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lectures/lqcontrol.md

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@@ -48,16 +48,16 @@ Moreover, while the linear-quadratic structure is restrictive, it is in fact far
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These themes appear repeatedly below.
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Mathematically, LQ control problems are closely related to {doc}`<kalman>`
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Mathematically, LQ control problems are closely related to {doc}`kalman`
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* Recursive formulations of linear-quadratic control problems and Kalman filtering problems both involve matrix [Riccati equations](https://en.wikipedia.org/wiki/Riccati_equation).
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* Classical formulations of linear control and linear filtering problems make use of similar matrix decompositions (see for example [Classical Control with Linear Algebra](https://python-advanced.quantecon.org/lu_tricks.html) and [Classical Prediction and Filtering With Linear Algebra](https://python-advanced.quantecon.org/classical_filtering.html)).
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* Classical formulations of linear control and linear filtering problems make use of similar matrix decompositions (see for example {doc}`advanced:lu_tricks` and {doc}`advanced:classical_filtering`).
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In reading what follows, it will be useful to have some familiarity with
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* matrix manipulations
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* vectors of random variables
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* dynamic programming and the Bellman equation (see for example {doc}`<intro:short_path>` and {doc}`<optgrowth>`)
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* dynamic programming and the Bellman equation (see for example {doc}`intro:short_path` and {doc}`optgrowth`)
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For additional reading on LQ control, see, for example,
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### Solution
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To solve the finite horizon LQ problem we can use a dynamic programming
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strategy based on backward induction that is conceptually similar to the approach adopted in {doc}`<intro:short_path>`.
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strategy based on backward induction that is conceptually similar to the approach adopted in {doc}`intro:short_path`.
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For reasons that will soon become clear, we first introduce the notation $J_T(x) = x^\top R_f x$.
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