Concise Syllabus

Brief Review of Basic State Space Control, Controllability, Observability, Dual System, Time- Varying System, Solution to Linear time varying Equation, Solution to linear state equation – with Inputs, Full State Feedback Control, Introduction to Optimal Control, Linear Quadratic Regulator, State-Variable Feedback, Output Feedback, Coupled Nonlinear Design Equations, Linear Quadratic Tracker, Optimal LQ Tracker, Conversion of an LQR to an LQ tracker, Output Feedback LQ tracker, Multivariable Frequency-Domain Techniques, Loop Transfer Recovery, Introduction to Robust Control, Matrices Lyapunov and Riccati Equations, Computing Transfer Functions Norms, Grammians and Linear System Behaviour, Modelling of uncertainty, Small Gain Theorem, Additive and Multiplicative uncertainty, Introduction to System Identification, ARX Models, Output Error Models, Noise Models and Prediction filters, Linear Black-box model parameterization, Adaptive Control, Self Tuning Regulators, Gain Scheduling, Automatic Tuning, Controller design, Estimator Issue, Interaction of Control and Estimation, Intelligent Control System, Neural network based System Identification.

Lecture Wise Break Up

I. Brief Review:

• Controllability, Observability, Dual System, Time- Varying System, Weighting Matrices, Definiteness Trace, Singularity, Inverse Transformations and Decompositions, Singular Value Decomposition, State Space Trajectories, Canonical form, Solution to Linear time Invariant Equations, Solution to Linear time varying Equation, Solution to linear state equation – with Inputs, Full State Feedback Control [4]

II. Optimal Control:

• Introduction, LINEAR QUADRATIC REGULATOR (LQR) - State-Variable Feedback, Linear Quadratic Performance Index, Optimal Time-Varying Feedback gain, Constant Feedback Gain, Guaranteed Stability of the LQR, Discrete-Time LQR Design Equations, Output Feedback, Coupled Nonlinear Design Equations, LINEAR QUADRATIC TRACKER - Optimal LQ Tracker, Conversion of an LQR to an LQ tracker, Output Feedback LQ tracker, Multivariable FrequencyDomain Techniques, Guaranteed Robustness of the LQR with State Feedback, Loop Transfer Recovery (LTR) [12]

III. Robust Control:

• Introduction, Matrices Lyapunov and Riccati Equations, Computing Transfer Functions Norms, Grammians and Linear System Behaviour, Modelling of uncertainty: the Linear Fractional transformation, Small Gain Theorem, Additive and Multiplicative uncertainty, S, T and S+T Measure, Anlysis [6]

IV. System Indentification:

• Introduction, LINEAR DIFFERNCE ENQUATIONS – ARX MODELS - The Models, The Least Square Method, Output Error Models, Noise Models and Prediction filters, Linear Black-box model parameterization, Fitting Models to Data, Model Quality, Experiment Design, Model Validation and Model Selection, Software for System Identification. [12]

IV. Adaptive Control:

• Introduction, Adjusting Many Parameters, The Lyapunov Rule, Self Tuning Regulators, Gain Scheduling, Automatic Tuning, Controller design, Estimator Issue, Interaction of Control and Estimation, Intelligent Control System, Neural network based System Identification. [6]