MECH_ENG 454: Optimal Control of Nonlinear Systems

Quarter Offered

Spring : MW 3:00-4:20pm ; T. Murphey


Differential equations and systems analysis. Undergraduate controls and/or signal processing course would satisfy this requirement. A graduate-level systems course is also helpful, but not necessary.


Who Takes It

Since optimization problems are encountered in every branch of science and engineering, students with diverse backgrounds would benefit from it. In particular. students with research interests in any area of mechanical engineering, physics, applied mathematics, chemistry, chemical engineering, and biomedical engineering are encouraged to register.

What It's About

This course will cover methods in numerical optimization and optimal control with an emphasis on engineering applications and computation. Topics include differentiation, gradient descent, Newton's method, optimal control, and optimal switching control. Examples will be drawn largely from aerospace, robotics, and biomedical applications. Students will be expected to complete numerical optimization exercises in homework sets as well as a final project.


  • Types of problems we care about
  • Differentiation in finite and infinite-dimensional spaces
  • Numerical Optimization: steepest descent and line searches
  • Numerical Optimization: Newton's method and trust region methods
  • Finite dimensional systems with algebraic costs
  • Finite dimensional systems with integral costs (Hybrid Systems)
  • Infinite dimensional systems: linear systems and LQR
  • Infinite dimensional systems: nonlinear systems


Homework, participation, final project


Functional Analysis and Linear Control Theory (Dover Books on Engineering) by J. R. Leigh
Iterative Methods for Optimization by C.T. Kelley (available online)


Professor: Todd D. Murphey

Course Syllabus