Stable receding-horizon scenario predictive control for Markov-jump linear systems

Sala, Antonio; Hernández-Mejías, Manuel A.; Ariño, Carlos

doi:10.1016/j.automatica.2017.07.032

Cited by 15 publications

(13 citation statements)

References 8 publications

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“…In recent years, MPC was applied widely in linear MJSs, as presented in [17]- [19]. The stability and feasibility of a tree-based MPC optimization was guaranteed as well as the full-scenario linear MJSs in [20]. Based on the periodic invariant set, a feedback predictive control method can reduce more conservativeness than that of using a modedependent feedback control law [21].…”

Section: Introductionmentioning

confidence: 99%

Constrained Model Predictive Control for Nonlinear Markov Jump System With Persistent Disturbance via Quadratic Boundedness

Feng

Gao

2020

IEEE Access

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In this paper, a robust quadratic-boundedness-based model predictive control (MPC) scheme, for a discrete-time nonlinear Markov jump system (MJS), is extended to the case with persistent bounded disturbance and nonhomogeneous transition probability. By applying the S-procedure, the constraint conditions, the persistent bounded disturbance and the sufficient stability conditions are all derived in term of a few linear matrix inequalities (LMIs), thus the original min-max optimization problem is transformed into a convex optimization problem in LMI paradigm. At each sampling time, the control moves satisfying the control constraint are obtained online and implemented in the nonlinear MJS. Quadratically boundedness and min-max MPC are combined to achieve the closed-loop stochastic stability of the controller with respect to the persistent bounded disturbance. A numerical example is presented to demonstrate the effectiveness of the proposed results. INDEX TERMS Model predictive control, nonlinear Markov jump system, quadratic boundedness, persistent disturbance, stochastic stability, linear matrix inequality.

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Section: Introductionmentioning

confidence: 99%

Constrained Model Predictive Control for Nonlinear Markov Jump System With Persistent Disturbance via Quadratic Boundedness

Feng

Gao

2020

IEEE Access

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“…Predictive control has the advantages of prediction, online optimisation, and processing delays [25][26][27]. Currently, theories and applications for linear predictive control are relatively mature [28][29][30][31][32]. However, research on non-linear predictive control methods is still under exploration [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Takagi–Sugeno fuzzy generalised predictive control of a time‐delay non‐linear hydro‐turbine governing system

Tian

Wang

Zhu

et al. 2019

IET Renewable Power Generation

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This study focuses on a fuzzy generalised predictive control (FGPC) method for a time-delay hydro-turbine governing system (HTGS). First, based on the time-delay Takagi-Sugeno fuzzy model, a time-delay HTGS and its fuzzy prediction model are given. Second, with the help of delay fuzzy linearisation and a fourth-order Runge-Kutta algorithm, a transformed controlled auto-regressive integrated moving average model is obtained. Then, a new FGPC scheme for the time-delay HTGS is proposed. Finally, numerical simulations are implemented to verify the validity and superiority of the proposed method. It also provides a reference for the stability control of relevant hydropower station systems.

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“…Reference [56], for MJLSs with polytopic uncertainties in both system matrices and transition probability matrices, studied a robust distributed model predictive control (DMPC) strategy. At the same time, the stable receding-horizon scenario predictive control of constrained discrete-time MJLSs was also studied [57]. For the Markovian jump linear systems with bounded disturbance, Lu et al [58] studied the constrained model predictive control method to achieve the disturbance rejection.…”

Section: Introductionmentioning

confidence: 99%

Robust Model Predictive Control for a Class of Discrete-Time Markovian Jump Linear Systems With Operation Mode Disordering

Cai

et al. 2019

IEEE Access

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For a class of discrete-time Markovian jump linear systems subject to operation mode disordering, a robust model predictive control method can be proposed to solve this issue. A bijective mapping scheme between the original random process and a new random process is studied to cope with the problem of operation mode disordering. At each sampling time, the original ''min-max'' optimization problem is transformed into a convex optimization problem with linear matrix inequalities so that the complexity of solving the optimization problem can be greatly reduced. The sufficient stability condition of the Markovian jump linear systems can be achieved by using the Lyapunov stability theory. Moreover, a state feedback control law is obtained, which minimizes an infinite prediction horizon performance cost. Furthermore, the cases of uncertain and unknown transition probabilities are also considered in this paper. The simulation results show that the proposed method can guarantee the optimal control performance and the stability of Markovian jump linear systems. INDEX TERMS Robust model predictive control, Markovian jump linear systems (MJLSs), operation mode disordering, linear matrix inequalities (LMIs).

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Stable receding-horizon scenario predictive control for Markov-jump linear systems

Cited by 15 publications

References 8 publications

Constrained Model Predictive Control for Nonlinear Markov Jump System With Persistent Disturbance via Quadratic Boundedness

Constrained Model Predictive Control for Nonlinear Markov Jump System With Persistent Disturbance via Quadratic Boundedness

Takagi–Sugeno fuzzy generalised predictive control of a time‐delay non‐linear hydro‐turbine governing system

Robust Model Predictive Control for a Class of Discrete-Time Markovian Jump Linear Systems With Operation Mode Disordering

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