Corso di laurea magistrale - Area di Ingegneria - Accesso libero con verifica del possesso dei requisiti curriculari - Classe LM-25 (D.M. 270/2004)
Informazioni generali
Descrizione e obiettivi formativi:
Il corso forma figure professionali operanti nei settori del controllo e dell'automazione dei sistemi e dei processi, della robotica e delle esplorazioni spaziali.
Il corso prevede lo studio di argomenti specifici di teoria del controllo, di automazione e robotica, nonché di molti argomenti interdisciplinari, poiché l’ingegnere dell’automazione deve spesso interagire con specialisti di altri ambiti dell’ingegneria. In particolare, vengono affrontati: sistemi dinamici a tempo continuo, a tempo discreto e ad eventi discreti; automazione dei processi industriali; automazione della fabbrica e del movimento; robotica industriale e spaziale; progettazione dei sistemi di controllo per macchine elettriche e per motori endotermici; progettazione di asservimenti per sistemi meccanici; progettazione di sistemi di controllo per satelliti; dinamica e controllo dei robot industriali e dei robot di servizio; progettazione dei dispositivi e dei sistemi per il controllo dinamico degli impianti e dei sistemi di produzione; modellistica e controllo di sistemi ecologici e sociali.
Gli obiettivi formativi prevedono l’utilizzo di tecniche e metodologie delle scienze di base (la matematica, la fisica, la chimica e l’informatica) per interpretare e descrivere per mezzo di modelli i problemi dell'ingegneria in generale e, in particolare, quelli dell'ingegneria dell'automazione, con particolare riferimento alla scrittura di modelli formali di processi e sistemi, alla loro simulazione, al progetto di leggi/strategie di controllo.
Le attività del corso, molte anche in laboratorio, permettono di acquisire capacità di condurre esperimenti, di analizzarne i dati per mezzo di ausili informatici, con lo scopo di caratterizzare il processo attraverso un modello matematico. Modelli di varia complessità così ottenuti sono la base per gli scopi progettuali: per l’ottenimento di tali scopi si alternano fasi di analisi e di sintesi, per le quali gli studenti apprendono sia tecniche classiche e consolidate in ambito industriale, sia molti strumenti sviluppati recentemente e basati su tecnologie innovative.
Tra gli obiettivi dei corsi impartiti, fondamentale è fornire agli studenti gli strumenti per l'aggiornamento continuo delle proprie conoscenze, sia attraverso il proseguimento degli studi con corsi di dottorato, sia attraverso lo studio individuale su libri e riviste scientifiche del campo.
Sbocchi professionali:
Il laureato magistrale in Ingegneria dell’Automazione opera in molteplici settori, laddove si utilizzino competenze nel controllo e nell'automazione dei sistemi e dei processi, nella robotica e nelle attività spaziali, in aziende ed enti di ricerca sia pubblici sia privati. Tali competenze sono al momento molto richieste in Italia e all’estero, e in particolare nel contesto europeo.
Esempi di profili professionali sono: ingegnere progettista di sistemi di controllo in aziende impegnate nella produzione industriale, nella progettazione di sistemi di automazione, nella trasformazione e smistamento dell'energia, in impianti petrolchimici e farmaceutici; ricercatore in enti di vari settori (tra cui spaziale e nucleare).
L'ingegnere dell'automazione ha competenze che gli permettono di operare in quattro aree principali: le aziende che producono e forniscono sistemi d'automazione; le aziende e le società che utilizzano impianti automatizzati di produzione o gestiscono servizi d'elevata complessità; le società d'ingegneria e di consulenza che studiano e progettano impianti e sistemi complessi, tecnologicamente sofisticati; gli enti di ricerca, soprattutto nell’ambito spaziale e dell’energia.
L'ingegnere dell'automazione può trovare impiego in tutte le industrie, aziende ed enti nei quali i sistemi di predizione, diagnosi, controllo e supporto alle decisioni sono tecnologicamente rilevanti.
