Constrained model predictive control for positive systems

Mehrivash, Hamed; Shafiei, Mohammad Hossein

doi:10.1049/iet-cta.2018.5755

Cited by 6 publications

(3 citation statements)

References 25 publications

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“…Moreover, a robust self-triggered controller is designed for discretetime nonlinear systems to guarantee input-to-state practical stability of an uncertain closed-loop system (Liu et al, 2018). With the aid of the linear programming techniques, the problem of MPC design for positive systems with state and input constraints has been solved in Mehrivash and Shafiei (2019). Moreover, the MPC method has been developed for switched systems (Benallouch et al, 2014;Esfahani and Pieper, 2019;Heidarinejad et al, 2013;Müller et al, 2012;Zhang et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Observer-based robust model predictive control of switched nonlinear systems with time delay and parametric uncertainties

Taghieh

Shafiei

2020

Journal of Vibration and Control

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In this study, an observer-based robust model predictive control scheme is proposed to control a class of switched nonlinear systems in the presence of time delay and parametric uncertainties under arbitrary switching. Constructing an appropriate Lyapunov–Krasovskii functional in conjunction with an infinite horizon cost function, sufficient conditions are obtained to guarantee the asymptotic stability of the closed-loop switched system in terms of linear matrix inequalities depending on the time delay, the upper bounds of uncertain parameters, and the Lipschitz constant of subsystems. To model the uncertainty of the system, the parametric uncertainty is used to reduce the computational burden and the conservatism of the method. In the proposed method, a predictive state observer and an observer-based controller are synthesized via an online optimization problem to minimize the upper bound of the cost function, while handling the constraints. Finally, the obtained results are validated using practical and numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Observer-based robust model predictive control of switched nonlinear systems with time delay and parametric uncertainties

Taghieh

Shafiei

2020

Journal of Vibration and Control

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“…Another control procedure that tries to improve the characteristics of the transient responses is composite nonlinear feedback (CNF) method (Binazadeh and Bahmani, 2018; Jafari and Binazadeh, 2018, 2019, 2020; Wang and Zhao, 2016). Model predictive control (MPC) scheme has also been used for improving the transient response (Köhler et al, 2018; Mehrivash and Shafiei, 2019; Aminsafaee and Shafiei, 2019). In all these methods, the Lyapunov analysis has been also utilized to investigate the steady-state error, besides the transient responses.…”

Section: Introductionmentioning

confidence: 99%

Robust output tracking of nonlinear systems with transient improvement via funnel-based sliding mode control

Zahedi

Binazadeh

2020

Transactions of the Institute of Measurement and Control

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This paper studies a new procedure for robust tracking of nonlinear systems. This procedure is based on the combination of the sliding mode control and the funnel control, which in addition to the robust performance of the closed-loop system in the face of model uncertainties and/or external disturbances also leads to improvement of the characteristics of the transient responses. Using funnel control and the appropriate choice of the funnel can affect the convergence rate and overshoot. In this regard, a theorem has been presented and the effective performances of the suggested controller have been guaranteed in various respects based on exact mathematical analysis. Simulations have also been carried out to illustrate the efficiency of the proposed approach and to verify the theoretical achievements of the paper despite model uncertainties and external disturbances.

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“…MPC is a step-by-step optimization technique, in which an optimal control input is obtained at each time instant by solving an optimization problem. To deal with the optimal control of positive systems, a linear centralized MPC framework was established in [29] , [30] , [31] . As described in above positive systems literature, linear Lyapunov functions and linear programming are used in the linear MPC framework.…”

Section: Introductionmentioning

confidence: 99%

Distributed model predictive control of positive Markov jump systems

Zhang

Deng

Zhang

et al. 2020

Journal of the Franklin Institute

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This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design.

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Constrained model predictive control for positive systems

Cited by 6 publications

References 25 publications

Observer-based robust model predictive control of switched nonlinear systems with time delay and parametric uncertainties

Observer-based robust model predictive control of switched nonlinear systems with time delay and parametric uncertainties

Robust output tracking of nonlinear systems with transient improvement via funnel-based sliding mode control

Distributed model predictive control of positive Markov jump systems

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