Robust model predictive control for polytopic uncertain systems with state saturation nonlinearities under Round‐Robin protocol

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Summary The fuzzy model predictive control (FMPC) problem is studied for a class of discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems with hard constraints. In order to improve the network utilization as well as reduce the transmission burden and avoid data collisions, a novel event‐triggering–based try‐once‐discard (TOD) protocol is developed for networks between sensors and the controller. Moreover, due to practical difficulties in obtaining measurements, the dynamic output‐feedback method is introduced to replace the traditional state feedback method for addressing the FMPC problem. Our aim is to design a series of controllers in the framework of dynamic output‐feedback FMPC for T‐S fuzzy systems so as to find a good balance between the system performance and the time efficiency. Considering nonlinearities in the context of the T‐S fuzzy model, a “min‐max” strategy is put forward to formulate an online optimization problem over the infinite‐time horizon. Then, in light of the Lyapunov‐like function approach that fully involves the properties of the T‐S fuzzy model and the proposed protocol, sufficient conditions are derived to guarantee the input‐to‐state stability of the underlying system. In order to handle the side effects of the proposed event‐triggering–based TOD protocol, its impacts are fully taken into consideration by virtue of the S‐procedure technique and the quadratic boundedness methodology. Furthermore, a certain upper bound of the objective is provided to construct an auxiliary online problem for the solvability, and the corresponding algorithm is given to find the desired controllers. Finally, two numerical examples are used to demonstrate the validity of proposed methods.

“…Next, we will throw lights on condition (b). To achieve this goal, we only need to show that the predicted state φ ( k τ +1| k τ ) belongs to the set Ω r . Letting

ϵ = 1 - \overset{α}{true}

and by using

G^{T} X^{- 1} G ⩾ - X + G^{T} + G

, we can get the following inequality from :

([], \begin{matrix} center center \\ array {\sum^{^}}_{r, 11}^{κ} & array * \\ array \sum_{c, r, 21}^{ι κ} & array \sum_{t, 22}^{l} \end{matrix}) ⩾ 0,

where

\begin{matrix} alignleft \\ align-1 {\sum^{^}}_{r, 11}^{κ} & align-2 = [\begin{array}{cccc} X_{1 r, 11}^{κ} & * & * & * \\ 0 & X_{2 r, 22}^{κ} & * & * \\ 0 & 0 & X_{3 r, 33}^{κ} & * \\ 0 & 0 & 0 & \frac{\overset{α}{true}}{ω^{2}} O_{11}^{T} O_{11} \end{array}], \\ align-1 X_{1 r, 11}^{κ} & align-2 = ϵ X_{1 r}^{κ}, X_{2 r, 22}^{κ} = ϵ X_{2 r}^{κ}, X_{...} \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic output‐feedback fuzzy MPC for Takagi‐Sugeno fuzzy systems under event‐triggering–based try‐once‐discard protocol

Dong

Song

Wang

et al. 2019

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“…The principal characteristic of MPC is the effectiveness of handling various constraints in multiple‐input multiple‐output complex systems for optimum control performance, which is why MPC has already been widely used in modern industry field 2,3 . The core idea behind the MPC is that the optimal control sequence is obtained by solving online the open‐loop, rolling optimization problem in every sampling instant, and then apply the first control input of the optimal sequence to the plant at the current moment 4,5 . Through years of continuous development and exploration of MPC, an increasing number of scholars widely focus on theoretical research 6,7 …”

Section: Introductionmentioning

confidence: 99%

A novel linear matrix inequality‐based robust event‐triggered model predictive control for a class of discrete‐time linear systems

Ding

Peng

et al. 2021

This paper studies a linear matrix inequality (LMI)‐based robust event‐triggered model predictive control (ET‐MPC) for a class of discrete linear time‐invariant systems subject to bounded disturbances. In the presented robust event‐triggered MPC, the event‐triggered mechanism is first set by the deviation between the optimal state and actual state. In addition, the Lyapunov‐based stability condition is employed in the constraints for simplifying parameters and enhancing the universality. Subsequently, a novel design framework that involves LMIs approach is developed. In such a framework, the Lyapunov weight matrix is predesigned by solving a convex optimization problem with LMIs and the infinite horizon MPC optimization problem is also transformed as LMIs such that the computational complexity is significantly reduced. To guarantee robust constraint satisfaction, a dual‐mode control strategy is adopted. In this way, the proposed robust ET‐MPC has the ability to deal with the constrained system. Furthermore, the theoretical analysis of the recursive feasibility and stability is provided. The numerical simulations and comparison studies demonstrate that the proposed robust ET‐MPC not only has satisfying control performance but also significantly reduces the computational burden.

“…Using this method, the RMPC problem has been discussed for a class of discrete‐time Takagi‐Sugeno fuzzy systems 8 with structured uncertainties, for the switched linear systems 9 and for a group of systems 10 with saturated inputs. Generally speaking, according to the different feedback schemes, the control strategy can be classified into the state feedback (SF) control 11,12 and the output feedback (OF) control 13,14 . In particular, the dynamic OF control problem 15,16 in the framework of RMPC has been discussed for linear systems with polytopic uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Robust model predictive control for multirate systems with model uncertainties and circular scheduling

Wang

Song

Wei

2020

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In this article, the robust model predictive control (RMPC) problem on the basis of output feedback (OF) is dealt with for a class of multirate time-varying systems with polyhedral uncertainties and limited-bandwidth channels. For alleviating the communication burden caused by the limited transmission capacity, the Round-Robin (RR) protocol is exploited to allocate transmission permissions in a pre-scheduled order. Meanwhile, in order to reduce the communication cost while ensuring the system performance, the multirate mechanism is presented to govern the update rate of the plant and the sampling rate of the sensors. By means of the lifting technique, given a uniform sampling rate, a comprehensive augmentation system is established on the fixed moving horizon. The objective of the addressed RMPC problem is to design a set of OF-based RMPC controllers such that, in the presence of the multirate scheme and the RR transmission protocol, the desirable performance is guaranteed. Then, the desired RMPC gains are directly obtained, with the help of inequality analysis technique and RR-dependent Lyapunov-like approach, to ensure the asymptotic convergence of system states. Two illustrative examples are given, which include a DC motor system and a numerical simulation example, to demonstrate the effectiveness of the proposed protocol-based RMPC controller design strategy.