Condizione occupazionale (indicatori di efficacia e livello di soddisfazione dei laureandi):
http://statistiche.almalaurea.it/universita/statistiche/trasparenza?CODICIONE=0580207302600001
Valutazione della didattica - Studenti
Anno accademico precedente
Riferimenti web e contatti:
Sito Web: http://dicii.uniroma2.it/?PG=48.12.1
Coordinatore: Prof. Sergio Galeani
tel 06 7259 7428
E-mail: sergio.galeani@uniroma2.it
Segreteria didattica:
Sig.ra Maria Luisa COTTONE e Sig.ra Maria Beatrice GIAMBENEDETTI
Tel. 06 7259.7003
E-mail: didattica.civile@ing.uniroma2.it
Per ulteriori informazioni consulta anche il sito web di Facoltà:
http://ing.uniroma2.it/didattica/corsi-di-laurea/
Single-DOF Linear mechanical system. Free vibrations. Forced vibrations. Determination of the damping factor. Vibration isolation. Average power dissipation. Impulse response. Flexural critical speed. Colombian damping. Linear models with two-degrees-of-freedom. Free vibration. Forced vibrations. Hysteretic damping. Viscous damping. Multidegree of Freedom System. Using Newton’s second law to derive Equations of Motion. Free and forced vibration of undamped systems. Forced vibration of viscously damped systems. Solution of the Eigenvalue Problem. Self-excited and stability analysis. Rayleigh’s method. Holzer’s method. Jacobi’s method. Choleski decomposition. Iterative methods for calculating eigenvalues by Guyan reduction. Rotor dynamics. Method Dunkerley . The model Föppl-de-Laval. Critical Speeds. Stability analysis. Balancing of shaft drives. Torsional vibrations . The method of Holzer. Analysis of systems subjected to impact . Analysis of the spectrum of the response to the shock . Analysis of the impact on the ground. Maximum acceleration and displacement . Padding characterized by nonlinear elasticity . Relations acceleration – time . Amplification factor . Vibration Measurement and Application. Spectrum analyzers. Bandpass filter. Modal Testing. Digital signal processing. Analysis of random signals. Determination of modal data from observed picks and from Nyquist Plot. Discrete Fourier transform (DFT). The convolution theorem. Errors in DFT. Aliasing and Leakage . Continuous systems. Longitudinal vibrations of bar or rod. Equation of motion and solution. Orthogonality of the normal functions. Transverse vibrations of beams. Initial and Boundary conditions. Model Euler-Bernoulli. Free transverse vibrations . Travelling wave solution . Forced vibrations . Timoshenko model . Torsional vibrations of beams. Torsional vibration free. Forced vibrations . Variational methods. The method of Rayleigh – Ritz. Lanczos algorithm . Finite element method. Beam element subjected to axial force. Local and global coordinate systems. Model of Euler – Bernoulli . Boundary conditions. Assembly of mass and stiffness matrices. Application experience in the laboratory. Finite element method in the dynamic analysis of an element of the machine. Acquisitions of signals through the use of accelerometric measurement chains. Development of the Discrete Fourier Transform. Experimental modal analysis. Acquisition of signals from impact tests.
PROGRAM: Section I: Machine Learning and Kernel-based Learning Overview of Supervised Leanring Methods. Probabilistic methods. Generative Methods. Unsupervised Methods. Clustering. Semantic Similarity metrics. Agglomerative Clustering. K-mean. Markov Models. Hidden Markov Models. Kernel-based Learning. Linear, Polynomial and RBF Kernels. String Kernels. Tree kernels. Latent Semantic kernels. Semantic kernels. Applications. Section II: Statistical Language Processing Supervised Language Processing tools. HMM-based POS tagging. Named Entity Recognition. Statistical parsing. PCFGs: Charniak parser. Lexicalized Parsing Models. Shallow Semantic Parsing: kernel based semantic role labeling. Information Extraction. Section III: Web Mining & Retrieval. Document Ranking Methods for the Web. Introduction to Social Network Analysis: rank and centrality. Random walk models: Page Rank. Search Engines. SEO. Google. Question Answering Systems. Open-domain Information Extraction. Knowledge Acquisition from open sources. Wikipedia. Social Web. Graph Algor
