RBF-ARX model-based robust MPC for nonlinear systems with unknown and bounded disturbance

Feng, Zhou; Peng, Hui; Zeng, Xiaoyong; Tian, Xiaoying; Peng, Xiaoyan

doi:10.1016/j.jfranklin.2017.10.002

Cited by 14 publications

(21 citation statements)

References 38 publications

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“…. , 2 m ; τ � 1, 2; the symbol * indicates a symmetric structure; Q ab � cP − 1 ab > 0; the feedback gain matrix is defined as F(t) � YG − 1 ; Z and K are the symmetric matrices, Z ii is the i-th diagonal element of the symmetric matrix Z, and K jj is the j-th diagonal element of the symmetric matrix K. In the above (26)- (29)…”

Section: Theoremmentioning

confidence: 99%

“…Similar to Ref. [35], the incremental constraints contained in (36) can ultimately be represented as LMI (28) and (29).…”

Section: Theoremmentioning

confidence: 99%

“…Based on the RBF-ARX model, Peng et al [28] designed a min-max MPC algorithm for nonlinear systems without external disturbance. Zhou et al [29] proposed a one-stage scheduling quasi-min-max MPC algorithm, in which the external bounded disturbance is considered. What is more, Zhou et al [30] further studied a two-stage scheduling quasi-min-max MPC algorithm based on the RBF-ARX model.…”

Section: Introductionmentioning

confidence: 99%

“…What is more, Zhou et al [30] further studied a two-stage scheduling quasi-min-max MPC algorithm based on the RBF-ARX model. Although some results have been achieved, the current literatures [28][29][30] are mainly focused on using the parameter bound information of the SD-ARX model to wrap the system's future dynamics, and these types of methods have serious conservatism when constructing the system's state-space model. To reduce the conservativeness of these type of methods, the variation range information of the SD-ARX model's parameters is further considered in this paper to compress the size of the convex polytopic sets which are designed to wrap the system's future dynamics.…”

Section: Introductionmentioning

confidence: 99%

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A Two-Stage Scheduling RPC Based on Time-Varying Coefficient Information of State-Dependent ARX Model

Feng

Zhu

Xie

et al. 2020

Mathematical Problems in Engineering

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A two-stage scheduling robust predictive control (RPC) algorithm, which is based on the time-varying coefficient information of the state-dependent ARX (SD-ARX) model, is designed for the output tracking control of a class of nonlinear systems. First, by using the parameter variation range information of the SD-ARX, a strategy for constructing the system’s polytopic model is designed. To further reduce the conservativeness of the convex polytopic sets which are designed to wrap the system’s future dynamics, the variation range information of the SD-ARX model’s parameters is also considered and compressed. In this method, the polytopic state-space model of the system is constructed directly based on the special structure of the SD-ARX model itself, and there is no need to make such assumption that the bounds on the parameter’s variation range in the system model are known or measurable. And then, a two-stage scheduling RPC algorithm is designed for the output tracking control. A numerical example is presented to demonstrate the effectiveness of the proposed RPC strategy.

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Section: Theoremmentioning

confidence: 99%

“…Similar to Ref. [35], the incremental constraints contained in (36) can ultimately be represented as LMI (28) and (29).…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Two-Stage Scheduling RPC Based on Time-Varying Coefficient Information of State-Dependent ARX Model

Feng

Zhu

Xie

et al. 2020

Mathematical Problems in Engineering

Self Cite

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show abstract

“…Firstly, it may be used for design and implementation of MPC algorithms [31], in particular computationally efficient MPC schemes [32]. In addition to classical MPC algorithms, robust versions with guaranteed stability may be considered [33]. Secondly, it may be also used in online process optimisation [31] cooperating with MPC.…”

mentioning

confidence: 99%

Towards Reduced‐Order Models of Solid Oxide Fuel Cell

Ławryńczuk

2018

Complexity

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The objective of this work is to find precise reduced-order discrete-time models of a solid oxide fuel cell, which is a multiple-input multiple-output dynamic process. At first, the full-order discrete-time model is found from the continuous-time first-principle description. Next, the discrete-time submodels of hydrogen, oxygen, and water pressures (intermediate variables) are reduced. Two model reduction methods based on observability and controllability Grammians are compared: the state truncation method and reduction by residualisation. In all comparisons, the second method gives better results in terms of dynamic and steady-state errors as well as Nyquist plots. Next, the influence of the order of the pressure models on the errors of the process outputs (the voltage and the pressure difference) is studied. It is found that the number of pressure model parameters may be reduced from 25 to 19 without any deterioration of model accuracy. Two suboptimal reduced models are also discussed with only 14 and 11 pressure parameters, which give dynamic trajectories and steady-state characteristics that are very similar to those obtained from the full-order structure.

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Introduction to Model Predictive Control

Ławryńczuk

2021

Nonlinear Predictive Control Using Wiener Models

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RBF-ARX model-based robust MPC for nonlinear systems with unknown and bounded disturbance

Cited by 14 publications

References 38 publications

A Two-Stage Scheduling RPC Based on Time-Varying Coefficient Information of State-Dependent ARX Model

A Two-Stage Scheduling RPC Based on Time-Varying Coefficient Information of State-Dependent ARX Model

Towards Reduced‐Order Models of Solid Oxide Fuel Cell

Introduction to Model Predictive Control

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