Gain‐scheduling MPC of nonlinear systems

Chisci, Luigi; Falugi, Paola; Zappa, G.

doi:10.1002/rnc.819

Cited by 66 publications

(43 citation statements)

References 31 publications

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“…Then, the set of linear controllers is implemented as a single controller whose parameters are changed by monitoring the scheduling variables. GSC schemes show a performance similar to that of nonlinear controllers applied to the same problems, with computational load being smaller in the GSC approach [27].…”

Section: B Gs Control (Gsc)mentioning

confidence: 64%

A Gain-Scheduling Model Predictive Controller for Blood Glucose Control in Type 1 Diabetes

Abu-Rmileh

Garcia-Gabin

2010

IEEE Trans. Biomed. Eng.

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Abstract-This paper presents a control strategy for blood glucose (BG) level regulation in type 1 diabetic patients. To design the controller, model-based predictive control scheme has been applied to a newly developed diabetic patient model. The controller is provided with a feedforward loop to improve meal compensation, a gain-scheduling scheme to account for different BG levels, and an asymmetric cost function to reduce hypoglycemic risk. A simulation environment that has been approved for testing of artificial pancreas control algorithms has been used to test the controller. The simulation results show a good controller performance in fasting conditions and meal disturbance rejection, and robustness against model-patient mismatch and errors in meal estimation.Index Terms-Gain scheduling (GS), model predictive control (MPC), type 1 diabetes mellitus (T1DM).

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Section: B Gs Control (Gsc)mentioning

confidence: 64%

A Gain-Scheduling Model Predictive Controller for Blood Glucose Control in Type 1 Diabetes

Abu-Rmileh

Garcia-Gabin

2010

IEEE Trans. Biomed. Eng.

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“…Then by designing a set of local controllers with their estimated regions of stability overlapping each other, supervisory scheduling of the local controllers can move the state through the intersections of the estimated regions of stability of different controllers to the desired operating point. Similar ideas were used in References [11,12] for scheduled predictive control of nonlinear systems. All of these approaches require the existence of an equilibrium surface that connects the scheduling points, and the resulting stability region estimate is the union of the local stability regions, which typically forms an envelope around the equilibrium surface.…”

Section: Introductionmentioning

confidence: 88%

“…Consider the constrained nonlinear system of Equation (12), with any initial condition xð0Þ x 0 2 Oðu max Þ; where Oðu max Þ was defined in Equation (7), under the model predictive controller of Equations (8)- (11). Let T k 50 be the earliest time for which and define…”

Section: Theoremmentioning

confidence: 99%

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Hybrid predictive control of nonlinear systems: method and applications to chemical processes

El‐Farra

Mhaskar

Christofides

2003

Intl J Robust & Nonlinear

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SUMMARYA hybrid control structure that unites bounded control with model predictive control (MPC) is proposed for the constrained stabilization of nonlinear systems. The structure consists of: (1) a finite-horizon model predictive controller, which can be linear or nonlinear, and with or without stability constraints, (2) a family of bounded nonlinear controllers for which the regions of constrained closed-loop stability are explicitly characterized and (3) a high-level supervisor that orchestrates switching between MPC and the bounded controllers. The central idea is to embed the implementation of MPC within the stability regions of the bounded controllers and employ these controllers as fall-back in the event that MPC is unable to achieve closed-loop stability (due, for example, to infeasibility of a given initial condition and/or horizon length, or due to computational difficulties in solving the nonlinear optimization). Switching laws, that monitor the closed-loop state evolution under MPC, are derived to orchestrate the transitions in a way that guarantees asymptotic closed-loop stability for all initial conditions within the union of the stability regions of the bounded controllers. The proposed hybrid control scheme is shown to provide a paradigm for the safe implementation of predictive control algorithms to nonlinear systems, with guaranteed stability regions. The efficacy of the proposed approach is demonstrated through applications to chemical reactor and crystallization process examples.

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“…[6,9], this paper embeds a constrained nonlinear system into a family of LPV systems. The parameter space is partitioned into a finite number of overlapping regions nearby equilibrium point based on a Piece-Wise Embedding strategy, and an LPV model is obtained for each region to approximate the nonlinear dynamic.…”

Section: Introductionmentioning

confidence: 99%

Min-max model predictive control for constrained nonlinear systems via multiple LPV embeddings

Zhao

2009

Sci. China Ser. F-Inf. Sci.

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A min-max model predictive control strategy is proposed for a class of constrained nonlinear system whose trajectories can be embedded within those of a bank of linear parameter varying (LPV) models. The embedding LPV models can yield much better approximation of the nonlinear system dynamics than a single LTV model. For each LPV model, a parameter-dependent Lyapunov function is introduced to obtain poly-quadratically stable control law and to guarantee the feasibility and stability of the original nonlinear system. This approach can greatly reduce computational burden in traditional nonlinear predictive control strategy. Finally a simulation example illustrating the strategy is presented.constrained nonlinear systems, predictive control, LPV embedding, parameter dependent Lyapunov function, LMI

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Gain‐scheduling MPC of nonlinear systems

Cited by 66 publications

References 31 publications

A Gain-Scheduling Model Predictive Controller for Blood Glucose Control in Type 1 Diabetes

A Gain-Scheduling Model Predictive Controller for Blood Glucose Control in Type 1 Diabetes

Hybrid predictive control of nonlinear systems: method and applications to chemical processes

Min-max model predictive control for constrained nonlinear systems via multiple LPV embeddings

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