shall focus on computer algebra methodology which can assist the user in producing LMIs for control design. We provide a step-by-step computer derivation of LMI formulas for the design of linear time-invariant dynamic controllers that achieve a prespecified performance measured by the H _∞ norm of a certain closed loop transfer function.     

基于教学控制论的CAI模型

本文基于教学控制论和知识工程技术，以充分体现个别教学为原则，提出了一个通用的智能型教学模型，详细讨论了知识的构成和表示方法，并提出教学内容，教学环节和教学过程的组织和控制方法，该模型基本独立于被教学的内容，因此具有广泛的适用性。     

Modeling the dynamic behavior of hypermedia applications

Hypermedia applications can be defined as collections of interactive and multimedia documents that are organized as a hypertext net. The development of hypermedia applications poses specific problems, such as the need for modeling sophisticated navigational structures, interactive behaviors, and harmonic presentations involving the synchronization of contents. Moreover, the increasing popularity of Internet based systems has put stress on the lack of mechanisms to formally specify security policies when designing hypermedia applications. Traditional design models and methodologies are not suitable for hypermedia applications and the up-to-now developed hypermedia oriented models do not cover the whole set of design needs. In this context, we present Labyrinth, a hypermedia oriented model providing formal elements to describe the static structure and dynamic behavior of this kind of nonlinear, multisensory, and interactive applications     

How to model and prove hybrid systems with KeYmaera: a tutorial on safety

This paper is a tutorial on how to model hybrid systems as hybrid programs in differential dynamic logic and how to prove complex properties about these complex hybrid systems in KeYmaera, an automatic and interactive formal verification tool for hybrid systems. Hybrid systems can model highly nontrivial controllers of physical plants, whose behaviors are often safety critical such as trains, cars, airplanes, or medical devices. Formal methods can help design systems that work correctly. This paper illustrates how KeYmaera can be used to systematically model, validate, and verify hybrid systems. We develop tutorial examples that illustrate challenges arising in many real-world systems. In the context of this tutorial, we identify the impact that modeling decisions have on the suitability of the model for verification purposes. We show how the interactive features of KeYmaera can help users understand their system designs better and prove complex properties for which the automatic prover of KeYmaera still takes an impractical amount of time. We hope this paper is a helpful resource for designers of embedded and cyber–physical systems and that it illustrates how to master common practical challenges in hybrid systems verification.     

Test Synthesis from UML Models of Distributed Software

The object-oriented software development process is increasingly used for the construction of complex distributed systems. In this context, behavior models have long been recognized as the basis for systematic approaches to requirements capture, specification, design, simulation, code generation, testing, and verification. Two complementary approaches for modeling behavior have proven useful in practice: interaction-based modeling (e.g., UML sequence diagrams) and state-based modeling (e.g., UML statecharts). Building on formal V&V techniques, in this article we present a method and a tool for automated synthesis of test cases from scenarios and a state-based design model of the application, remaining entirely within the UML framework. The underlying "on the fly" test synthesis algorithms are based on the input/output labeled transition system formalism, which is particularly appropriate for modeling applications involving asynchronous communication. The method is eminently compatible with classical OO development processes since it can be used to synthesize test cases from the scenarios used in early development stages to model global interactions between actors and components, instead of these test cases being derived manually. We illustrate the system test synthesis process using an air traffic control software example     

基于扩展的UML构建Web应用系统的WAMDM模型

Windows DNA形态的Web应用正在变得越来越广泛，越来越复杂，越来越难以控制。给出了一种利用扩展UML构建Web应用的方法模型(WAMDM，Web Application Modeling and Developing Methodology)。应用该方法模型来开发Web应用，不仅可以很好地控制系统的复杂性，使Web应用的开发和维护更容易进行，而且将windows DNA的3层设计以一致的方式完全集成，使整个设计开发过程平滑一致。     

Hypermedia systems for improving knowledge,understanding and skills in engineering degree courses

Two contrasting computer based learning applications have been introduced into engineering degree courses. Both are based upon the “open” hypermedia approach, and both use Microcosm to organise and link resources, and Toolbook to present much of the material. One of the applications uses a traditional, “linear”, tutorial style approach, while the other presents students with a design problem and provides them with a large and diverse amount of poorly structured information which the students have to use to generate an engineering design. Both applications were evaluated in several ways and analysis of the responses leads to the conclusion that carefully written computer based applications can be effective not only for teaching basic knowledge at this level, but can also be used as a means of allowing students to develop skills in complex areas such as generating solutions to open-ended mechanical engineering design problems.