LQR Problem of Linear Discrete Time Systems with Nonnegative State Constraints

作     者：Kostova, S. Imsland, L. Ivanov, I. 

作者机构：Institute of System Engineering and Robotics Bulgarian Academy of Sciences Sofia Bulgaria Department of Engineering Cybernetics NTNU Trondheim Norway Department of Statistics and Econometrics FEBA St. Kliment Ohridski University of Sofia Bulgaria 

出 版 物：《AIP Conference Proceedings》 (美国物理学会会议录)

年 卷 期：2015年第1684卷第1期

页      面：1-7页

学科分类：07[理学] 0702[理学-物理学] 

主　　题：LINEAR systems DISCRETE-time systems NONNEGATIVE matrices CONSTRAINTS (Physics) INVARIANT sets 

摘      要：In the paper the infinite-horizon Linear Quadratic Regulator (LQR) problem of linear discrete time systems with nonnegative state constraints is presented. Such kind of constraints on the system determine the class of positive systems. They have big application in many fields like economics, biology, ecology, ICT and others. The standard infinite LQR-optimal state feedback law is used for solving the problem. In order to guarantee the nonnegativity of the system states, we define the admissible set of initial states. It is proven that, for each initial state from this set the nonnegative orthant is invariant set. Two cases are considered, first, when the initial state belongs to the admissible set, and the second, when the initial state does not belong to the admissible set. The procedures for solving the problem are given for two cases. In second case we use a dual-mode approach for solving the problem. The first mode is until the state trajectory enters the admissible set and after that the procedure for the first case is used. The illustrative examples are given for both cases. [ABSTRACT FROM AUTHOR]