Sliding Mode Control under State and Control Constraints

Abstract

In this paper, we propose a method of continuoustime sliding mode control(SMC) system design so as not to violate state and control constraints. To circumvent chattering problem, we use continuous control law. And, we employ the inner approximation of maximal admissible set for a nonlinear continuous-time system to guarantee the satisfaction of constraints. This approach has the advantages that it is robust over initial state error and that save the on-line computing time required to inclusion check of maximal admissible sets. Moreover, we propose a control strategy of switching "sliding" hyperplanes to achieve better performance.

On the implementation of reference governor

“…Then, by (15), (20), (21), x 0 ∈ Ω ∞ (r, ξ) if and only if h j,k x 0 + g j,kr < = m j (ξ), j ∈ J , k ∈ K.…”

Constrained sliding mode control of MIMO nonlinear systems

“…文献 [16] 针对受约束的滑模控制提出了一种几何分析方法, 并且详细介绍了在执行 器饱和的情况下如何分析滑模运动的最大吸引域. Ferrara 等 [17] 分析了一类非线性不确定系统执行器 饱和情形下的次优二阶滑模控制, 并在文献 [18,19] 中分析了执行器饱和以及状态受约束情形时的滑 模条件. 值得指出的是, 这些研究结果都假设了原控制系统状态是完全已知的.…”