Robust discrete-time set-based adaptive predictive control for nonlinear systems

Gonçalves, Guilherme; Guay, Martin

doi:10.1016/j.jprocont.2015.12.006

Cited by 25 publications

(96 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In general, RAMPC schemes [5], [6], [7], [8], [9], [10], [11], [12] use set membership estimation to provide a set of non falsified parameters, which is utilized in a robust tubebased MPC approach to provide robustness w.r.t. uncertain parameters and disturbances.…”

Section: Related Workmentioning

confidence: 99%

“…Recently, in [9] a RAMPC scheme for the special case of feedback linearizable nonlinear systems has been proposed using boundary layer control [20]. Except for this recent approach for feedback linearizable systems, existing RAMPC schemes for nonlinear systems with theoretical guarantees have been developed exclusively 1 by Martin Guay and coauthors [10], [11], [12], [25], [26].…”

Section: Related Workmentioning

confidence: 99%

“…In particular, parameter update schemes have been developed that provide guaranteed bounds on the parameter error for a large class of nonlinear systems, including continuous time [10], discrete time [12], time varying [25], and nonlinearly parametrized systems [26], compare [11] for a general overview. However, all these approaches consider a simple robust tube approach based on Lipschitz constants similar to [27], [28], which can be prohibitively conservative in many scenarios, see numerical comparisons in [23], [29], [30].…”

Section: Related Workmentioning

confidence: 99%

“…In this paper, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for a class of uncertain nonlinear systems subject to additive disturbances and parametric uncertainty. The paper contains the following contributions: (i) present a general theoretical framework for nonlinear RAMPC; (ii) provide a computationally efficient RAMPC framework by extending the robust MPC framework in [23] to allow for recursive model updates; (iii) provide explicit design procedures, which contain the approaches in [10], [11], [12] as a special case.…”

Section: Contributionmentioning

confidence: 99%

“…This has motivated an increasing amount of research focused on online model adaptation/learning in MPC, spanning the last two This work was supported by the German Research Foundation under Grants GRK 2198/1, AL 316/12-2, and MU 3929/1-2, and by the International Max Planck Research School for Intelligent Systems (IMPRS-IS). 1 decades [2], [3], [4], with current research focused on robust adaptive formulations [5], [6], [7], [8], [9], [10], [11], [12], dual/learning formulations [13], [14] and machine learning based approaches [15], [16], [17], [18]. However, all of these approaches suffer from at least one of the following shortcomings: a) limitation to restrictive system classes, such as linear systems [5], [6], [7], [8] or feedback linearizable systems [9], b) failure to provide theoretical guarantees regarding recursive feasibility, closed-loop stability and constraint satisfaction [14], [15], [16], [18], c) significant increase in the computational complexity [11,Chap.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

134

133

View full text Add to dashboard Cite

In this paper, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared to robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain L2 stability w.r.t. additive disturbances.As a first contribution we derive suitable monotonicity and non-increasing properties on general parameter estimation algorithms and tube/set based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this paper, we provide similar conditions for a tube based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared to state of the art approaches.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Contributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

134

133

View full text Add to dashboard Cite

show abstract

An adaptive model predictive control strategy for a class of discrete‐time linear systems with parametric uncertainty

Gou

Ding

et al. 2021

Adaptive Control & Signal

View full text Add to dashboard Cite

In this study, an adaptive model predictive control (MPC) strategy is proposed for a class of discrete-time linear systems with parametric uncertainty. In the presented adaptive MPC, an updating law is firstly designed to update the estimated parameters online. By utilizing the estimated parameters, a standard MPC optimization problem for unconstrained systems is established. Then, to deal with constrained systems, the min-max MPC technique is developed under the set-based approach for the estimated parameters. Furthermore, it is shown theoretically that the recursive feasibility and closed-loop stability can be rigorously proved, respectively. Finally, numerical simulations and comparative analysis are presented to illustrate the superiority of the proposed algorithms in control performance.

show abstract

Data‐Driven Performance Monitoring for Model Predictive Control Using a mahalanobis distance based overall index

Zhang

et al. 2018

Asian Journal of Control

View full text Add to dashboard Cite

This paper proposes a data-driven approach for model predictive control (MPC) performance monitoring. It explores the I/O data of the MPC system. First, to evaluate the MPC performance and capture the fluctuation of the process variables, we present an overall performance index based on Mahalanobis distance (MDBI) with its deduced benchmark. The Mahalanobis distance can better characterize the change of the process variable in both principal component space and residual space. As the proper vectors of the two spaces are orthogonal, the MDBI eliminates the correlation between the process variables while considering the variables' characteristics in both spaces simultaneously, which helps evaluate the MPC performance more effectively with fewer monitoring parameters. Furthermore, for the MPC performance diagnosis, we use the MDBI as inputs and construct a support vector machine (SVM) pattern classifier. The classifier can achieve a higher accuracy when recognizing four common performance degradation patterns and determine the root cause of performance degradation. The results of simulations on the Wood-Berry distillation column process and experiments on NIAT multifunctional experiment platform illustrate the effectiveness of the proposed performance assessment/diagnosis strategies.

show abstract

Robust discrete-time set-based adaptive predictive control for nonlinear systems

Cited by 25 publications

References 19 publications

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

An adaptive model predictive control strategy for a class of discrete‐time linear systems with parametric uncertainty

Data‐Driven Performance Monitoring for Model Predictive Control Using a mahalanobis distance based overall index

Contact Info

Product

Resources

About