Solvability of the discrete LQR-problem under minimal assumptions

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Authors	HILSCHER Roman ZEIDAN Vera
Year of publication	2005
Type	Article in Proceedings
Conference	Difference Equations and Discrete Dynamical Systems
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Discrete linear regulator; Discrete quadratic functional; Riccati matrix equation
Description	The purpose of this paper is to provide a solution to the classical discrete linear-quadratic regulator problem under minimal assumptions. In particular, we do not assume the positive or nonnegative definiteness of the coefficients. Instead, a natural condition is imposed which is necessary for minimizing the involved discrete quadratic functional. The optimal solution is constructed from a generalized discrete Riccati equation and has a feedback form.
Related projects:	Optimality conditions on time scales Difference Equations and Dynamic Equations on Time Scales. Linear Hamiltonian dynamic systems and half-linear dynamic equations