Convex Optimization for Control Engineering

Control system design often requires finding optimal parameters under strict performance and safety constraints, which can be computationally challenging. Convex optimization provides a powerful mathematical framework to solve these complex engineering problems reliably and efficiently. This text-only course guides you from the absolute basics of optimization theory to formulating real-world control design challenges as solvable convex programs. You will learn how to translate stability, performance, and robustness requirements into mathematically tractable structures. What you'll learn: - Understand the foundational concepts of convex sets, convex functions, and optimization theory. - Formulate control system objectives using Linear Matrix Inequalities (LMIs) and quadratic programs. - Apply semidefinite programming to analyze system stability using Lyapunov functions. - Design state-feedback controllers and estimators using convex formulation techniques. - Explore modern Model Predictive Control (MPC) formulations and constraint-handling methods. - Learn to structure control problems systematically for modern numerical solvers. This course begins with essential terminology and the mathematical foundations of convexity before advancing to practical control synthesis and stability analysis. It is designed for engineering students, control practitioners, and technical professionals looking to build a strong foundation in optimization-based design. Start reading today to master the mathematical tools shaping modern control engineering.