Graduate Courses

Graduate courses in the area of Systems Control are listed below. Course descriptions can be obtained by clicking on the course number. More detailed descriptions may be available on individual professor's home pages.

WINTER TERM 2013

ECE 557H - Systems Control - M. Maggiore
State-space approach to linear system theory. Mathematical background in linear algebra, state space equations vs transfer functions, solutions of linear ODE's, state transition matrix, Jordan form, controllability, eigenvalue assignment using state feedback, observability, designing observers, separation principle, Kalman filters, tracking and the regulator problem, linear quadratic optimal control, stability. Four labs cover the state space control design methodology.

ECE 1617H - Large-Scale System Theory and Control - E.J. Davison
This course is an introduction to the control of large scale systems: decentralized fixed mode characterization/computation, interconnected systems, decentralized control, decentralized pole assignment, decentralized robust servomechanism problem, expanding system control problem.

ECE 1619H - Linear Geometric Control Theory - M. Broucke
The course presents a more advanced treatment of linear control theory via the geometric approach. The coverage roughly corresponds to the first six chapters of "Linear Multivariable Control: A Geometric Approach", by W.M. Wonham. We adopt the abstract algebra approach of the text to study controllability, observability, controlled invariant subspaces, controllability subspaces, and controllability indices. These concepts are applied to solve the problems of stabilization, output stabilization, disturbance decoupling, and the restricted regulator problem. Areas of current research in linear geometric control will also be discussed.

ECE 1634H - Real-Time Computer Control
Sampling, aliasing, signal filtering; choice of sampling rate. Multi-mode systems; control saturation, integrator windup, mode switching. Issues of task scheduling, priority and urgency, data base consistency. Laboratory experiments and a significant individual laboratory project form the major part of this course.

ECE 1635H - Modern Control Methodology: Case Study Active Suspension - J. Apkarian
This is a project based course involving mathematical modeling, realtime systems, control design, hardware in the loop simulations and VR simulations as applied to automotive active suspension control systems. The course will cover the following: car modelling and control design - integration and testing using supplied VR simulator; car hardware experiments to validate model and controller - actual implementation on real hardware available in the lab. Introduction of full car model with passive suspension (developed in MapleSim); Design and integration of active suspension system with full car model, Integration of full model with realtime interactive 3D graphical simulator.

ECE 1636H - Control of Discrete-Event Systems I - W.M. Wonham
This course is an introduction to the control of discrete, asynchronous, nondeterministic systems like manufacturing, traffic and communication systems. Architectural issues (modular, decentralized and hierarchical control) are emphasized. The theory is developed in an elementary framework of automata, formal languages and Petri nets, and is supported by a software package for creating applications. Course notes are provided. (Prerequisite: A previous course in discrete mathematics (elementary logic and set theory) would be helpful but is not essential.)

ECE 1637H - Control of Discrete-Event Systems II - W.M.Wonham
This course is a continuation of ECE 1636H, and is conducted on a seminar basis. Participants will present and discuss articles in the current literature, and complete a project that could lead into graduate research in the discrete-event system area. Topics recently examined include controlled Petri nets, min-max algebra, real-time control via timed-transition-models (TTMs), recursive process algebras, and state charts.

ECE 1639H - Analysis and Control of Stochastic Systems I - R.H. Kwong
This is the first course of a two-term sequence on stochastic systems designed to cover some of the basic results on estimation, identification, stochastic control and adaptive control. Topics include: stochastic processes and their descriptions, analysis of linear systems with random inputs; prediction and filtering theory: prediction for ARMAX systems, the Kalman filter and the Riccati equation; stochastic control methods based on dynamic programming; the LQG problem and the separation theorem; minimum variance control.

ECE 1640H - Analysis and Control of Stochastic Systems II - Not offered
This course is the continuation of ECE 1639H. Topics include: parameter estimation theory for parametric models: least squares and maximum likelihood estimators; offline identification methods for linear systems; identifiability, convergence, and consistency; recursive methods for system identification; introduction to convergence analysis of recursive schemes using the ordinary differential equation method and the martingale method. Adaptive control of stochastic systems: self-tuning regulators, direct adaptive control schemes, stability and convergence analysis using martingale theory.

ECE 1641H - Multivariable Control Design - Not offered
Design techniques for linear multivariable systems. State variable and transfer matrix models; performance measures in terms of norms of signals and systems; design by H2 and H-infinity optimization; uncertainty models, including structured uncertainty; stability and performance robustness; design by mu synthesis. Students do a major design project using MATLAB and mu-Tools. Click here for more information.

ECE 1643H - Special Topics: Game Theory and Evolutionary Games - L. Pavel
This course presents a mathematical treatment of classical and evolutionary game theory. Topics covered in classical game theory: matrix games, continuous games, Nash equilibrium (NE) solution, existence and uniqueness, Pareto optimal solution. Topics covered in evolutionary games: evolutionary stable strategy (ESS) concept, NE versus ESS, replicator dynamics (population dynamics), adaptation (strategy) dynamics, stability concepts and relation to dynamic asymptotic stability. The two areas will be connected by learning in games via imitation dynamics, fictitious play and their relation to replicator dynamics. Engineering applications to communication networks, multi-agent learning, network formation will be discussed.
Prerequisites: ECE410 or ECE557 or equivalent.

ECE 1644H - Large Scale System Theory and Control II - Not offered
This course is a continuation of ECE 1617H: model reduction problem, approximate decentralized fixed modes, decentralized control of descripter systems, robust control, optimal decentralized control, computer-aided design, case studies - traffic light control, control of flexible space structures, building temperature control, load and frequency power control.

