Module 1: State Space Representation and Feedback Control
Review of state variable representation of systems
Controllability and Observability concepts
Modeling of Single Input – Single Output (SISO) systems
Controllable and Observable Companion Forms
Effect of State Feedback on controllability and observability
Pole Placement by state feedback
Module 2: Nonlinear System Analysis
Classification of Non-linearities
Phenomena exhibited by nonlinear systems
Limit cycles
Jump resonance
Sub-harmonic oscillations
Phase Plane Analysis
Singular points
Trajectory construction
Isocline method
Delta method
Measurement of time on phase plane trajectories
Module 3: Stability Analysis Using Lyapunov Methods
Stability Analysis Using Lyapunov Methods
Concept and definition of stability
Lyapunov stability theory
Lyapunov’s first method
Lyapunov’s second methods
Stability of Linear Time-Invariant (LTI) systems using Lyapunov’s second method
Generation of Lyapunov functions
Krasovskii’s Method
test
Variable Gradient Method 2
Module 4: Optimal Control Theory
Fundamental theorem and boundary conditions
Constrained Minimization techniques
Dynamic Programming
Hamilton’s Principle of Optimality
Jacobi-Bellman Equation
Pontryagin’s Minimum Principle
Formulation of optimal control problems
Module 5: Adaptive Control
Introduction to Adaptive Control
Types of Adaptive Control Systems
Design of Model Reference Adaptive Control Systems (MRAC) using MIT Rule
Design of Model Reference Adaptive Control Systems (MRAC) using Lyapunov Stability Theorem
Fundamental concepts