0. Descriptive statistics: datasets, descriptive statistics, mode, mean, order statistic, median, quantiles, percentiles, variance and standard deviation, skewness and kurtosis, covariance and correlation, frequency tables, graphs and chart pies, box graphs and outliers, histograms, kenel density estimates, empirical distribution of a dataset, PP-plots and QQ-plots, from descriptive statistics to inferential statistics, the need for a probability theory. 1. Probability spaces: outcomes of random phenomena and experiments, events, event σ-algebras, probability, Dirac probability, Bernoulli probability, uniform discrete probability, discrete and continuous probability densities, binomial, hypergeometric, geometric, Poisson densities, uniform continuous density, exponential density, Gaussian density, independent events, conditioning of events, conditioned probabilities, total probability theorem, Bayes theorem. 2. Random Variables: distribution and distribution function of a random variable, median, quantiles, mode, discrete random variables, Dirac random variable, Bernoulli and Rademacher random variables, uniform discrete random variable, binomial, and hypergeometric random variables, geometric and Poisson random variables, continuous and absolutely continuous random variables, density of an absolutely continuous random variable, uniform continuous random variable, exponential and Gaussian random variables. 3. Moments of a random variable: moment of the first order (xpectation), moments of higher order, variance, skewness, and kurtosis, Markov inequalities, Tchebychev inequality, Holder and Minkowski inequalities, spaces of random variables. 4. Random vectors: joint and marginal distribution, distribution function of a random vector, absolutely continuous random vectors, density of an absolutely continuous random vector, marginal densities, moments of a random vector, expectation of a random vector, variance-covariance matrix of a random vector, multi-variate Gaussian distributions. 5. Independent and conditioned random variables: information model, independent random variables, conditioning of random variables with respect to some available information, conditional expectation, conditional expectation and linear regression, conditional expectation for jointly Gaussian random variables. 6. Modes of convergence of a succession of random variables: almost sure convergence, convergence in probability, convergence in mean and quadratic mean, convergence in distribution, Laws of Large Numbers, Central Limit Theorem. 7. Introduction to Statistical inference: populations and samples, size of a sample, random samples, independent and non-independent samples, simple random samples, the role of the Laws of Large numbers and Central Limit Theorem. 8. Point estimators: unbiased and dbiased parametric estimators, mean square error, consistent and sufficient estimators, sample mean, sample variance, other point estimators, point estimator distributions, Gamma distribution, Student distribution, Chi-square distribution, independence between media and sample variance of a simple Gaussian random sample. 9. Determination of point estimators: method of moments and maximum likelihood method, properties of maximum likelihood estimators. 10. Interval estimators: confidence intervals, confidence intervals for a population mean, confidence intervals for a population variance, confidence intervals for the difference between the means of two populations, prediction intervals. 11. Hypothesis test: conceptual foundations of a hypothesis test, null hypothesis and alternative hypothesis, types of error, rejection regions and p-value, hypothesis tests for a population mean, hypothesis test for a population variance, hypothesis test for the difference of two populations mean, "randomness" tests, normality tests, analysis of variance (ANOVA).
EMBEDDED SYSTEMS Introduction to the embbeded systems. Technologies adopted for the embedded systems. The ARM architecture. Bare-metal system based on ARM (introduction, cross-compiler, makefile, linker script, LED programming, initializations of memory segments and stack; hardware registers abstraction; initialization of the exception vector; serial port output; hardware interrupts; periodic tick; real-time scheduler with non-preemptible jobs; the low-level handler of the interrupts; real-time scheduler with preemptible jobs; policy EDF; server CBS; experimental measures and tests for worst-case execution times and latencies) REAL-TIME SYSTEMS Introduction to real-time systems. Reference model for real-time systems. Clock-driven scheduling. Priority-driven scheduling algorithms. Optimality of priority-driven algorithms. Scheduling test for fixed-priority policies. Schedulability conditions for Rate Monotonic (RM), Deadline Monotonic (DM), Earliest Deadline First (EDF). Scheduling of blocking jobs. Work-conserving algorithms for aperiodic job handling. Resource control to shared resources. Real-time on multiprocessors. Real-time operating systems. Use of the Linux kernel in real-time systems.
