Robust MPC under event-triggered mechanism and Round-Robin protocol: An average dwell-time approach

Ding

2018

Self Cite

Summary This paper addresses the resilient robust model predictive control (RMPC) problem for a class of polytopic uncertain systems under the try‐once‐discard (TOD) protocol. At each transmission instant, only one sensor node obtains the privilege to access the shared communication network in order to prevent the data from collision. The measurements transmission order of the sensor nodes is orchestrated, and a switched system is constructed according to the underlying TOD protocol. The aim of this paper is to design a set of desired resilient dynamic output feedback controllers in the framework RMPC such that the switched system with the underlying TOD protocol is exponentially stable. By taking the influence of the TOD protocol into account, sufficient conditions are provided to guarantee the recursive feasibility of the RMPC strategy and the stability of the established closed‐loop system in terms of the average dwell time method. Moreover, the effective resilient controllers in RMPC framework are derived by solving an online constrained optimization problem. Finally, a network‐based direct current motor example is utilized to illustrate the effectiveness of the proposed model predictive control strategy.

“…which guarantees (14) and (16). By virtue of Lemma 2, it follows from (29) and (30) that V * (k) (k) is exponentially stable, which completes the proof.…”

Section: Theoremmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Resilient RMPC for polytopic uncertain systems under TOD protocol: A switched system approach

Zhu

Ding

2018

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“…Proof The proof can be easily obtained by the similar lines to that in the work of Zhu et al, and it is thus omitted.…”

Section: Resultsmentioning

confidence: 89%

“…In line with the work of Zhu et al, the event‐triggered mechanism that contributes to the event‐triggering instant sequence

0 ⩽ k_{1} < k_{2} < ⋯ < k_{τ} < ⋯

can be given by

k_{τ + 1} = \inf ({}, k false| k > k_{τ}, false‖ e false(k false) {false‖}^{2} > \frac{ρ false(k false)}{\sqrt{\overset{ρ}{true}}}),

where k τ and k τ +1 denote the adjacent two event‐triggering instants.

ρ false(k false) ≜ \sqrt{ε^{- γ k} + ε_{0}}

is a time‐varying threshold with known scalars ε >1,

0 ⩽ γ < 1

, ε 0 >0, and

\overset{ρ}{true} > 0

.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 74%

“…A typical negative phenomenon of network connection is the data collision, which usually occurs during data transmission through a shared communication network. Fortunately, some communication protocols have been put forward to handle this problem, which include but are not limited to the stochastic communication protocol (SCP), [31][32][33][34] the round-robin (RR) protocol, [35][36][37][38] and the try-once-discard (TOD) protocol. [39][40][41] Among these protocols, the TOD protocol is extremely superior at allocating resource since the current information of the system is fully considered into the scheduling.…”

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

Wang

et al. 2019

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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.

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

Wang

Wei

et al. 2019

Self Cite

Summary This paper is concerned with the robust model predictive control (RMPC) problem for polytopic uncertain systems with state saturation nonlinearities under the Round‐Robin (RR) protocol. With respect to the practical application, one of the most commonly encountered obstacles that stem from the physical limitation of system components, ie, state saturation, is adequately taken into consideration. In order to reduce the network transmission burden and improve the utilization of the network from the controller nodes to the actuator node, a so‐called RR protocol is employed to orchestrate the data transmission order. At each transmission instant, only one controller node that obtains the priority is accessible to the shared communication network. Our aim of the underlying problem is to design a set of controllers in the framework of RMPC such that the closed‐loop system is asymptotically stable. By taking the influence of the RR protocol and the state saturation precisely into account, some sufficient criteria are established in terms of the token‐dependent Lyapunov‐like approach. Then, an online optimization problem subjected to some matrix inequality constraints is provided, and the desired controllers can be obtained by solving the certain upper bound of the objective addressed. Finally, a distillation process example is provided to illustrate the effectiveness of the proposed RMPC approach.