Sliding Mode Control for Uncertain T-S Fuzzy Singular Biological Economic System

Abstract

In this paper, the design of sliding mode controller for a singular biological economic model with a stage structure and uncertain parameters is studied. First, a biological economic system with uncertain parameters for the invasion of alien species is modeled by a singular system. Then, according to the theory of the T-S fuzzy system, an uncertain T-S fuzzy singular model is established and the stability of the model at the positive equilibria is discussed. Furthermore, a fuzzy integral sliding surface and a sliding mode controller are designed for the T-S fuzzy singular system with an uncertain term. At the same time, the state trajectories can be driven onto the integral sliding surface in finite time and a sufficient condition about the global asymptotic stability of sliding motion is obtained. Finally, a simulation is given to verify the effectiveness of the obtained results. INDEX TERMS The invasion of alien species, Positive equilibria, sliding mode controller, global asymptotic stability.

Adaptive Optimal Multi-Surface Back-Stepping Sliding Mode Control Design for the Takagi-Sugeno Fuzzy Model of Uncertain Nonlinear System With External Disturbance

“…In contrast, sliding mode control (SMC) is a powerful technique that make ensures robustness of the desired system performance in presence of uncertainty [20][21][22][23][24][25]. It has received a great deal of attention in study of nonlinear control field such as biological systems, fault-tolerant control systems, robotic systems, space, and so on [26][27][28][29]. In addition, SMC has been utilized to compensate the additional uncertainties of the T-S fuzzy system [30].…”

An Adaptive Real-Time Third Order Sliding Mode Control for Nonlinear Systems

“…Thus, adaptive control is combined with BSC to mitigate the requirement of exact model. On the other hand, SMC shows great capabilities of dealing with nonlinearity and uncertainties [9][10][11]. The more the degree of nonlinearity and uncertainty, the more need to design robust controllers for control systems.…”

“…Accordingly, many researchers have been working towards developing robust controllers that are able to mitigate these uncertainties [15][16][17]. Among many developed solutions, SMC is one of the most popular and effective solutions that can cope with significant uncertainties, and parameters' variations [9][10][11]. Moreover, SMC technique shows a strong capability to compensate for external perturbations.…”

Network‐based integral sliding mode control for descriptor systems with event‐triggered sampling scheme

“…Descriptor systems are also regraded as generalized state‐space systems, singular systems, or differential‐algebraic systems. Descriptor systems are described by both differential equation and algebraic equation . Descriptor systems have been extensively employed to power systems, economic systems, and circuits systems.…”

“…Descriptor systems are described by both differential equation and algebraic equation. [28][29][30] Descriptor systems have been extensively employed to power systems, economic systems, and circuits systems. Many outstanding research results have been published, such as descriptor time-delay systems, descriptor uncertain systems, and descriptor stochastic systems.…”