TY - JOUR
T1 - State-feedback control of Markov jump linear systems with hidden-Markov mode observation
AU - Ogura, Masaki
AU - Cetinkaya, Ahmet
AU - Hayakawa, Tomohisa
AU - Preciado, Victor M.
N1 - Funding Information:
Victor M. Preciado received his Ph.D. degree in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology in 2008. He is currently the Raj and Neera Singh Assistant Professor of Electrical and Systems Engineering at the University of Pennsylvania. He is a member of the Networked & Social Systems Engineering (NETS) program, the Warren Center for Network & Data Sciences, and the Applied Math and Computational Science (AMCS) program. He is a recipient of the 2017 National Science Foundation Faculty Early Career Development (CAREER) Award. His main research interests lie at the intersection of Big Data and Network Science; in particular, in using innovative mathematical and computational approaches to capture the essence of complex, high-dimensional dynamical systems. Relevant applications of this line of research can be found in the context of socio-technical networks, brain dynamical networks, healthcare operations, biological systems, and critical technologicalinfrastructure.
Publisher Copyright:
© 2017 Elsevier Ltd
PY - 2018/3
Y1 - 2018/3
N2 - In this paper, we study state-feedback control of Markov jump linear systems with partial information about the mode signal responsible for switching between dynamic modes. We assume that the controller can only access random samples of the mode signal according to a hidden-Markov observation process. Our formulation provides a novel framework to analyze and design feedback control laws for various Markov jump linear systems previously studied in the literature, such as the cases of (i) clustered observations, (ii) detector-based observations, and (iii) periodic observations. We present a procedure to transform the closed-loop system with hidden-Markov observations into a standard Markov jump linear system while preserving stability, H2 norm, and H∞ norm. Furthermore, based on this transformation, we propose a set of Linear Matrix Inequalities (LMI) to design feedback control laws for stabilization, H2 suboptimal control, and H∞ suboptimal control of discrete-time Markov jump linear systems under hidden-Markov observations of the mode signals. We conclude by illustrating our results with some numerical examples.
AB - In this paper, we study state-feedback control of Markov jump linear systems with partial information about the mode signal responsible for switching between dynamic modes. We assume that the controller can only access random samples of the mode signal according to a hidden-Markov observation process. Our formulation provides a novel framework to analyze and design feedback control laws for various Markov jump linear systems previously studied in the literature, such as the cases of (i) clustered observations, (ii) detector-based observations, and (iii) periodic observations. We present a procedure to transform the closed-loop system with hidden-Markov observations into a standard Markov jump linear system while preserving stability, H2 norm, and H∞ norm. Furthermore, based on this transformation, we propose a set of Linear Matrix Inequalities (LMI) to design feedback control laws for stabilization, H2 suboptimal control, and H∞ suboptimal control of discrete-time Markov jump linear systems under hidden-Markov observations of the mode signals. We conclude by illustrating our results with some numerical examples.
KW - H control
KW - H control
KW - Markov chains
KW - Stabilization
KW - State-feedback control
UR - http://www.scopus.com/inward/record.url?scp=85038077679&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85038077679&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2017.11.022
DO - 10.1016/j.automatica.2017.11.022
M3 - Article
AN - SCOPUS:85038077679
SN - 0005-1098
VL - 89
SP - 65
EP - 72
JO - Automatica
JF - Automatica
ER -