Robust MPC for linear systems with bounded disturbances based on admissible equilibria sets

Santos, Tito L.M.; Cunha, Victor M.

doi:10.1002/rnc.5409

Cited by 7 publications

(9 citation statements)

References 32 publications

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“…1,2 The principle concept for ensuring nominal and robust stability involves the inclusion of stabilizing constraints. 3 A significant process has taken place in the area of nominal and robust stability of linear MPC 4,5 and nonlinear MPC (NMPC). [6][7][8][9] A number of stability results for MPC are available in the literature, for example, for constrained piece-wise affine systems, 10 for constrained linear periodic systems, 11 robust MPC for generic state costs, 12 constrained MPC with null controllable initial condition 13 and so forth.…”

Section: Introductionmentioning

confidence: 99%

Application of terminal region enlargement approach for discrete time quasi infinite horizon nonlinear model predictive control

Gupta,

Rajhans

2024

Adaptive Control & Signal

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SummaryEnsuring nominal asymptotic stability of the nonlinear model predictive control (NMPC) controller is not trivial. Stabilizing ingredients such as terminal penalty term and Terminal Region (TR) are crucial in establishing the asymptotic stability. Approaches available in the literature provide limited degrees of freedom for the characterization of the TR for the discrete time quasi infinite horizon NMPC formulation. Current work presents alternate approaches namely arbitrary controller based approach and linear quadratic regulator (LQR) based approach, which provide larger degrees of freedom for enlarging the TR. Both the approaches are scalable to system of any dimension. Approach from the literature provides a scalar whereas proposed approaches provide two additive matrices as tuning parameters for shaping of the TR. Proposed approaches involve solving modified Lyapunov equations to compute terminal penalty term, followed by explicit characterization of the TR. Efficacy of the proposed approaches is demonstrated using benchmark two state system. TR obtained using the arbitrary controller based approach and LQR based approach are approximately 10.4723 and 9.5055 times larger by area measure when compared to the largest TR obtained using the approach from the literature. As a result, there is significant reduction in the prediction horizon length while retaining the feasibility of the controller.

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Section: Introductionmentioning

confidence: 99%

Application of terminal region enlargement approach for discrete time quasi infinite horizon nonlinear model predictive control

Gupta,

Rajhans

2024

Adaptive Control & Signal

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“…Over the past few decades, model predictive control (MPC) is widely used in the industrial process as a modern control strategy. [1][2][3][4][5] MPC is implemented using a receding horizon methodology to optimize predicted future system behaviors under explicit constraints. At each sampling time, MPC solves a finite-horizon optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

“…To reduce the conservatism of RMPC methods for tracking problems, an STMPC method for tracking tasks is presented in literature 11 by extending the notion of the terminal invariant set in the works of literatures 13 and 14 to the SMPC framework. Moreover, literature 4 presents a new RMPC approach for linear systems subject to additive disturbances. This method leverages admissible equilibria sets and is further extended to SMPC.…”

Section: Introductionmentioning

confidence: 99%

A chance‐constrained tube‐based model predictive control for tracking linear systems using data‐driven uncertainty sets

Zhang,

Jia,

et al. 2023

Intl J Robust & Nonlinear

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This article presents a chance‐constrained tube‐based model predictive control (MPC) method for tracking linear time‐invariant systems based on data‐driven uncertainty sets. By defining the terminal admissible set to consider all the possible steady‐states and reformulating the stochastic tube‐based MPC framework, the proposed method can systematically hedge against the impact of uncertainties and ensure tracking for all reachable operating setpoints. To reduce the conservatism of control performance while enlarging the feasible region, a data‐driven polyhedral uncertainty set is constructed by using the principal component analysis technique, which can effectively capture correlations among uncertain variables. Since state constraint violations in a certain probability are allowed, a probability uncertainty set is constructed by using statistic limit and cutting plane methods to formulate a stochastic tube to ensure constraint satisfaction. The recursive feasibility and stability can be guaranteed if the uncertainties are bounded. The effectiveness of the proposed method is verified by numerical examples and tracking problems of a thickening process.

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“…In the proposed method, satisfying the terminal equality constraint is difficult and leads to poor tracking performance. In [38], a robust tracking predictive controller was proposed to deal with piecewise constant setpoints and additive stochastic disturbance or deterministic constant disturbance. The proposed method was applied to the robust tracking MPC based on nominal predictions and stochastic MPC with individual chance constraints.…”

Section: Introductionmentioning

confidence: 99%

“…Several robust tracking predictive controllers were presented to deal with both changing setpoints and additive unknown disturbance in discrete-time linear [34][35][36][37][38] and non-linear [39][40][41] systems. The tube-based MPC was used to ensure recursive feasibility in the presence of deterministic disturbance in [35] and deterministic disturbance mixed with stochastic disturbance in [34].…”

Section: Introductionmentioning

confidence: 99%

Robust MPC for tracking changing setpoints in discrete‐time non‐linear systems with non‐additive unknown disturbance

Zamani

Bolandi

2022

IET Control Theory & Appl

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This paper develops a novel observer-based robust tracking predictive controller for discrete-time nonlinear affine systems capable of dealing with changing setpoints and nonadditive non-slowly varying unknown disturbance with bounded variations. The existence of disturbance and/or sudden changes in a setpoint may lead to feasibility and stability issues in the stabilizing terminal constraint-based MPC. Since robust tracking MPCs usually consider additive disturbance, the recursive feasibility of these methods may be lost in the presence of non-additive non-slowly varying disturbance. The robust tracking MPC presented here extends the artificial reference-based MPC to deal with both changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state constraints as new system constraints. The authors also guarantee the boundedness of disturbance observation error and closed-loop tracking error. In this method, the optimal tracking error converges asymptotically to the terminal region, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. It is shown that the proposed controller can achieve offset-free tracking in the presence of constant disturbance. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.

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Robust MPC for linear systems with bounded disturbances based on admissible equilibria sets

Cited by 7 publications

References 32 publications

Application of terminal region enlargement approach for discrete time quasi infinite horizon nonlinear model predictive control

Application of terminal region enlargement approach for discrete time quasi infinite horizon nonlinear model predictive control

A chance‐constrained tube‐based model predictive control for tracking linear systems using data‐driven uncertainty sets

Robust MPC for tracking changing setpoints in discrete‐time non‐linear systems with non‐additive unknown disturbance

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