Decentralized sliding mode control for a class of nonlinear interconnected systems by static state feedback

Abstract

Summary In this paper, a class of interconnected systems is considered, where the nominal isolated systems are fully nonlinear. A robust decentralized sliding mode control based on static state feedback is developed. By local coordinate transformation and feedback linearization, the interconnected system is transformed to a new regular form. A composite sliding surface which is a function of the system state variables is proposed and the stability of the corresponding sliding mode dynamics is analyzed. A new reachability condition is proposed and a robust decentralized sliding mode control is then designed to drive the system states to the sliding surface in finite time and maintain a sliding motion thereafter. Both uncertainties and interconnections are allowed to be unmatched and are assumed to be bounded by nonlinear functions. The bounds on the uncertainties and interconnections have more general forms when compared with existing work. A MATLAB simulation example is used to demonstrate the effectiveness of the proposed method.

Decentralized adaptive tracking control for nonlinear large‐scale systems with unknown control directions

“…Remark Note that the system model (1) is common in many practical system such as the mass‐spring‐damper model, 1 the helicopter dynamics 22 and the coupled inverted pendulum 26 . Besides, compared with the recent results, 1‐4,17,19,20,25,26,37 the system (1) is more general mainly because the unknown interconnections rely on the state of all subsystems and the actuator fault is allowed to exist.…”

“…Remark Since the unknown control direction appears in front of the control input , the existing controller design methods for strong interconnected LSSs 1,19,20,27,28 are not applicable in this article. By introducing the Nussbaum gain, the fault‐tolerant controller (27) is designed to compensate the unknown direction, which can be applied to solve the control problem of the practical system with unknown motion direction, for example, course control of marine vessels and combustion control systems.…”

“…When the interconnected functions or their bounds for each subsystem only depend on the outputs of other subsystems and its own states, called weak interconnection, the corresponding decentralized control problem has been considered 14‐16 . Recently, the decentralized control of strongly interconnected nonlinear systems has also been investigated, where both the interconnected functions and their bounds are related to the states of all subsystems, while the local control law only depends on the state of the corresponding subsystem 1,17‐20 . Note that the above results all require the system to be in an ideal environment without failure.…”

Dynamic event‐triggered decentralized control of interconnected systems

“…More specifically, the sub‐controller for each subsystem is designed without using information from other subsystems. Recently, the decentralized control theory has been extensively investigated for interconnected systems 3,8,9 . Such as, in the linear situation, Jiang and Jiang 8 studied the decentralized control problem for a class of interconnected systems by using robust adaptive dynamic programming theory.…”

“…Over the previous few decades, physically interconnected systems have witnessed more attention, [1][2][3] which have been extensively employed in practical domains such as networked multi-robot systems, 4 cyber-physical systems, 5 and power systems. 6 These complex systems are composed of a set of lower-dimensional subsystems that interact with each other via physical connections.…”