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limerenc equation 3-2. A first-order discrete system is described by the x(k + 1) = -0.5x(k) + u(k). The performance measure to be minimized is J = É lx(k), and the admissible states and controls are constrained by -0.2 < x(k) < 0.2, k = 0, 1, 2 -0.1 < u(k) < 0.1, k = 0, 1. (a) Carry out by hand the computational steps required to determine the optimal control law by using dynamic programming. Quantize both u(k) and x(k) in steps of 0.1 about zero, and use linear interpolation. (b) What is the optimal control sequence for an initial state value of 0.2?

limerenc equation 3-2. A first-order discrete system is described by the x(k + 1) = -0.5x(k) + u(k). The performance measure to be minimized is J = É lx(k), and the admissible states and controls are constrained by -0.2 < x(k) < 0.2, k = 0, 1, 2 -0.1 < u(k) < 0.1, k = 0, 1. (a) Carry out by hand the computational steps required to determine the optimal control law by using dynamic programming. Quantize both u(k) and x(k) in steps of 0.1 about zero, and use linear interpolation. (b) What is the optimal control sequence for an initial state value of 0.2?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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e di сe еquation 3-2. A first-order discrete system is described by the x(k + 1) = -0.5x(k) + u(k). The performance measure to be minimized is J = E |x(k)\, k=0 and the admissible states and controls are constrained by -0.2 < x(k) < 0.2, k = 0, 1, 2 -0.1 < u(k) < 0.1, k = 0, 1. (a) Carry out by hand the computational steps required to determine the optimal control law by using dynamic programming. Quantize both u(k) and x(k) in steps of 0.1 about zero, and use linear interpolation. (b) What is the optimal control sequence for an initial state value of 0.2?
Transcribed Image Text:e di сe еquation 3-2. A first-order discrete system is described by the x(k + 1) = -0.5x(k) + u(k). The performance measure to be minimized is J = E |x(k)\, k=0 and the admissible states and controls are constrained by -0.2 < x(k) < 0.2, k = 0, 1, 2 -0.1 < u(k) < 0.1, k = 0, 1. (a) Carry out by hand the computational steps required to determine the optimal control law by using dynamic programming. Quantize both u(k) and x(k) in steps of 0.1 about zero, and use linear interpolation. (b) What is the optimal control sequence for an initial state value of 0.2?
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