Gain‐Scheduled Worst‐Case Control on Nonlinear Stochastic Systems Subject to Actuator Saturation and Unknown Information

In this paper, we propose a method for designing continuous gain‐scheduled worst‐case controller for a class of stochastic nonlinear systems under actuator saturation and unknown information. The stochastic nonlinear system under study is governed by a finite‐state Markov process, but with partially known jump rate from one mode to another. Initially, a gradient linearization procedure is applied to describe such nonlinear systems by several model‐based linear systems. Next, by investigating a convex hull set, the actuator saturation is transferred into several linear controllers. Moreover, worst‐case controllers are established for each linear model in terms of linear matrix inequalities. Finally, a continuous gain‐scheduled approach is employed to design continuous nonlinear controllers for the whole nonlinear jump system. A numerical example is given to illustrate the effectiveness of the developed techniques.