This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Ito-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.
Under the weaker conditions on the power order and the nonlinear functions, this paper investigates the output-feedback stabilization problem for a class of stochastic high-order nonlinear systems. Based on the backstepping design method and homogeneous domination technique, the closed-loop system can be proved to be globally asymptotically stable in probability.
: The principal goal of this three years research effort was to enhance the research base which would support efforts to systematically control, or take advantage of, dominant nonlinear or distributed parameter effects in the evolution of complex dynamical systems. Such an enhancement is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft and missiles. The principal investigating team has succeeded in the development of a systematic methodology for designing feedback control laws solving the problems of asymptotic tracking and disturbance rejection for nonlinear systems with unknown, or uncertain, real parameters. Another successful research project was the development of a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems. The technical details which needed to be overcome are discussed more fully in this final report.