Graduate Courses

ECE = Electrical and Computer Engineering

Core Courses

The official list of core courses can be found in the Graduate Academic Calendar.

Related Courses

Special Topics in Control

Course Descriptions

ECE 780 T02: Discrete Event Systems

Rising levels of automation pose new challenges for control. Control theory has historically been based on differential- or difference-equation models, and its primary preoccupation has been control synthesis for individual, small-scale subsystems. But today's highly computerized and networked control systems are complex, and require the coordination of large numbers of interacting subsystems. Such large-scale coordination problems are often best framed in terms of more high-level discrete-event models, based on state machines (or automata), formal languages, formal logic, etc. Since the early eighties, control scientists have been developing comprehensive approaches to the control of discrete event systems (DES); this course provides an introduction to this now well established branch of control.

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ECE 700 T03: Algebraic Fundamentals for Computation, Communication and Control

Equivalence relations and congruences. Morphisms, semigroups and monoids. Groups: cyclic groups, subgroups and quotient groups. Rings: subrings, quotient rings, integral domains and fields. Partial orders, lattices and fixed-points of monotone operators.

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ECE 780 T06: Humanoid robotics

This course provides an overview of the fundamentals and the recent research in the field of humanoid robotics. The course will cover kinematics and dynamics, postural stability, control, gait and trajectory generation and inertial parameter estimation. Additional advanced topics in learning, human-robot interaction and manipulation and grasping and human motion modeling will be covered as time permits.

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ECE 780 T08: Topics in Motion Coordination and Planning

This course will cover aspects of path planning, dynamic vehicle routing, and coordination for mobile robots. Topics include:

  1. Path planning: graph search methods; traveling salesman problems
  2. Multi-robot coordination: the consensus and rendezvous problems; sensor coverage; workspace partitioning/load balancing
  3. Dynamic vehicle routing: overview of Poisson processes and birth-death processes; path planning for tasks arriving in real-time; relation to automated material handling, mobility-on-demand

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ECE 780 T09: Network Systems and Control

Many large-scale natural and engineering systems can be modelled as collections of independent agents or subsystems which interact with one another through physical coupling, communication, or both. Examples include flocking birds, schooling fish, electric power systems, mobile robot teams, and sensor networks. The dynamic behaviour of these network systems depends on the nature of the agents, the nature of the inter-agent physical or communication-based coupling, and most interestingly on the global pattern of interaction between all agents. This course is concerned with analyzing and designing the dynamics of multi-agent network systems, and is intended primarily for graduate students in engineering and applied math interested in dynamics over networks, cooperative and distributed control, and distributed algorithms. Topics include:

  • theory of nonnegative matrices (Perron–Frobenius theory);

  • graph theory, with an emphasis on algebraic graph theory;

  • discrete-time and continuous-time distributed averaging (consensus) algorithms;

  • positive and compartmental linear systems;

  • circuit theory: graph models, dynamic stability, effective resistance, model reduction;

  • distributed optimization using multi-agent systems;

  • applications to networks of coupled oscillators, viral spread models, sensor networks, power system dynamics, resource allocation problems, and population dynamics.

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ECE 780 T10: Multivariable Control Systems II

This course covers advanced topics in linear control theory and multivariable linear time-invariant controller design, and is intended primarily for graduate students in engineering and applied mathematics interested in dynamics and control. The course material is drawn from the broad area of robust control, with an emphasis on modern convex optimization approaches to robust stability/performance certification and optimal controller synthesis. Students will learn the fundamental theoretical concepts underlying robust control theory, and will be exposed to the computational frameworks used for robust stability analysis and robust controller design. Topics (subject to change) include:

  • historical context and motivation for robust control;

  • state-space LTI systems: review, Lyapunov equations, observability/controllability Gramians;

  • linear matrix inequalities (LMIs) and semidefinite programming;

  • the Kalman-Yakubovich-Popov (KYP) Lemma and dissipative systems theory;

  • the generalized plant framework for feedback control; uncertainty modelling;

  • input-output LTI systems: signal spaces, rational function spaces, signal and system norms;

  • H2 and H-Infinity performance analysis;

  • statement and solution of H2 and H-Infinity control problems;

  • robust stability and performance analysis via integral quadratic constraints.

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