Nonlinear Control Design

ABOUT THE COURSE:Nonlinear systems are ubiquitous and therefore their study and control design are prevalent in the control engineering community. This course will focus on, by now, classical methods for control design of nonlinear systems. We introduce the Lyapunov theorems in brief to enable us to analyze the stability of the closed-loop systems involved. Design methods such as Backstepping, Passivity based design and feedback linearization will be looked at in detail. The course will be interspersed with examples from aero-mechanical systems such as ground/aerial robots, spacecraft attitude dynamics and so on. We will end with some advanced design methods for state constrained control and adaptive control. This course will be of interest to junior/senior researchers in advanced tech like drones, autonomous cars, Launch vehicle control, aerospace control, smart grid systems, battery electric vehicles and so on.INTENDED AUDIENCE: Senior undergraduates, graduate studentsPREREQUISITES: Linear Systems – background in state space dynamical systemsINDUSTRY SUPPORT: Mathworks, John Deere, Mercedes Benz research, Defense research agencies, ISRO

Week 1: Nonlinear Systems Examples, Existence and Uniqueness of Solutions; Common myths in control; Vector, Matrix and Signal Norms.
Week 2:Lyapunov Stability definitions – stability, uniformity, attractivity, asymptotic stability, exponential stability; Stability of Linear systems.
Week 3:Function classes; Definiteness, radial boundedness, decrescence; Lyapunov stability theorems.
Week 4:Proof of stability theorems – Stability in the sense of Lyapunov and Asymptotic Stability.
Week 5:La Salle’s Invariance principle; Krasovskii-Barbashin-LaSalle stability theorems; Proof of LaSalle’s invariance principle, worked out examples
Week 6:Control Lyapunov Functions; Small Control Property;
Week 7:Arstein Sontag Universal Controller; Backstepping method for control design, integrator backstepping
Week 8:Passivity based control design – input-output passivity, feedback passivation, spacecraft attitude control example
Week 9:Feedback linearization – motivation, Lie derivatives, relative degree results, Diffeomorphism coordinate transformation
Week 10:Feedback linearization – Zero dynamics, local Asymptotic Stability, Frobenius theorem with proof, integrable distributions, examples.
Week 11:Advanced Design Methods – Constrained control via Barrier functions, Adaptive control
Week 12:Advanced design methods – Finite Time Control, Sliding Mode Control.