Foundations of Optimal Control: Theory and Practical Applications

Designing systems that operate at peak efficiency is a fundamental challenge in modern engineering. From trajectory planning to process automation, understanding how to mathematically optimize control inputs is essential for building next-generation technologies. This written course guides you from the fundamental principles of mathematical optimization to advanced control strategies, helping you gain a solid intuitive and mathematical understanding of how to formulate, analyze, and solve optimal control problems. What you'll learn: - Understand the foundational mathematics of static optimization and variational calculus. - Formulate optimal control problems for both deterministic and stochastic systems. - Apply dynamic programming and Pontryagin's maximum principle to find optimal trajectories. - Explore model predictive control principles and modern numerical search algorithms. - Analyze discrete and continuous system dynamics using clean mathematical frameworks. - Implement basic optimization concepts using modern computational approaches and pseudo-code. The course begins with core terminology, foundational calculus of variations, and basic optimization concepts. You will then progress through dynamic programming, state-space formulations, and modern model predictive control strategies applied to practical engineering scenarios. This course is designed for engineering students, roboticists, and developers new to control theory. A basic background in calculus and linear algebra is helpful, but no prior control systems experience is required as we build all concepts from the ground up. Start reading today to master the mathematical foundations of modern optimal control.