Introduction to reinforcement learning, non-associative methods for learning, introduction to Markov decision processes, dynamic programming, tabular methods for learning (Monte Carlo, temporal difference, elegibility traces), coupling learning and planning, prediction and control with functional approximation (linear and nonlinear), optimal control based on data for systems with continuous state and action spaces, analysis of partially observable systems, examples of application
KINEMATICS: Kinematic structure analysis of mechanisms. Nomenclature, classification of kinematic pairs. Computation of degrees-of-freedom with Gruebler and Kutzbach formulas. Graphs-mechanisms correspondence. Loop closure equations method. Newton-Raphson iteration. Matrix method of degrees-of-freedom analysis. Review of velocity and accelerations formulas in rigid systems. Method of polar diagrams. Coriolis acceleration in mechanisms. Aronhold-Kennedy theorem. Grashof rule. Finite motions. Center of finite rotations. Kinematic synthesis of four-bar for 2 and 3 finite displacements: displacement matrices for absolute and relative motions. Method of Suh-Radcliffe and its extensions. Freudenstein equation. Motion polodes. Curvature analysis. Euler-Savary equation. Center of acceleration. Bresse circles. Generation of conjugate profiles (method of epicycle). Freudenstein theorem. MECHANICAL TRANSMISSIONS: Typologies of gear transmissions. Involute profile features. Modular design. Line of contacts and arc of action. Interference and methods for its elimination. Minimum number of teeth. Helicoidal teeth. Kinematic analysis of differential gear trains. Willis formula. Mechanical joints: Cardan, Tracta, Tripode, Rzeppa. Geometric conditions for homokinetic motion transmission. STATICS & DYNAMICS Classification of forces in machines. Equivalent system of forces. Resultant of forces: Funicular diagrams. Energy balance in machines. Efficiency of elementary machines. Efficiency of series and parallel connected units. Lumping of masses and stiffness. Review of dynamic of rigid bodies. Principle of virtual work and its application to mechanics of machines.. Inverse dynamic analysis of four-bar and slider-crank mechanisms. Reduction of inertia forces. Simplified dynamics of the slider-crank mechanisms for balancing. Flywheel and Tredgold method. VIBRATIONS: Free and forced vibrations of systems with 1 dof. Identification of damping with the logarithmic decrement and average dissipated power methods. Amplification factor. Vibration of systems with a mobile base. Force and displacement transmissibility coefficients. Critical speeds of shafts. Isolation of vibrations. Systems with 2 dofs. The dynamic damper. Numerical integration methods: Eulero, Heun and Runge. Vibration of N dofs systems. Orthogonality of vibration modes. Decoupling of motion equations.
1) Structural properties: reachability, controllability, observability, reconstructability. 2) Eigenvalue assignment through static state-feedback (Mitter formula, Ackermann formula). 3) State observer design and dynamic output feedback. 4) Elements of realization theory. 5) Youla-Kucera parametrization of stabilizing controllers (the SISO case).
Programma di Prototipazione Virtuale: Virtual Prototyping (6 Credits – Instructor: Pier Paolo Valentini) Aim of the Course: The main objective of the course is to discuss both theoretical basis and practical methodologies to build virtual prototypes of mechanical assemblies. The course also includes an extensive training on professional software applications. At the end of the course, students will have acquired the skills necessary to build and analyze complex virtual prototypes based on the use of computer-aided engineering tools. Prerequisites: There is no mandatory prerequisite to meet. Anyway, a basic knowledge of element of machinery is recommended. Teaching methods: Classroom teaching Examination procedures: Applicative test with a personal computer and discussion of a student project. Contents: Introduction to the course. Tools and Methodologies of the virtual engineering. The representation of three-dimensional geometry: wireframe, B-rep, CSG, Octree and polygonal modellers. Parametric and feature-based modelling. Direct modelling. Mathematical representation of curves and surfaces. Interpolating and approximating curves and surfaces. Linear, parabolic and cubic interpolants. Lagrange polynomials. Bézier Curves, Hérmite Curves, B-spline and NURBS curves and surfaces. Coons’ Patches. Examples and numerical implementation. Differential geometry of curves and surfaces. Precision classes of surfaces. Professional CAE environments: strengths, weaknesses and conscious usage. Parts, Assembly and Drawing documents. Top-down and Bottom-up modelling strategies. 2D and 3D sketching: entities, dimensional and geometrical constraints. Layout sketches and kinematic sketches. Solid modelling strategies: basic and advanced features. Boolean operators and free-form deformers. Surface modelling strategies. Sheet metal modelling tools. Configurations of parts and assemblies. Equation-driven modelling. Basic and advanced assembly constraints. Flexible assemblies. Functionality checks of part and assemblies. Use of part libraries and customization of standard parts. Reverse Engineering pieces of equipment and methodologies. Photorealistic Rendering. Neutral formats for exchanging geometrical information. Cost simulation. Relationship between shape and manufacturing cost. More information about the course and lessons are available at the web pages http://dmmf.mec.uniroma2.it/CorsiPV.html
Introduction to robust and adaptive control; Norms of signals and systems; Small gain; Dissipativity; Modeling of uncertainty; The H-infinity control problem: formulation and solutions; Riccati equations; Loopshaping; The regulator theory; The internal ,model principle; Parametric uncertainties; Estimation and observers; Adaptive control; Introduction to nonlinear robust and adaptive control; Examples and applications.
