CS545_Lecture_16

# CS545_Lecture_16 - CS545—Contents XVI Adaptive Control...

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Unformatted text preview: CS545—Contents XVI Adaptive Control Model Reference Adaptive Control Self-Tuning Regulators Linear Regression Recursive Least Squares Gradient Descent Feedback-Error Learning Reading Assignment for Next Class See http://www-clmc.usc.edu/~cs545 The Adaptive Control Problem Characterize the desired behavior of the closed loop system Determine a suitable control law with adjustable parameters Find a mechanism for adjusting the parameters Implement the control law Model-Reference Adaptive Control (Direct Learning) Performance is given to correspond to a particular reference model E.g. Adjustment of controller is done directly E.g., adjust controller parameter by gradient descent m ˙ ˙ x + b ˙ x + c = u Controller Robot Adjustment Mechanism Model x desired u y y desired adjustment Model-Reference Adaptive Control – Example Consider the generic control system For this example, make this an even simpler system Assume that f is unkown and needs to be estimated by a learning process. Thus, we can formulated a control law: Where we replaced f with a simple linear function x = f x ( ) + g x ( ) u x = f x ( ) + u u = − ˆ f x ( ) + x d − k x − x d ( ) = − x ˆ θ + x d − k x − x d ( ) Model-Reference Adaptive Control – Example The goal of model-reference adaptive control is to adjust the open parameter and the control law such that the system is ALWAYS stable The system dynamics are now Define errors Thus: x = x θ − x ˆ θ + x d − k x − x d ( ) x = x θ + x d + ke = x θ + e + ke e = − x θ − ke e = x d − x θ = θ − ˆ θ Model-Reference Adaptive...
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CS545_Lecture_16 - CS545—Contents XVI Adaptive Control...

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