Constrained model predictive control synthesis for uncertain discrete‐time Markovian jump linear systems

Lǚ, Jianbo; Li, Dewei; Xi, Yugeng

doi:10.1049/iet-cta.2012.0884

Cited by 53 publications

(76 citation statements)

References 33 publications

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“…It should be noted that the probability distributions of these two random variables are assumed to be known in advance, which are determined by historical data or obtained by experiments. Besides, it should be noted that the uncertainties described by (1) are norm-bounded and satisfy (3). Since the randomly occurring parameter variations have been considered, the discussed systems in this paper are more general than most of those in existing literatures.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Robust Model Predictive Control for Linear Discrete‐Time System With Saturated Inputs and Randomly Occurring Uncertainties

Wang

Song

Zhang

et al. 2017

Asian Journal of Control

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This paper investigates the robust model predictive control (RMPC) problem for a class of linear discrete-time systems subject to saturated inputs and randomly occurring uncertainties (ROUs). Due to limited bandwidth of the network channels, the networked transmission would inevitably lead to incomplete measurements and subsequently unavoidable network-induced phenomenon that include saturated inputs as a special case. The saturated inputs are assumed to be sector-bounded in the underlying system. In addition, the ROUs are taken into account to reflect the difficulties in precise system modelling, where the norm-bounded uncertainties are governed by certain uncorrelated Bernoulli-distributed white noise sequences with known conditional probabilities. Based on the invariant set theory, a sufficient condition is derived to guarantee the robust stability in the mean-square sense of the closed-loop system. By employing the convex optimization technique, the controller gain is obtained by solving an optimization problem with some inequality constraints. Finally, a simulation example is employed to demonstrate the effectiveness of the proposed RMPC scheme.

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Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Robust Model Predictive Control for Linear Discrete‐Time System With Saturated Inputs and Randomly Occurring Uncertainties

Wang

Song

Zhang

et al. 2017

Asian Journal of Control

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“…Therefore by optimizing , the MPC controller optimizes the objective function (23) approximately. Notice that by discussions in [14], the optimization problem of (24) may suffer from loss of recursive feasibility at some time instant. Since it is the expected value of ( , ) rather than its deterministic value is guaranteed to decrease by the controller design at each time .…”

Section: Mpc Designmentioning

confidence: 99%

Stabilization of linear discrete-time periodic systems with uncertain period

Lǚ

2013

2013 9th Asian Control Conference (ASCC)

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In this paper, stabilization problem for constrained linear discrete-time periodic systems with uncertain period is investigated, where the uncertain period is caused by the probabilistic transitions of some mode to the next mode or to itself. Results are given for three cases, robust stabilization, stochastic stabilization by utilizing the transition probabilities, and MPC design. All these designs are based on the use of mode-dependent state feedback control law. Conditions guaranteeing the close-loop stability and satisfaction of constraints on inputs and states are given in terms of LMIs. Finally a numerical example is given to verify the efficiency of the developed results.

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“…Model predictive control (MPC), also called receding horizon control, has been widely applied into the process industries in the past few decades because of its ability to handle input/state constraints and compensate time delays [1][2][3]. Different from the conventional control with a pre-computed control law, MPC requires online optimization to compute an optimal control sequence at every sampling interval and implements the first one of the control sequence.…”

Section: Introductionmentioning

confidence: 99%

Robust model predictive control under redundant channel transmission with applications in networked DC motor systems

Song

Wang

Ding

et al. 2016

Intl J Robust & Nonlinear

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Abstract-In networked systems, intermittent failures in data transmission are usually inevitable due to the limited bandwidth of the communication channel, and an effective countermeasure is to add redundance so as to improve the reliability of the communication service. This paper is concerned with the model predictive control (MPC) problem by using static output feedback for a class of polytopic uncertain systems with redundant channels under both input and output constraints. By utilizing the min-max control approach combined with stochastic analysis, sufficient conditions are established to guarantee the feasibility of the designed MPC scheme that ensures the robust stability of the closed-loop system. In terms of the solution to an auxiliary optimization problem, an easy-to-implement MPC algorithm is proposed to obtain the desired sub-optimal control sequence as well as the upper bound of the quadratic cost function. Finally, to illustrate its effectiveness, the proposed design method is applied to control a networked direct current (DC) motor system.

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Constrained model predictive control synthesis for uncertain discrete‐time Markovian jump linear systems

Cited by 53 publications

References 33 publications

Robust Model Predictive Control for Linear Discrete‐Time System With Saturated Inputs and Randomly Occurring Uncertainties

Robust Model Predictive Control for Linear Discrete‐Time System With Saturated Inputs and Randomly Occurring Uncertainties

Stabilization of linear discrete-time periodic systems with uncertain period

Robust model predictive control under redundant channel transmission with applications in networked DC motor systems

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