Prerequisites: Nonlinear Systems (MAE 281A) or consent of instructor
Course Objective: The course will give the students an in-depth introduction to nonlinear controllability and stabilizability theory, with elements of robust and optimal nonlinear control.
Topics: Circle and Popov criteria, small gain theorem, passivity. Describing functions. Nonlinear controllability, feedback linearization, input-state and input-output linearization, zero dynamics. Stabilization, Brockett's necessary conditions for local stabilizability, control Lyapunov functions, Sontag's formula for global stabilizaiton. Methods for design of control Lyapunov functions and stabilization: integrator backstepping, forwarding. Inverse optimality and stability margins. Disturbance attenuation for nonlinear systems, deterministic and stochastic, nonlinear H-infinity control. Examples from robotics, satellite and underwater vehicles, compressors and combustion.