Robust Integral Sliding Mode Control for Uncertain Impulsive Stochastic Systems with Time Delays

Venue: IEEE_org_ICIST_2024_Conference
Published: 2024-08-16 10:00:21

Abstract: This paper studies the integral sliding mode control (ISMC) for uncertain impulsive stochastic systems with time delays. An ISMC law is proposed by designing a new integral sliding surface. Then, by constructing a piecewise time-dependent Lyapunov function, the uniformly almost surely exponentially stability conditions of the closed-loop system are established. Furthermore, an optimal design algorithm of solving control gains is formulated based on the established stable conditions and linear matrix inequalities (LMIs) theory.

Main paper: 
 ii. system description and preliminaries: 
 Consider the linear uncertain impulsive stochastic systems with time delay: EQUATIONEQUATIONwhere () m u tEQUATION( ) i i i D t D D t = +  , ( ) ( ) di di di D t D D t = +  , nn i AR   , nn di AR   , nm i CR   , mn i DR   , mn di DR   , nn i ER   are real constantn n m n p n n q m q m m A R B R C R D R D R E R               . If there exists a constant 0   such that 1 1 0 T TT AB DD C C E  - -  - + +   -   (2)where 12T T T D D D  =  and 0 T pm CC   =  , then the following inequality holds 1 2 2 He( ) ( ) ( ) 0 T A D GC B D GC E B D GC -+ + + +  (3) for any matrix qp GR   satisfying 1 G  .The control objective in this study is to construct a SMC strategy to guarantee that the uncertain stochastic linear impulsive system with time delay (1) is uniformly mean-square exponentially stable.It is follows from the ISMC theory that the ISMC law is chosen the following form12 ( ) ( ) ( ) u t u t u t =+ (4)where the role of 1 () ut is stabilizing the dynamic and 1 () ut is designed to reject the disturbance and maintains the dynamic. To design the sliding mode surface, a continuous sliding mode function which depend on the impulse information is proposed at first. Then, 1 () ut and 2 () ut is designed to assure the reachability of the sliding mode surface.Inspired by [] and [], we design an integral sliding surface for system (1) as:1 1 1 0 0 1 ( ) ( ) ( ) ( ) [ ( ( ) ( ) ( )) ( )] t p d p s t Qx t t Q x t Q Ax A x Bu Q x d         = + - + -+ -  (5)where Q is designed to satisfy that QB is nonsingular and 0 QC = , 1 () Q Q I J =-,Q B Z = .Because the states () xt is discontinuous at t  , it can be seeming from the continuous of () st at t  that the sliding surface ()st established for system (1) is continuous on [0, )  . Based on ( ) 1 t   = and ( ) 0 t   -= , it follows from 1 QC Q Q += that 1 0 ( ) ( ) ( ) ( ) ( ) = ( ) t s t QC Q x t Q A BK x d st     - - = + - +  (6) so, () st is continuous on [0, )  .To guarantee the reachability of the designed sliding surface ( ) 0 st = , the SMC law 2 () ut is designed in Theorem 1.Theorem 1: Consider the system (1) under Assumptions -, if we adopt the sliding mode function () and the SMC law: EQUATIONSubstituting ( 10) into (11), we getEQUATIONChoosing the Lyapunov function EQUATIONEQUATIONEQUATION          -  = + + - + + + - -  + + -    =   + =  -  (12) where 1 () TT B B B ZB B Z - = .To set up the criterion of stability for system (15), theEQUATION) ), 0, 1 i t id t i d i N       + + +  - , in which 1 tt d N   + - =. Then, we define:  .EQUATION( ) [0,1] t   such that 1 1 0 ( ) ( ) l 
 
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Reviews: review: title: title: This manuscript contains numerous formatting errors, presents simplistic content, lacks innovation, and appears to be an unfinished version of a paper. Therefore, it is recommended for rejection.
main_review: main_review: This manuscript contains numerous formatting errors, presents simplistic content, lacks innovation, and appears to be an unfinished version of a paper. Therefore, it is recommended for rejection. Some of the major issues are listed below: 
1. Formulas are excessively long and overlap, such as formula (5). 
2. The paper lacks experimental and simulation validations. 
3. The introduction is overly cursory. 
4. The paper is deficient in necessary content such as references.
title: title: Recommended rejection
main_review: main_review: The paper lacks a significant contribution to the existing body of knowledge and fails to provide a clear advancement or novel insights into integral sliding mode control for stochastic systems. As such, I do not think this paper is suitable for ICIST 2024.
title: title: Recommended rejection
main_review: main_review: The innovation points of this manuscript are insufficient and the logic is unclear. It is not recommended to publish this paper in ICIST 2024.