Hardware insights Pipelining and super-scalar processors Speculative hardware Multi-processors and multi-cores Physical memory organization Memory coherency and consistency Hardware synchronization support Advanced interrupt architectures Kernel Internals Addressing and software protection models Kernel access GATEs System calls dispatching System level memory management Advanced management of interrupts System (kernel) scalability Virtual file system structures Software interactions with the memory hierarchy Advanced thread coordination approaches Security System security aspects Authentication and habilitation Protection domains and secure operating systems System internal attacks and countermeasures IDS and Reference Monitor architectures Attacks at the border between hardware and software Case studies: Linux kernel 2.4/2.6/3.xx/4.xx (x86 architectures) Boot basics Main data structures and initialization Steady state behavior Kernel hacking Modules
Part one Introduction to Computer Networks. Access and Core networkS. Transmission media. Delay & loss in packet-switched networks. Protocols Layers and service models. Internet backbone Principles of application layer protocols. The World Wide Web: HTTP. File Transfer: FTP. E-mail on the Internet. DNS: the directory service of the Internet. TRansport layer principles. Multiplexing and demultiplexing. UDP protocol. Reliable data transfer: principles. Congestion control: principles. TCP Protocols. Network service models. Routing principles. Hierarchical routing. IP protocol. Routing in the Internet. Router Architecture. The link layer: introduction and services. Multiple Access Protocols and LANs. LAN Addresses and ARP. Ethernet network. Hub, Bridge and Switch. LAN 802.11. Part two Programming network applications. Socket. Connection-oriented and connectionless Applications. Multiplexing / O. Examples of Applications. Software components of the Web: Web Client; Web Server; Web Proxy. HTTP / 1.1 protocol. General characteristics and evolution of the protocol. Methods, headers and response codes. Mechanisms for the optimization of the network bandwidth. Connection Management: persistent connections and pipelining. Web Server Architecture and components. Software architectures. Management of static resources. The Apache Web server. Technologies for the generation of dynamic resources. Logical levels of a Web-based service. Multi-tier architectures.
http://didattica.uniroma2.it/docenti/curriculum/5216-Antonio-Tornambe
Robotics: introduction, mechanical characteristics of a robot, the working space, the operating load, joints, degrees of freedom, the standardization of symbols. Rotations, translations, and roto-translations: the coordinates of a rigid body, rotations in R3, the use of quaternions to represent rotations, infinitesimal rotations in R3, translations in R3, roto-translations in R3, anti-symmetric matrices. Direct kinematics: Denavit-Hartenberg notation, planar robot with 2 links with hinged pivot joints, planar robot with 3 links with pivot joints hinge, cartesian robot, cylindrical robot, SCARA robot, spherical robot, spherical robot (the manipulator of Stanford), spherical wrist, anthropomorphic robot, the manipulator of Stanford, the PUMA robot, the robot SCORTEC-ER I. Inverse kinematics: calculation in closed form for position and orientation, the inverse kinematic problem in closed form, dynamic inversion kinematics. Kinetic and potential energy: calculation of the kinetic/potential energies, the Steiner theorem. The Euler-Lagrange equation: calculus of variations, the principle of Hamilton, statics, conservation of total energy, dynamic models of simple mechanical systems. Fundamentals of robotic manipulation: the matrix gripping, manipulation of an object, scheduling of the task. Trajectory and path planning: trajectory planning, minimum energy, minimum time, Bezier curves. Motion planning: the graph of visibility, decomposition in cells, the method of lines. Control: position control and trajectory tracking, calculated control torque, PD control. Vision: direct mathching, information extraction, method of projections. Devices: encoders, PWM modulation systems for transmission of motion.
