Static output‐feedback sliding mode control under round‐robin protocol

Abstract

Summary This paper addresses the static output‐feedback sliding mode control (SMC) problem for a class of uncertain control systems subject to the round‐robin protocol scheduling, in which the communication between the controller and the actuators is regulated by the round‐robin protocol, that is, only one actuator node gets the access to the transmission network at each instant and the other actuators utilize the values stored in the zero‐order holders. A key issue of the addressed problem is how to design both the sliding surface and the sliding mode controller subject to the kind of actuator signals depending on protocol scheduling and zero‐order holders. By only using the measured output information, a linear sliding surface is constructed, and then, a token‐dependent SMC law is designed properly with the aid of an updating rule on actuator input. Moreover, suitable token‐dependent Lyapunov functions are exploited to obtain sufficient conditions for guaranteeing the asymptotic stability of the closed‐loop systems and the reachability of the specified sliding surface. Furthermore, based upon a separation strategy, a convex optimization algorithm is proposed to obtain the controller gains. Finally, the effectiveness of the developed static output‐feedback SMC design scheme is verified in an industrial continuous‐stirred tank reactor system.

An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information

“…Since (ii) holds, we have from Theorem 1 with ii = 1 and 2 ∞ = that there exists Q i > 0,M (0) i > 0,S (o) i > 0, and N (o) i such that (12)-(13) hold for  ∈ ℭ and system matrices given in (5) to (6). Consider the partitions for Q i and Q −1 i as in (20) and the matrices T i , H i as in (22). By applying the congruence transformation diag(T i , I r ) and the Schur complement to (12) followed by the congruence transformation diag(T i , I r , H i , I p ∞ ), we get that (25)- (26)…”

“…The design of state‐feedback controllers was considered by Ogura et al through the hidden model previously described, in which the controller depends on the most recent value of the cluster of the observed variable and the time elapsed since the last observation, with the results given in the LMI framework. According to Remark 18 of Ogura et al, even though the detector approach can be retrieved via the observation model presented in that paper, the proposed design conditions for the control can lead to a potential underperformance with respect to the ones presented by Costa et al The separation method has been used in dealing with the coupling problem in BMI conditions by several authors (see, for instance, the works of Song et al and Oliveira et al for a small sample of studies under this formulation). The paper by Song et al studied the design of static output feedback sliding mode controllers subject to a round‐robin protocol in the context of networked control system (NCS), with a separation strategy employed for avoiding nonlinear terms in the design conditions.…”

“…According to Remark 18 of Ogura et al, even though the detector approach can be retrieved via the observation model presented in that paper, the proposed design conditions for the control can lead to a potential underperformance with respect to the ones presented by Costa et al The separation method has been used in dealing with the coupling problem in BMI conditions by several authors (see, for instance, the works of Song et al and Oliveira et al for a small sample of studies under this formulation). The paper by Song et al studied the design of static output feedback sliding mode controllers subject to a round‐robin protocol in the context of networked control system (NCS), with a separation strategy employed for avoiding nonlinear terms in the design conditions. In the work of Song et al, the problem of asynchronous H ∞ output feedback control of uncertain MJLS in a finite‐time setting is analyzed through a separation method in which the closed‐loop system is rewritten in terms of a new set of signals that uses matrices obtained in an LMI decision problem.…”

“…Oliveira et al 14,15 presented a similar separation procedure for the hidden MJLS as the one used in this work, but neither the H ∞ and the mixed H 2 ∕H ∞ control was fully studied, nor an iterative method was presented. Moreover, the works of Ogura et al 13 and Song et al 11,22 are different with respect to our results in the sense that: (1) we deal with dynamic output feedback control in the hidden MJLS or detector approach, following the formulation by Costa et al, 10 and (2) our iterative separation method employs a state-feedback controller as an input to the algorithm so that the dynamic controller by the end of the iterations is composed by the state-feedback gain and a filter structure.…”

Dynamic output feedback sliding mode control for Markovian jump systems under stochastic communication protocol and its application

“…An effective strategy of avoiding data collisions is to utilize a scheduling protocol to regulate the communication network. 8 There exist several kinds of protocols covering event-triggered protocol, [9][10][11] Round-Robin protocol, 9,12,13 try-once-discard protocol, 1 and stochastic communication protocol (SCP), 14,15 among which the SCP has gained wider attention. In Reference 16, an independent and identically distributed stochastic process has been utilized to describe the SCP, and using a time-delay approach, a stochastic impulsive system with delay has been obtained for further study.…”