The Continuous-Time Linear Quadratic Regulator Problem

David F. Delchamps
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David F. Delchamps: Cornell University, School of Electrical Engineering

Chapter 27 in State Space and Input-Output Linear Systems, 1998, pp 406-415 from Springer

Abstract: Abstract We turn now to the continuous-time linear quadratic regulator problem(s). Recall from §26 that the finite time horizon problem is to choose u: [0, t 1) →R m so as to minimize $$J_{{0^1}}^t = \int\limits_0^{{t_1}} {{u^T}} \left( t \right)u\left( t \right) + {y^T}\left( t \right)y\left( t \right)dt + {x^T}\left( {{t_1}} \right)Qx\left( {{t_1}} \right),$$ subject to $$J_0^\infty = \int\limits_0^\infty {{u^T}} \left( t \right)u\left( t \right) + {y^T}\left( t \right)y\left( t \right)dt.$$ whereas the infinite-time or stationary version of the problem is to find u:[0, ∞) → R m which minimizes $$J_0^\infty = \int\limits_0^\infty {{u^T}} \left( t \right)u\left( t \right) + {y^T}\left( t\right)y\left( t \right)dt.$$

Date: 1998
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DOI: 10.1007/978-1-4612-3816-4_28

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