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| 0512-4360 | Introduction to Modern Linear Control Theory | |||||||||||||||||||||||||||||||||||||||||||||||
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| FACULTY OF ENGINEERING | ||||||||||||||||||||||||||||||||||||||||||||||||
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University credit hours: 4.0
Course description
Credit Points: 3.5
Prerequisites: Introduction to Control Theory; Random Signals & Noise (cuncurrent).
Time domain solution of the state space equations for continuous linear time varying (LTV) systems and linear time invariant systems (LTI).
Controllability and observability, PBH criteria. State-Feedback Control : Pole placement, optimal regulator problem, Riccati equation of the optimal state feedback control law. Frequency domain steady-state solution of the optimal regulator problem, spectral factorization, McFarlane equation. State-Estimation : The deterministic observer. Response of a linear system to white noise, optimal state-estimaton in the presence of white noise: The Kalman filter, the Riccati equation of optimal estimation. Frequency domain steady-state solution to the optimal estimator problem : the Wiener filter. Output Feedback Control : The separation principle, solution of the LQG problem. Optimal tracking problem.
Linear Discrete-Time Systems: Basic definitions, state feedback control and estimation problems, Optimal control of Discrete-time systems.
1. Linearization of nonlinear systems with examples.
2. Continuous-time linear systems: controllability, observability, canonical forms, transfer matrix.
3. State-feedback control: pole placement, optimal control problem (Linear Quadratic Regulator).
4. Lyapunov method for stability of linear systems, zeros of MIMO systems.
5. Observers: notion of observer, observer-based control, Kalman lter.
6. Linear Quadratic Gaussian (LQG) control and optimal tracking.
7. Discrete-time systems: transition matrix, controllability, observability, stability, pole placement, LQR, observers, Kalman lter, LQG.