Welcome to Optimization and Optimal Control!
Optimization and Optimal Control focuses on designing systems to perform efficiently while minimizing cost, time, or resources. It connects mathematics to practical problems, such as fuel-efficient spacecraft trajectories, energy optimization in robotics, and improving machine learning models. By relating abstract ideas to real-world applications, I help students bridge the gap between theory and practice using optimization.
My Expertise
I specialize in Optimization and Optimal Control, focusing on both theoretical foundations and computational methods related to:
- Non-linear Programming: Techniques for solving static optimization problems—minimizing functions subject to constraints.
- Calculus of Variations: Methods for solving dynamic optimization problems—minimizing functionals subject to constraints.
- Optimal Control:
- Maximum Principle: A powerful framework to solve optimal control problems and determine feedforward control inputs.
- Dynamic Programming: A general framework to solve optimal control problems and derive feedback control laws or control policies.
Teaching
I use an innovative teaching approach to make complex concepts in optimization and control accessible and engaging. My method emphasizes:
- Step-by-Step Analogies: Building from simple, familiar problems like minimizing a quadratic function to more complex problems.
- Interactive Learning: Encouraging active participation, from hands-on MATLAB coding to solving real-world engineering problems.
- Bridging Disciplines: Linking optimization to applications in robotics, aerospace, and mechanics for a holistic understanding.