MIT6_241JS11_lec03

# MIT6_241JS11_lec03 - 6.241 Dynamic Systems and Control...

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6.241 Dynamic Systems and Control Lecture 3: Least Square Solutions of Linear Problems Readings: DDV, Chapter 3 Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology February 9, 2011 E. Frazzoli (MIT) Lecture 3: Least Squares Feb 9, 2011 1 / 5

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Outline 1 Least Squares Control E. Frazzoli (MIT) Lecture 3: Least Squares Feb 9, 2011 2 / 5
Least Squares Control Consider a system of m equations in n unknowns, with m < n , of the form 1 y = A x . In these conditions, there are in general many possible values for x that make A x = y . It may be of interest to Fnd such a solution x of minimum (weighted) Euclidean norm, i.e., of minimum x . Example This situation occurs often in the context of control. ±or example, consider the simple discrete-time system x [ i + 1] = ax [ i ] + bu [ i ], with initial condition x [0] = 0. It is desired to bring this system to x [ N ] = y , while minimizing the cost N i =1 | u [ i ] | 2 . This problem can be written as min u u 2 , s.t.

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## This note was uploaded on 01/12/2012 for the course ECE 6.241j taught by Professor Prof.emiliofrazzoli during the Spring '11 term at MIT.

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MIT6_241JS11_lec03 - 6.241 Dynamic Systems and Control...

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