problem6

problem6 - EE221A Linear System Theory Problem Set 6...

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Unformatted text preview: EE221A Linear System Theory Problem Set 6 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2010 Issued 10/28; Due 11/5 Problem 1. Consider an object of mass m = 1 moving along the x-axis in response to a force input u ( t ). The object’s dynamics can be described simply as ¨ x = u ( t ). Suppose you would like to design an input u ( t ) which will move the object from any initial position and velocity, to come to rest at the position x = 4. Using the linear quadratic regulator discussed in class, formulate an appropriate quadratic cost functional, and solve the problem in MATLAB, showing simulations of your results for different weightings on the state and input. Problem 2. Consider the control system ˙ x 1 = ax 2 + u ˙ x 2 = bx 2 with cost J = integraltext T ( x 2 1 + hx 2 2 + u 2 ) dt with h > 0 and no terminal cost. (a) Show that the optimal control for this system is given by u ( t ) =- p 1 ( t ) x 1 ( t )- p 2 ( t ) x 2 ( t ) where...
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This note was uploaded on 04/11/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at Berkeley.

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