Continuous-Time Markov Jump Linear Systems, 2013 Probability and Its Applications Series

It has been widely recognized nowadays the importance of introducing mathematical models that take into account possible sudden changes in the dynamical behavior of a high-integrity systems or a safety-critical system. Such systems can be found in aircraft control, nuclear power stations, robotic manipulator systems, integrated communication networks and large-scale flexible structures for space stations, and are inherently vulnerable to abrupt changes in their structures caused by component or interconnection failures. In this regard, a particularly interesting class of models is the so-called Markov jump linear systems (MJLS), which have been used in numerous applications including robotics, economics and wireless communication. Combining probability and operator theory, the present volume provides a unified and rigorous treatment of recent results in control theory of continuous-time MJLS. This unique approach is of great interest to experts working in the field of linear systems with Markovian jump parameters or in stochastic control. The volume focuses on one of the few cases of stochastic control problems with an actual explicit solution and offers material well-suited to coursework, introducing students to an interesting and active research area.

The book is addressed to researchers working in control and signal processing engineering. Prerequisites include a solid background in classical linear control theory, basic familiarity with continuous-time Markov chains and probability theory, and some elementary knowledge of operator theory. ?

1.Introduction.- 2.A Few Tools and Notations.- 3.Mean Square Stability.- 4.Quadratic Optimal Control with Complete Observations.- 5.H2 Optimal Control With Complete Observations.- 6.Quadratic and H2 Optimal Control with Partial Observations.- 7.Best Linear Filter with Unknown (x(t), θ(t)).- 8.H_$infty$ Control.- 9.Design Techniques.- 10.Some Numerical Examples.- A.Coupled Differential and Algebraic Riccati Equations.- B.The Adjoint Operator and Some Auxiliary Results.- References.​- Notation and Conventions.- Index.

Oswaldo Luiz do Valle Costa is Professor in the Department of Telecommunications and Control Engineering at the University of São Paulo – USP, São Paulo, SP.

Marcelo Dutra Fragoso is Professor in the Department of Systems and Control at the National Laboratory for Scientific Computing – LNCC/MCTI, Petrópolis, Rio de Janeiro.

Marcos Garcia Todorov is currently a postdoctoral researcher at the National Laboratory for Scientific Computing – LNCC/MCTI, Petrópolis, Rio de Janeiro.