An introduction to control theory for linear time-invariant finite-dimensional systems from both the state-space and input-output viewpoints. State-space theory: the concepts of controllability, observability, stabilizability, and detectability; the pole-assignment theorem; observers and dynamic compensation; LQR regulators. Input-output theory: the ring of polynomials and the field of rational functions; the algebra of polynomial and rational matrices; coprime factorization of transfer matrices; Youla parametrization, introduction to optimal control.
This is a course on continuous-parameter state estimation and control for stochastic linear systems. It is based on a single unifying theme, namely that state estimation in linear systems is equivalent to projection onto a closed linear subspace generated by an observation process in a Hilbert space of random variables. This formulation of state estimation leads to the innovations theorem of Kailath, and this in turn has a number of corollaries of considerable practical importance, such as the Kalman-Bucy filtering formulae and the Rauch-Tung-Striebel prediction formulae which are much used for example in problems of inertial guidance and control in aerospace, in stochastic optimal control, and (more recently) in econometrics.
(Cross-listed with ECE 486) Homogeneous transformations. Kinematics and inverse kinematics. Denavit-Hartenberg convention. Jacobians and velocity transformations. Dynamics. Path planning, nonlinear control. Compliance and force control.
Equilibrium points, linearization; second order systems; contraction mapping principle; existence and uniqueness of solutions to nonlinear differential equations; periodic solutions; Lyapunov stability; the Lure problem; introduction to input-output stability, introduction to nonlinear control techniques.
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 fixpoints of monotone operators.
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.
This course will discuss the design and control of fault-tolerant and secure dynamical systems. Topics include: models of faults and attacks in dynamical systems, graphical models of dynamical systems, structured system theory, model-based fault-diagnosis and analytical redundancy, unknown-input observers and residual generators, fault-tolerant combinatorial systems, applications of error-control coding to reliable controller design, stability under packet dropouts in networked control systems, identifying malicious attackers in multi-agent networks, attack and fault-tolerance of large-scale complex networks.
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.
Adaptive control is an approach used to deal with the unavoidable problem of plant uncertainty. Rather than providing a fixed linear time-invariant controller, this approach yields a controller whoes parameters change with time. This controller typically consists of a linear time-invariant compensator together with a tuning mechanism which adjusts the controller gains; typical control objectives are stabilization and tracking.The bulk of the course will be centered on an identifier based approach. Here one chooses a model for the plant, whose parameters are unknown, and the plant parameters are recursively estimated; controller gains are computed assuming that the present estimate is corrent. We first study algorithms to carry out parameter estimation, we then look at various control laws, and finally these are combined to yield an adaptive controller. Related Background: knowledge of linear system.
Monotone and Dynkin class theorems, introduction to discrete and continuous parameter martingales, stochastic integrals, Ito formula, Girsanov transformation. Held with: STAT 902.
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University of Waterloo
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Last updated Aug 2011