Course Title: Optimal and Adaptive Controls
Course Code: ECEg-6242
Pre-requisites: Linear System Theory, Random Process and Estimation in Control
Description:
Calculus of Variation and the Euler-Lagrange Necessary Condition; The Maximum Principle of Pontryagin and its Application; Derivation of the Hamilton-Jacobi-Bellman Equation via Dynamic Programming and its Application to the Optimal Regulator Problem; The Matrix Riccati Equation and its Solution; Solution of Optimal Control Equations by Gradient Methods, Parameter Optimization Problems with Equality and Inequality Constraints, The Penalty Function Method, Applications in Regulator and Tracking Problems; Characterization of Noise; Definition for the terms: Smoothing, Prediction, Filtering; Estimation of States of a System using Models; Estimation Criteria, Wiener and Levinson Filtering; Gradient methods for Adaptive control; Periodic Perturbation of systems for Adaptation; MRAS and Hyper-stability approach for Parameter Estimation; Exponential data weighting, forgetting factor; LSQ Procedures for State Estimation and Parameter Estimation; Kalman Filter approach for State Estimation, Prediction and Smoothing for discrete time and continuous time systems; Square Root Filtering, Smoothing of Discrete-Time Signals; Spectral Factorization, Suboptimal Filtering; Learning Systems; Adaptive phased arrays for detecting signal direction; Application of Adaptive and Optimal Control; Case studies: Adaptive Radar tracking, Control of robot arm, Satellite altitude control.
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