Adaptive control-based Barrier Lyapunov Functions for a class of stochastic nonlinear systems with full state constraints
Adaptive control-based Barrier Lyapunov Functions for a class of stochastic nonlinear systems with full state constraints
复制标题
一类具有全状态约束的随机非线性系统的基于自适应控制的Barrier Lyapunov函数
DOI：
10.1016/j.automatica.2017.07.028
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发表时间：
2018-01-01
期刊：
影响因子：
6.4
通讯作者：
Li, Dong-Juan
中科院分区：
文献类型：
--
作者：
Liu, Yan-Jun;Lu, Shumin;Li, Dong-Juan
针对参数未知的非线性随机系统，提出了一种自适应控制方法。要求系统中的所有状态都约束在一个有界紧集中，即，在系统中考虑了全状态约束。这是第一次控制非线性随机系统的全状态约束。与确定性系统相比，具有完全状态约束的随机系统更难稳定，设计过程也更复杂。通过构造对称和非对称形式的障碍李雅普诺夫函数（BLF），可以保证随机系统的所有状态都不超出其约束界。因此，该方案不仅解决了随机系统的稳定性问题，而且还克服了全状态约束对控制性能的影响。最后，证明了闭环系统中所有的信号在概率上是半全局一致最终有界的（SGUUB），系统输出被驱动跟随参考信号，并且所有的状态都保持在预定义的紧集中.仿真实例验证了该方案的有效性。(C)2017爱思唯尔有限公司版权所有
An adaptive control scheme is developed in the paper for nonlinear stochastic systems with unknown parameters. All the states in the systems are required to be constrained in a bounded compact set, i.e., the full state constraints are considered in the systems. It is for the first time to control nonlinear stochastic systems with the full state constraints. In contrast to deterministic systems, the stochastic systems with the full state constraints are more difficult to be stabilized and the design procedures are more complicated. By constructing Barrier Lyapunov Functions (BLF) in symmetric and asymmetric forms, it can be ensured that all the states of the stochastic systems are not to transgress their constraint bounds. Thus, the proposed scheme not only solves the stability problem of stochastic systems, but also overcomes the effect of the full state constraints on the control performance. Finally, it is proved that all the signals in the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) in probability, the system output is driven to follow the reference signals, and all the states are ensured to remain in the predefined compact sets. The validity of the proposed scheme is verified by a simulation example. (C) 2017 Elsevier Ltd. All rights reserved.