Finite-Time Adaptive Control for Uncertain High-Order Stochastic Nonlinear Systems With Unknown Time-Varying Control Coefficients
针对一类不确定高阶随机非线性系统，提出了一种基于反步法和加幂积分器的自适应控制器，使系统在随机意义下有限时间稳定，并通过仿真验证了理论结果。
This research article considers the subject of finite-time control for a set of uncertain high-order stochastic nonlinear systems (HOSNSs) with unknown time-varying control coefficients. The growth conditions for the uncertain nonlinearities are more inclusive compared to those found in most previous studies. The exponents of high-order systems can take arbitrary rational numbers, which can be represented by two positive odd integers, and they are not all exactly larger than 1. Based on the conventional backstepping idea, the method of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">adding a power integrator</i> is adopted to design an adaptive controller that renders the closed-loop system stochastically finite-time stable (SFTS). Due to the general nonlinearities, high-order exponents, and stochastic characteristics, the design process requires more effort, so domination instead of cancellation techniques is used. A simulation example demonstrates the correctness of the theoretical results.