Nonlinear Dynamics and Control Certificate

Program Overview

The Nonlinear Dynamics and Control Certificate program provides a comprehensive study of modern principles in nonlinear dynamics and control theory. It includes four required courses, three elective courses, and one graduate-level course in mathematics, control, or optimization. The program is complemented by research at the Center for Nonlinear Dynamics & Control (CENDAC).

Program Outline

Outline:

The Nonlinear Dynamics and Control Certificate program includes a concentrated study of modern principles with both breadth and depth of coverage being emphasized. The research program at the Center for Nonlinear Dynamics & Control (CENDAC) serves to complement the course. The certificate program requires the completion of four courses:

Required Course:

• EGR 8304 - Nonlinear Control: Advanced treatment of nonlinear dynamical systems and control theory using modern techniques with applications.
Topics include: Lyapunov stability theory, partial stability finite-time stability and control design, control Lyapunov functions, nonlinear optimal control, sliding mode control, and adaptive control.

Elective Courses (Choose three):

• EGR 8302 - Digital Control: Introduction to digital control analysis & design techniques applied to discrete-time & sampled continuous-time systems.
Sampling, difference equations, the Z-transform & modified Z-transform, discrete transfer function & state-space models, discrete-time regulator & observer design, stability of discrete-time systems, discrete linear quadratic regulator & linear quadratic Gaussian formulation.
• EGR 8304 - Nonlinear Control: Advanced treatment of nonlinear dynamical systems and control theory using modern techniques with applications.
Topics include: Lyapunov stability theory, partial stability finite-time stability and control design, control Lyapunov functions, nonlinear optimal control, sliding mode control, and adaptive control.
• EGR 8305 - System Identification: Introduction to system identification techniques for linear systems.
Topics include: non-parametric time- and frequency-domain methods, parametric model structures, noise models, parametrc estimation methods, recursive estimation, bias and data pre-filtering, validation methods.
• EGR 8306 - Nonlinear Dynamics: Introduction to nonlinear dynamic analysis using analytical, graphical & numerical techniques.
Linear system theory, the nonlinear pendulum, stability concepts, bifurcation theory, self-excited oscillations, overview of asymptotic methods, Floquet theory, Poincare maps, & chaos.
• EGR 8308 - Feedforward Control: Introduction to feedforward control techniques with an emphasis on model-based methods.
Design of feedforward inputs for linear systems, nonlinear systems, nonminimum phase systems, and systems with actuator redundancy; integration of feedforward and feedback; iterative control; dealing with plant uncertainty.
• EGR 8309 - Adv Topics in Dynam & Control: Advanced treatment of various aspects of nonlinear dynamics and control.
Prerequisite: Depends on the topic covered each semester. Contact instructor for specific details.

Graduate Level Mathematics Course (One may be chosen):

• CHE 8579 - Adv Process Modeling/Analysis: Mathematical techniques for analyzing chemical engineering problems: development of mathematical models of physical and chemical problems, time dependent and position dependent models, solution of model equations by numerical techniques, computer applications
• ECE 8001 - Engineering Math I: Applied mathematics course tailored to the needs of EE graduate students.
Topics: i) Complex variable theory, ii) Sturm-Liouville problem, eigen-function expansion and special functions, iii) Matrix theory, eigen value and diagonalization, iv) Fourier analysis, multi-dimensional Fourier series and transforms, and v) Partial differential equations. Various examples from engineering and physics will be incorporated as appropriate.
• ECE 8007 - Matrix Theory: Linear transformations and linear optimization as applied to vector spaces.
Topics include solution of linear algebraic equations, linear transforms and their matrices, system decomposition (diagonalization), nondiagonalization operators and Jordan form, inner products, orthogonal projection, and pseudoinverse.
• ME 7000 - Advanced Engineering Analysis: Solutions of ordinary differential equations, series solutions, special functions, boundary-value problems, partial differential equations, vector calculus, calculus of variations, and engineering applications.
Undergraduate students must obtain permission of the department chair.

Graduate Level Control or Optimization Course (One may be chosen):

• ME 8204 - Robotics:Analysis & Control: Forward and inverse kinematics of non-redundant and redundant robotic arms; kinematics and dynamics of wheeled robots; path planning and control of mobile robots; alternative locomotion mechanisms.
Approval of instructor.