Asymptotic Stability Identification And the Horizon Problem
Asymptotic Stability Identification And the Horizon Problem
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26) and (2. 28) imply (2. 29) iim^_ sup |b^_^^ - B*^J ^ 2p^ U^U2/(l-p^) which may be made arbitrarily small by proper choice of s. This completes the proof of theorem 2.
We may summarize the results of this section as follov7s. Let u (N) be the optimal first period controls given by (1. 6) as (2. 30) u (N) = -C (N)x I - 1/2 h"-'-(N)z' (N) .
o o o I o o o Let D be of full rank and let Q, and Q„ be pd. Then u (N) converges to L A o (2. 31) u^ = -c^x^i^ - 1/2 h;^ z; as N -> ». The values of the pa...rameters in (2. 31) are given below and x i is o|o the linear least squares estimate of the system at the present time.
(2. 32) R^ = A'(R^ - R*D[Q2 + D' R^D]"-'-D'R^)A + Q^ (2. 33) C^ = [Q2 + D'R^D]"-'"D'R^A (2. 34) H^ = Q^ = D'R^D (2. 35) Z^ = G^D + G2 + B^D (2. 36) B^ = [G^(A - DC^) + G^C^]!! - A + DC^]"''- It should be remarked that in practice one would determine R^ by iteration of (2. 9) with k ^ N-k until successive values of R, and R. , -, were within a de- sired tolerance. In this process it should be recalled that convergence of R, to R^ is uniform.
What to read after Asymptotic Stability Identification And the Horizon Problem?
You can find similar books in the "Read Also" column, or choose other free books by Paul R Kleindorfer to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
26) and (2. 28) imply (2. 29) iim^_ sup |b^_^^ - B*^J ^ 2p^ U^U2/(l-p^) which may be made arbitrarily small by proper choice of s. This completes the proof of theorem 2.
We may summarize the results of this section as follov7s. Let u (N) be the optimal first period controls given by (1. 6) as (2. 30) u (N) = -C (N)x I - 1/2 h"-'-(N)z' (N) .
o o o I o o o Let D be of full rank and let Q, and Q„ be pd. Then u (N) converges to L A o (2. 31) u^ = -c^x^i^ - 1/2 h;^ z; as N -> ». The values of the pa...rameters in (2. 31) are given below and x i is o|o the linear least squares estimate of the system at the present time.
(2. 32) R^ = A'(R^ - R*D[Q2 + D' R^D]"-'-D'R^)A + Q^ (2. 33) C^ = [Q2 + D'R^D]"-'"D'R^A (2. 34) H^ = Q^ = D'R^D (2. 35) Z^ = G^D + G2 + B^D (2. 36) B^ = [G^(A - DC^) + G^C^]!! - A + DC^]"''- It should be remarked that in practice one would determine R^ by iteration of (2. 9) with k ^ N-k until successive values of R, and R. , -, were within a de- sired tolerance. In this process it should be recalled that convergence of R, to R^ is uniform.
What to read after Asymptotic Stability Identification And the Horizon Problem?
You can find similar books in the "Read Also" column, or choose other free books by Paul R Kleindorfer to read onlineMoreLess
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