Control Of Extended Markov Jump Linear System

Markovian jump systems(also called jump systems briefly), where the transitionsbetween the different regimes are random and are further supposed as a Markov pro-cess, is a special class of hybrid systems. Due to the complicated hybrid informationstructure,the research of jump systems cannot be treated as simple combination oftradition control theories for the continuous systems or discrete events systems respec-tively. It bridges various subjects such as mathematica,control theory and computertechnology,and so on.Thus,the investigation of Markovian jump systems is a newand challenging task.Ontheotherhand, timedelayarisesquitenaturallyinvariouspracticalengineeringsystems such as drive systems, chemical processes, economic systems, network controlsystems and so on. The existence of delay always makes system analysis and synthesisbecomemorecomplicatedanddifficult. Meanwhile,timedelayisfrequentlyasourceofinstabilityandperformancedegradationinmanydynamicsystems. Therefore,thestudyon time delayed jump systems is also of great significance in theoretical and practicalapplications.Inthisdissertation,stochasticstabilityandoptimalcontrolproblemsforMarkovianjump (time-delayed) linear systems with modified transition rate matrices are investi-gated, andourworkincludes:robuststabilizationfortime-varyingdelayedjumplinearsystems with perturbation both in system matrices and transition matrices, robust adap-tive control for time delayed jump linear systems with state-dependent transition rate,gradient projection based performance improvement for Markovian jump linear sys-tems under Markovian decision processes, and related applications. The main contentsand contributions of the dissertation are as follows:The basic conceptions and the practical models of jump systems are presented.Then the overall research situations and some auxiliary results are classified andsummarized, and the research objects and contents of this dissertation are intro-duced.Based on Lyapunov-Krasovskii functional method, sufficient conditions for ex-ponential stability in the mean-square sense for a class of time-varying delayedMarkovian jump linear systems is achieved and robust stability conditions areobtained when the system matrices and transition rate are not precisely known. Moreover, a practical model– single-tool orthogonal cutting system using vary-ing feed rate controlling is presented and the effects of delay parameters on theexponential convergence rate of the system are discussed.Exponential mean-square stability for a class of time-delay Markovian jump lin-ear systems with state-dependant switching are investigated. By solving a setof Linear matrix inequalities (LMIs), a state-feedback nonlinear controller is ob-tained, which guarantees globally exponential stability of such systems in themean-square sense. Based on this, an adaptive state-feedback control law is thendesigned with less knowledge of the homogeneous generator.TheJLQproblemforaclassofMarkovianJumpLinearSystemswheretheregimetransitionratesaredeterminedthroughacertainpolicyisconsidered. Atwo-levelregulating method is adopted to design of the state-feedback controller and thepolicy separately. The problem of tuning the existing policy with respect to aprescribed quadratic performance criterion is formulated as a gradient projectionbased iterative optimization and the convergence proof is given. Moreover, someusefulcharacteristicsofsuchapolicysuchastimeconsistencyarealsodeveloped.For application, we develop a methodology via Markovian control theory to eval-uatefault-tolerantwheeledmobilemanipulators. Thetransitionrateuncertaintiesare allowed within an uncertainty domain. Since the velocity signals are gener-ally not available and indirectly obtained from the measured positions, we areconcerned with the output feedback H_∞control based on a high-gain observerfor wheeled mobile manipulators, which guarantees not only the robust stochas-tic stability but also a prescribed disturbance attenuation level for the resultingclosed-loop system.