Modern Control Paradigms

What this course is about?

This course will introduce you to modern control paradigms through the use of theoretical foundations and an emphasis on numerical methods and optimization. Proofs and in-depth theoretical reasoning, on the other hand, will be avoided whenever possible (due to time constraints and the amount of material).

The concepts covered in this class are based on technologies that, in my opinion, are not only fascinating from a theoretical standpoint but also have important applications in the real world. That said, the reviewed algorithms are by no means a magic bullet for fixing all of your control issues. However, it might shed light on the state of the art in the modern control theory.

Introduction to Modeling

• The notion of dynamical system, classification, continues and discrete models.
• Simulation of ODE
• What is control system and how we build one.
• Practical issues in control design, implementation in multiprocessing fashion.

Review of System Analysis and Control

• System analysis, Stability, Controlability.
• Pole placement, Optimal linear control, linear quadratic regulator (LQR)
• Nonlinear control via Linearization.
• Lyapunov theory for nonlinear systems.
• Region of Attraction via sampling.

Optimization in Planning and Control

• Simultaneous planning and optimization by linear and nonlinear model predictive control (MPC/NMPC)
• Design of stable nonlinear controllers with control Lyapunov functions (CLF)
• Safety critical control via control barrier functions (CBF)

Identification and Data Driven Methods

• Building the linear models from data with dynamic mode decomposition (DMD)
• Identifying nonlinear models with sparse identification of nonlinear dynamics (SINDY)
• Koopman linear approximation of nonlinear behavior with extended DMD
• Output identification and eigensystem realization algorithm (ERA)

Other Topics

• Nonlinear planning with Differential flatness
• Optimal design of linear controllers with LMIs
• Advanced Analysis: Region of Attraction, Sensitivity, Controlability and Observability,
• Sum of Squares Optimization in analysis and control of nonlinear systems
• Design and Analysis via Contraction Theory
• Constrained and unconstrained state observer, linear