Requirement engineering. Software Process. Software Analysis and Design. Software Dev. Syllabus and schedule. Types of the software process. Form Iterative to Agile. Rational Unified Process (RUP). Sketching on the homework project. Requirements Management. Presentation of the homework project. UC Modeling. Discussion of the homework project. Use case Realization. OO Thinking and Software Modeling. UML-Use cases. UML-Activity diagram. Classes, Objects, and Information Hiding. Class Diagram. Inheritance. Polymorphism. Examples. Binding of methods in Java. Interfaces. Multiple Inheritance among interfaces in Java. Associations, Aggregations, and Compositions. Differences from Inheritance. Implementation of associations. Dependences and their types. UML and OOP in Java. Sequence Diagrams. State Machines and related UML diagrams. GoF design patterns and their implementation in Java. Other types of Patterns. Subsystems: Interfaces and Components. Exceptions and their Java model. Meta-classes. Java Reflection. File Java. Serialization/Deserialization. Examples of definition and usage of Java Files. Software Verification and Validation 1. Testing by JUnit. Java Language and Platform. Concurrent Programming. And Web Applications. Syllabus and schedule. Concurrency models, Heavy and light processes. Java Threads. Types of, and codes for, Java threads. Concurrency in global environment (shared memory). Java thread states. Monitors and their types. Java monitor. Lock, and implicit Java lock. Usage of Synchronized in Java. Java Lock and Condition. Reading-writing Java Lock. Other types of problems with global concurrency, and their Java solutions. Models of concurrency in local environments. Asynchronous/Synchronous, symmetric/asymmetric, extended/tight rendezvous communication models. Pointing to next course of Distributed systems for Java RMI and CORBA, and related evolutions. Bean. Elements of Hibernate. Events and their management in Java. Java Graphics by Swing. MVC Architecture of a Web Application. HTML, JSP, and related examples. Java Annotations.
Elements of measurement theory and errors treatment. Objectives of the diagnostic measurements in thermonuclear fusion reactors. Measurements and reconstructions of electromagnetic fields • Elements of electromagnetism for the passive identification of the magnetic fields • Introduction to laser and neutral beam technologies for the internal measurements of the magnetic fields • Integration of diagnostic measurements for the identification and control of the magnetic configuration Diagnostics for the kinetic quantities • Basics elements of interferometry and reflectometry for the measurements of the electron density • Cyclotron emission and Thomson scattering for the measurements of the electron temperature profiles Measurements of the fusion products • Basics of fusion reactions • Physics of neutron detectors • Measurements techniques for the alpha particles Basics of atomic physics for the spectroscopic measurements of impurities Post processing techniques of experimental data
PROGRAM: Section I: Machine Learning and Kernel-based Learning Overview of Supervised Leanring Methods. Probabilistic methods. Generative Methods. Unsupervised Methods. Clustering. Semantic Similarity metrics. Agglomerative Clustering. K-mean. Markov Models. Hidden Markov Models. Kernel-based Learning. Linear, Polynomial and RBF Kernels. String Kernels. Tree kernels. Latent Semantic kernels. Semantic kernels. Applications. Section II: Statistical Language Processing Supervised Language Processing tools. HMM-based POS tagging. Named Entity Recognition. Statistical parsing. PCFGs: Charniak parser. Lexicalized Parsing Models. Shallow Semantic Parsing: kernel based semantic role labeling. Information Extraction. Section III: Web Mining & Retrieval. Document Ranking Methods for the Web. Introduction to Social Network Analysis: rank and centrality. Random walk models: Page Rank. Search Engines. SEO. Google. Question Answering Systems. Open-domain Information Extraction. Knowledge Acquisition from open sources. Wikipedia. Social Web. Graph Algor
1. Games in normal form. Nash equilibria. Pareto optimality. Weakly and strictly dominant strategies. Conservative strategies. Payoff and total preorders. 2. An application of dominant strategies: auction mechanisms. First price and second price (Vickrey) auctions. An application of Nash equilibria: law of accident. 3. Zero-sum games. Saddle points and Nash equilibria for zero-sum games. Strictly competitive games. 4. Extension in mixed strategy of a game. Existence of an equilibrium in mixed strategy for zero-sum games. Von Neumann's theorem. Bluff, underbid and Kuhn's poker. 5. Cooperative games. Core of a game. The theorem of Bondareva-Shapley. Markets with transferable utility. Shapley value. Simple games. 6. Cooperative games with nontransferable utility. The house allocation problem. The stable marriage problem. 7. Facility location: theory and exact approximate algorithms, deterministic and randomized. Primal dual schemes. Facility location games. 8. Minimum spanning tree: theory and exact algorithms. Steiner trees: theory and approximate algorithms. Primal dual schemes. Cost sharing mechanisms. Steiner trees games.
http://didattica.uniroma2.it/docenti/curriculum/3546-Roberto-Basili
Description of the main control architectures and necessary diagnostics for the control of nuclear fusion plants
Introduction, mathematical tools for non linear differential equations, Lyapunov, Controllability and Observability for nonlinear systems, Geometric Control, Feedback linearization, Feedforwarding, High-gain observers, certainty equivalent controllers, application to robotics systems
