Stability of finite horizon model predictive control with incremental input constraints

Yu, Shuyou; Qu, Ting; Xu, Fang; Chen, Hong; Hu, Yunfeng

doi:10.1016/j.automatica.2017.01.040

Cited by 46 publications

(79 citation statements)

References 20 publications

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“…In the literature, there are several methods to find an invariant set and a terminal penalty cost such that the stability of the quasi-infinite horizon-based MPC (3) can be guaranteed, e.g., [5,25,26]. In these studies, V(x) = x T Px is shown as a local Lyapunov function in the set E = {x|x T Px ≤ α} under a stabilizing control law κ(x) = Kx, meaning that A1-A4 in Lemma 1 are satisfied.…”

Section: Mpc Based On the In-between Terminal Setmentioning

confidence: 99%

“…Note that (8) is equivalent with (7). A method based on the existing method [5,25,26] can also be employed to make Assumption 2 holds true. In fact, the following lemma can be obtained by extending the result in [26].…”

Section: Mpc Based On the In-between Terminal Setmentioning

confidence: 99%

“…Although the resulting terminal set is not the convex hull of the predefined sets, the proposed method can be easily employed for a nonlinear system without the need for an LDI argument. Moreover, the ingredient sets E i can be obtained using a similar procedure as in [5,25], or [26]. In the next section, numerical simulations are used to investigate the performance of the proposed MPC for a nonlinear system.…”

Section: Mpc Based On the In-between Terminal Setmentioning

confidence: 99%

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A Nonlinear Model Predictive Control with Enlarged Region of Attraction via the Union of Invariant Sets

Fitri

Kim

2020

Mathematics

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In the dual-mode model predictive control (MPC) framework, the size of the stabilizable set, which is also the region of attraction, depends on the terminal constraint set. This paper aims to formulate a larger terminal set for enlarging the region of attraction in a nonlinear MPC. Given several control laws and their corresponding terminal invariant sets, a convex combination of the given sets is used to construct a time-varying terminal set. The resulting region of attraction is the union of the regions of attraction from each invariant set. Simulation results show that the proposed MPC has a larger stabilizable initial set than the one obtained when a fixed terminal set is used.

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Section: Mpc Based On the In-between Terminal Setmentioning

confidence: 99%

Section: Mpc Based On the In-between Terminal Setmentioning

confidence: 99%

Section: Mpc Based On the In-between Terminal Setmentioning

confidence: 99%

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A Nonlinear Model Predictive Control with Enlarged Region of Attraction via the Union of Invariant Sets

Fitri

Kim

2020

Mathematics

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“…The predictive controller design based on input-output description does not use it in a basic formulation of the cost function. The terminal state is obviously introduced in the extensions concerning the stability and robustness; see, e.g., [9][10][11][12][13][14][15]. The terminal state brings into the cost function dependence on all state variables.…”

Section: Standard Controller Designmentioning

confidence: 99%

Desired Terminal State Concept in Model Predictive Control: A Case Study

Dušek

Honc

2019

Journal of Control Science and Engineering

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The paper deals with an online optimization control method for dynamical processes called Model Predictive Control (MPC). It is a popular control method in industry and frequently treated in academic areas as well. The standard predictive controllers usually do not guarantee stability especially for the case of short horizons and large control error penalization. Terminal state is one way to ensure stability or at least increase the controller robustness. In the paper, deviation of the predicted terminal state from the desired terminal state is considered as one term of the cost function. Effect of the stability and control quality is demonstrated in the simulated experiments. The application area for online optimization methods is very broad including various logistics and transport problems. If the dynamics of the controlled processes cannot be neglected, the optimization problem must be solved not only for steady state but also for transient behaviour, e.g., by MPC.

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“…Most industrial processes are inherently non‐linear and multivariable, as well as constraints on control amplitude, output or state, and their variations should be taken into account to calculate the control law. If inherent constraints of the system are not considered, control of the closed‐loop system can become progressively worse . On this matter more advanced control strategies, such as MPC, should then be used.…”

Section: Introductionmentioning

confidence: 99%

Offline Robust Model Predictive Control for Lipschitz Non‐Linear Systems Using Polyhedral Invariant Sets

Shokrollahi

Shamaghdari

2018

Asian Journal of Control

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In this paper the concept of maximal admissible set (MAS) for linear systems with polytopic uncertainty is extended to non-linear systems composed of a linear constant part followed by a non-linear term. We characterize the maximal admissible set for the non-linear system with unstructured uncertainty in the form of polyhedral invariant sets. A computationally efficient state-feedback RMPC law is derived off-line for Lipschitz non-linear systems. The state-feedback control law is calculated by solving a convex optimization problem within the framework of linear matrix inequalities (LMIs), which leads to guaranteeing closed-loop robust stability. Most of the computational burdens are moved off-line. A linear optimization problem is performed to characterize the maximal admissible set, and it is shown that an ellipsoidal invariant set is only an approximation of the true stabilizable region. This method not only remarkably extends the size of the admissible set of initial conditions but also greatly reduces the on-line computational time. The usefulness and effectiveness of the method proposed here is verified via two simulation examples.

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Stability of finite horizon model predictive control with incremental input constraints

Cited by 46 publications

References 20 publications

A Nonlinear Model Predictive Control with Enlarged Region of Attraction via the Union of Invariant Sets

A Nonlinear Model Predictive Control with Enlarged Region of Attraction via the Union of Invariant Sets

Desired Terminal State Concept in Model Predictive Control: A Case Study

Offline Robust Model Predictive Control for Lipschitz Non‐Linear Systems Using Polyhedral Invariant Sets

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