Robust distributed model predictive control for uncertain networked control systems

Abstract

In this study, an approach to design robust distributed model predictive control (MPC) is proposed for polytopic uncertain networked control systems with time delays. To reduce the computational complexity and improve the flexibility, the entire system is decomposed into multiple smaller dimensional subsystems. For each subsystem, the proposed robust distributed MPC algorithm requires solving multiple linear matrix inequality optimisation problems to minimise an upper bound on a robust performance objective. An augmented polytopic uncertainty description is invoked to handle the input delays. The conservativeness of distributed MPC algorithm is reduced by utilising a sequence of feedback control laws. An iterative on-line algorithm for robust distributed MPC is developed to coordinate the distributed MPC controllers. Convergence and robust stability of the proposed distributed MPC are investigated. A numerical example is carried out to demonstrate the effectiveness of the proposed algorithm.

LMI‐based cooperative distributed model predictive control for Lipschitz nonlinear systems

“…where P = M −1 . From (21), it can be deduced that Ω(M −1 ) is an invariant set corresponding to all control inputs u i (k). Thus, the state trajectory x will remain inside Ω(M −1 ) and asymptotically goes toward x eq (p) .…”

“…To avoid this limitation, cooperative distributed schemes can be considered. Therefore, LMI‐based CDMPC algorithms are proposed for linear systems . Al‐Gherwi et al have derived CDMPC for linear systems with polytopic uncertainty, which incorporates the information of all states of other subsystems in computing each local input while optimizing a global objective function.…”

“…Since only the inputs of the system are actually decomposed and all states are fed back to each subsystem, this approach is more practical to control systems, which have no proper decomposition in states or have strong interaction among subsystems. A similar approach has been also developed for linear systems with state and input time delays, linear systems with actuator saturation, and linear systems with structured uncertainty . To reduce the computational demand of the method, a dual‐mode approach is suggested to transfer most of the needed computations to the offline part .…”

“…Therefore, LMI-based CDMPC algorithms are proposed for linear systems. [20][21][22][23] Al-Gherwi et al 20 have derived CDMPC for linear systems with polytopic uncertainty, which incorporates the information of all states of other subsystems in computing each local input while optimizing a global objective function. Since only the inputs of the system are actually decomposed and all states are fed back to each subsystem, this approach is more practical to control systems, which have no proper decomposition in states or have strong interaction among subsystems.…”

The Design of Output Feedback Distributed Model Predictive Controller for a Class of Nonlinear Systems

“…A distributed model predictive control strategy for interconnected process systems is proposed in reference [10]. In literature [11], a design approach of robust distributed model predictive control is proposed for polytopic uncertain networked control systems with time delays. Reference [12] presents that the distributed model predictive control method is applied for an accurate model of an irrigation canal.…”