Control of Markov Jump Linear Systems with uncertain detections. - Stadtmann, Frederik (2019)
This monograph addresses control and filtering problems for systems with sudden changes in their behavior and whose changes are detected and estimated by an imperfect detector. More precisely it considers continuous-timeMarkov Jump Linear Systems (MJLS) where the current mode of operation is estimated by a detector. This detector is assumed to be imperfect in the sense that it is possible that the detected mode of operation diverges from the real mode of operation. Furthermore the probabilities for these detections are considered to be known. It is assumed that the detector has its own dynamic, which means that the detected mode of information can change independently from the real mode of operation. The novelty of this approach lies in how uncertainties are modeled. A Hidden Markov Model (HMM) is used to model the uncertainties introduced by the detector. For these systems the following problems are addressed: i) Stochastic Stabilizability in mean-square sense, ii) H2 control, iii) H? control and iv) the H? filtering problem. Solutions based on Linear Matrix Inequalities (LMI) are developed for each of these problems. In case of the H2 control problem, the solutionminimizes an upper bound for the H2 norm of the closed-loop control system. For the H? control problem a solution is presented that minimizes an upper bound for the H? norm of the closed-loop control system. In the case of the H? filtering, the solution presented minimizes the H? norm of a system representing the estimation error. The solutions for the control problems are illustrated using a numerical example modeling a simple two-tank process.