Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control Export

@article{Ji_TAC90, abstract = {Consideration is given to the control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes. The relationship between appropriately defined controllability, stabilizability properties, and the solution of the infinite time jump linear quadratic (JLQ) optimal control problems is also examined. Although the solution of the continuous-time Markov JLQ problem with finite or infinite time horizons is known, only sufficient conditions for the existence of finite cost, constant, stabilizing controls for the infinite time problem appear in the literature. In this paper necessary and sufficient conditions are established. These conditions are based on new definitions of controllability, observability, stabilizability, and detectability that are appropriate for continuous-time Markovian jump linear systems. These definitions play the same role for the JLQ problem as the deterministic properties do for the linear quadratic regulator (LQR) problem}, author = {Ji, Y. and Chizeck, H. J.}, booktitle = {Automatic Control, IEEE Transactions on}, citeulike-article-id = {4505448}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/9.57016}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=57016}, doi = {10.1109/9.57016}, journal = {Automatic Control, IEEE Transactions on}, keywords = {jump\_processes\_random\_networks, lqg\_lqr, optimal\_control, stochastic\_control}, number = {7}, pages = {777--788}, posted-at = {2009-05-12 17:27:37}, priority = {2}, title = {Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control}, url = {http://dx.doi.org/10.1109/9.57016}, volume = {35}, year = {1990} }

TY - JOUR ID - Ji_TAC90 L3 - citeulike-article-id:4505448 N2 - Consideration is given to the control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes. The relationship between appropriately defined controllability, stabilizability properties, and the solution of the infinite time jump linear quadratic (JLQ) optimal control problems is also examined. Although the solution of the continuous-time Markov JLQ problem with finite or infinite time horizons is known, only sufficient conditions for the existence of finite cost, constant, stabilizing controls for the infinite time problem appear in the literature. In this paper necessary and sufficient conditions are established. These conditions are based on new definitions of controllability, observability, stabilizability, and detectability that are appropriate for continuous-time Markovian jump linear systems. These definitions play the same role for the JLQ problem as the deterministic properties do for the linear quadratic regulator (LQR) problem IS - 7 JF - Automatic Control, IEEE Transactions on EP - 788 TI - Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control VL - 35 T2 - Automatic Control, IEEE Transactions on SP - 777 KW - jump_processes_random_networks KW - lqg_lqr KW - optimal_control KW - stochastic_control AU - Ji, Y AU - Chizeck, HJ PY - 1990/// UR - http://dx.doi.org/10.1109/9.57016 ER -