ECE 1646H - Digital Control - Not offered
An advanced course on digital control. Topics: sample-and-hold; discretization of analog systems; discrete-time systems analysis and design; simulation; effects of sampling on controllability and observability; internal stability; digital loop-shaping; induced norms; L1, H2, and H-infinity optimization; multirate systems.

ECE 1647H - Introduction to Nonlinear Control - B. Francis
Outline: Basic Dynamics: Finite dimensional phase flows and their relationship to vector fields. Continuity and differentiability. Existence and uniqueness of solutions of ODEs. Stable and unstable manifolds, and structural stability. Basic Stability Theory: Stability definitions. Direct Lyapunov theorems for autonomous systems. Invariance and LaSalle's invariance principle for autonomous systems. Control design using Lyapunov functions. Basic Nonlinear Regulator Theory: centre manifold theory and regulator equations. Nonlinear internal models.
Applications: Research examples illustrating the design approaches.

ECE 1648H - Nonlinear Control Systems - M. Maggiore
This course is a continuation of ECE1647. It focuses on geometric methods and structural properties of nonlinear control systems. Course prerequisites: ECE1647 and ECE557 (or an equivalent state space linear systems course). Topics covered in the course include: introduction to differentiable manifolds; the feedback equivalence problem; feedback linearization; stabilization and tracking for feedback linearizable systems, with application to robotics; invariant and controlled invariant manifolds; the zero dynamics algorithm; invariant distributions and quotient systems; introduction to nonlinear controllability.

ECE 1649H - Adaptive Control - Not offered
Course is a state-of-the art presentation of adaptive control from a determinstic (versus stochastic) viewpoint. Control of linear, time-invariant, continuous-time plants with unknown parameters is emphasized, although straightforward extensions to linearly parameterized nonlinear plants are explored. Stability is analyzed rigorously. Measures to improve robustness (e.g. sigma-modification) are presented. Examples are drawn from robotics, mechanics, process control, etc.

ECE 1650H - Multirate DSP and Wavelets - B.A. Francis
Wavelets are basis functions for the analysis and processing of signals that allow good resolution in both time and frequency. The subject has grown rapidly since the early 1980s and is now a major research field. Techniques exist for both 1-dimensional and multidimensional signals and one successful application has been to image compression, including fingerprints. Click here for more information.

ECE 1651H - Adaptive Signal Processing and Control - Not offered
This course provides an introduction to the theory and applications of adaptive signal processing and control. Topics include: the structure of adaptive algorithms, performance surfaces; the LMS algorithm in adaptive signal processing, adaptive IIR filters; applications to echo cancellation, noise cancellation, channel equalization, etc.; model reference adaptive control systems, adaptive stabilization, robustness issues, stochastic adaptive control; applications to process control.

ECE 1652H - Stochastic Processes with Applications - R.H. Kwong
Review of probability. Definition and examples of stochastic processes. Markov chains and applications, introduction to queueing. Renewal processes, generalized semi-Markov processes, stochastic discrete event systems. Introduction to dynamic programming and optimization applications. Stationary processes, spectral analysis and linear systems, state space models. Introduction to estimation and filtering. (Prerequisites: Linear systems and signal processing (e.g., ECE310/311 or ECE355/356), undergraduate course on probability theory (e.g., ECE302).)

ECE 1653H - Hybrid Systems and Control Applications - M. Broucke
Recent research results in hybrid systems are covered. Hybrid models, qualitative theory including non-blocking analysis, Zeno phenomena, and stability of switched systems; reachability, safety, liveness as fixpoint analyses; Bisimulation; safety controller synthesis, optimal controller synthesis; robustness. Applications in nonlinear control, multivehicle systems, and transportation systems are discussed. (Prerequisites: ECE1647F, ECE1619F.)

ECE 1654H - Optical Networks: A Systems Control Perspective - L. Pavel
Topics in system control for communication networks, specifically optical networks. This is an interdisciplinary research direction emerging in the context of re-configurable, dynamic networks. Topics include: dynamics and control of network elements: optical amplifiers, dynamic filters; adaptive filters concepts (LMS algorithm); stability of interconnected systems (time-scale decomposition); robust stability concepts (H- infinity control, small gain theorem); network modeling as time-delay system; stability analysis via robust control; end-to-end network control: wireless, optical and congestion control examples; network control based on SNR optimization (decentralized iterative algorithms); introduction to game theory concepts.

ECE 1655H - Optimal Control - B. Francis
This is a graduate course on optimal control theory. The pre-requisite is an undergraduate course on state-space control systems, such as ECE557. There is also a design project. The main topics are these: the calculus of variations, the maximum principle, dynamic programming, optimization in Hilbert and Banach spaces, H-2 optimal control, H-infinity optimal control.

ECE 1656H - Nonlinear Modeling and Analysis of Biological Systems - L. Scardovi
This course studies dynamical models used in biology and introduces the nonlinear dynamics tools necessary for their analysis. The first part reviews basic nonlinear dynamics concepts with illustrations on biological models like population growth and logistic models. The second part focuses on biochemical reactions and genetic regulation while the third part reviews and analyzes basic neuronal models. The last part of the course introduces specific nonlinear systems concepts (such as passivity, monotonicity, cooperativity) for the quantitative study of biological networked systems (such as biochemical reaction networks and neuron populations). Selected topics will be covered independently via small research projects or paper reading and presented in workshop style meetings.
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