Estimation And Quadratic Optimal Control For Linear Systems With Multiplicative Noise

Stochastic systems are of wide application background, and are available in many fields such as signal processing in wireless sensor networks, economic man-agement, communication systems, and financial mathematics. Hence, the control and estimation problems for the stochastic systems have been intriguing many researchers for decades. However, they are known to be complicated due to the presence of stochastic uncertainties, some fundamental and theoretical problems stay unsettled as a great challenge. The control and estimation problems for stochastic systems remain to be perfected further.The dissertation focuses on the quadratic optimal control for multiplicative noise systems with input delay, duality between estimation and optimal control for multiplicative noise systems, the novel estimator problem for measurement missing systems, the quadratic optimal control for ItO stochastic systems with input delay and the Kalman filtering problem for ltO stochastic systems with measurement delay. Our main results are as follows.●It resolves the quadratic optimal control problem for multiplicative noise systems with two channels single input delay via dynamic programming approach and completing square technique. The controller is designed by solving partial difference equation with the same dimension as the original systems. It is superior to the augmentation method in computation espe-cially when the time delay is large.●It proposes a novel estimator for stochastic system with multiplicative noise, establishes the duality between the optimal control and estimation, and testi-fies the convergence of a forward generalized Riccati equation as the system is stabilizable and exactly observable. Associating time stamp technique with the idea above, we present the filter and smoother for measurement missing systems, which can be designed by solving a generalized Riccati equation, analyze the convergence of the estimator and show that the pro-posed estimator is a trade-off over performance between the MMSE filter and the intermittent Kalman filter. ●It considers the linear quadratic optimal control for ItO stochastic systems with single channel single input delay. By constructing a novel Lyapunov functional, making use of ItO formula and complete square technique, we provide the optimal controller via solving partial differential equation. In addition, we also apply discretization approach to study the problem in a special case and give the optimal controller based on a differential Riccati equation.●It considers the optimal estimation problem for ItO stochastic systems with measurement delay. By taking advantage of the reorganized innovation anal-ysis and making use of Ito formula, the optimal estimator is designed via solving two Riccati equations and a Lyapunov equation.●It proposes a new estimator for ItO stochastic systems where the estimator gain is calculated by solving a forward generalized Riccati equation, and establishes the duality between estimation and optimal control problem.In a word, this dissertation focuses on the estimation and quadratic opti-mal control problem for stochastic systems, the obtained results make stochastic estimation and optimal control theory better.