State Feedback Control Problem For Two Kinds Of Stochastic Feedforward Nonlinear Systems

Ever since the stochastic stability theory was established, the stabilization analysis problems for stochastic feedback(lower-triangular) nonlinear systems have made a great number of development in recent years. Stochastic feedforward systems, which are also called stochastic upper-triangular systems, are another important class of stochastic nonlinear system. From the theoretical viewpoint, they are not feedback linearizable and cannot be stabilized by the conventional backstepping method. To some extent, the study on control problem of such systems is more difficult than feedback systems. On the other hand, some simple physical models, for example the cart-pendulum system and the ball-beam system with a friction term, can be described by equations with the feedforward form. So the research on stochastic feedforward nonlinear systems has theoretical and practical significance. This paper mainly investigates the state feedback stabilization problem for two kinds of stochastic feedforward nonlinear systems. The main contents as follows:1. We first consider the state feedback stabilization problem for a class of stochastic nonlinear systems with strict feedforward form. By using the homogeneous domination approach, a state feedback controller is constructed to ensure that the closed-loop system is globally asymptotically stable in probability.2. Next, we deal with the state feedback stabilization for a class of stochastic high-order feedforward nonlinear systems. By adopting the homogeneous domination approach and introducing an appropriate coordinate transformation, a state feedback controller is explicitly designed to guarantee that the closed-loop system is globally asymptotically stable in probability.