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 concepts
Functionals and their variations
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
Class PPT on Adaptive Control
