Neural Network-Based Model Predictive Control with Input-to-State Stability

Seel, Katrine; Grøtli, Esten Ingar; Moe, Signe; Gravdahl, Jan Tommy; Pettersen, Kristin Y.

doi:10.23919/acc50511.2021.9483190

Cited by 10 publications

(10 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proposition 11: The feedback interconnection in Figure 1 of the systems ( 24)- (25) in the class (4) lies in the class (4).…”

Section: B Feedback Interconnectionmentioning

confidence: 99%

“…Also model predictive control (MPC) has been investigated as a method for the design of efficient controllers applicable to systems described by specific classes of RNNs. For instance, the ISS of a MPC-controlled neural nonlinear autoregressive exogenous (NNARX) system is discussed in [25]. Also, MPC regulation strategies for other RNN architectures are presented in [26] and [27], ensuring closed-loop stability if the RNN-based model of the controlled system enjoys the δISS property.…”

Section: A State Of the Art And Contributionmentioning

confidence: 99%

See 1 more Smart Citation

An Incremental Input-to-State Stability Condition for a Class of Recurrent Neural Networks

D'Amico,

La Bella,

Farina

2024

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

This paper proposes a novel sufficient condition for the incremental input-to-state stability of a class of recurrent neural networks (RNNs). The established condition is compared with others available in the literature, showing to be less conservative. Moreover, it can be applied for the design of incremental input-to-state stable RNN-based control systems, resulting in a linear matrix inequality constraint for some specific RNN architectures. The formulation of nonlinear observers for the considered system class, as well as the design of control schemes with explicit integral action, are also investigated. The theoretical results are validated through simulation on a referenced nonlinear system.

show abstract

“…Proposition 11: The feedback interconnection in Figure 1 of the systems ( 24)- (25) in the class (4) lies in the class (4).…”

Section: B Feedback Interconnectionmentioning

confidence: 99%

Section: A State Of the Art And Contributionmentioning

confidence: 99%

An Incremental Input-to-State Stability Condition for a Class of Recurrent Neural Networks

D'Amico,

La Bella,

Farina

2024

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

show abstract

“…For example, under the assumption that the prediction error is sufficiently bounded, the NN-based NMPC, even in the presence of noise, the controller can successfully drive the system from random initial conditions to the reference equilibrium point. 116 Kohler 154 is based on the nonlinear robust MPC constraint compaction method of incremental stability, and proposes a robust NMPC framework that can stabilize nonlinear systems. In Xin Xu and Li, 102 the control task of each layer is described as a closed-loop nonlinear optimal control problem, and the finite-layer iterative RL algorithm is used to obtain the closed-loop optimal/suboptimal solution.…”

Section: Stability Of Lb-nmpcmentioning

confidence: 99%

“…There are other methods to ensure the stability of LB‐NMPC. For example, under the assumption that the prediction error is sufficiently bounded, the NN‐based NMPC, even in the presence of noise, the controller can successfully drive the system from random initial conditions to the reference equilibrium point 116 . Kohler 154 is based on the nonlinear robust MPC constraint compaction method of incremental stability, and proposes a robust NMPC framework that can stabilize nonlinear systems.…”

Section: Stability Of Lb‐nmpcmentioning

confidence: 99%

Emerging methodologies in stability and optimization problems of learning‐based nonlinear model predictive control: A survey

Meng

Shen

Karimi

2022

Circuit Theory & Apps

View full text Add to dashboard Cite

Since last 40 years, the theory and technology of model predictive control (MPC) have been developed rapidly. However, nonlinear MPC still faces difficulties such as high online computational complexity and inability to accurately model the system. In order to improve or solve the problems mentioned above of MPC, recent researches have deepened the learning‐based control. The learned method can model unknown or highly uncertain nonlinearities. And the emergence of efficient algorithms has greatly improved the feasibility of computing. Stability is at the heart of control design. Learning‐based nonlinear model predictive control (LB‐NMPC) has achieved systematic research results in the past 10 years. But the stability of LB‐NMPC is still an open question that has not been fully addressed in the literature. This review mainly summarizes the latest research progress of LB‐NMPC. More specifically, the uncertainty and online optimization problems of the considered systems are investigated mainly focusing on the use of learning techniques. At the same time, the research hotspots such as the control stability and constraint satisfaction of LB‐NMPC are briefly discussed. Finally, the application of LB‐NMPC technology in integrated circuits, path tracking control, and other fields is reviewed, which provides a reference for the research and application of LB‐NMPC.

show abstract

“…In that context, neural networks (NNs) have typically been used for learning an approximation of the system dynamics from data, which is then used as the prediction model in the MPC scheme, see e.g. [1], [2], [3]. However, it is in general difficult to conclude regarding the closed-loop optimality of the resulting MPC scheme.…”

Section: Introductionmentioning

confidence: 99%

Convex Neural Network-Based Cost Modifications for Learning Model Predictive Control

Seel

Kordabad

Gros

et al. 2022

IEEE Open J. Control. Syst.

View full text Add to dashboard Cite

Developing model predictive control (MPC) schemes can be challenging for systems where an accurate model is not available, or too costly to develop. With the increasing availability of data and tools to treat them, learning-based MPC has of late attracted wide attention. It has recently been shown that adapting not only the MPC model, but also its cost function is conducive to achieving optimal closed-loop performance when an accurate model cannot be provided. In the learning context, this modification can be performed via parametrizing the MPC cost and adjusting the parameters via, e.g., reinforcement learning (RL). In this framework, simple cost parametrizations can be effective, but the underlying theory suggests that rich parametrizations in principle can be useful. In this paper, we propose such a cost parametrization using a class of neural networks (NNs) that preserves convexity. This choice avoids creating difficulties when solving the MPC problem via sensitivity-based solvers. In addition, this choice of cost parametrization ensures nominal stability of the resulting MPC scheme. Moreover, we detail how this choice can be applied to economic MPC problems where the cost function is generic and therefore does not necessarily fulfill any specific property.

show abstract

Neural Network-Based Model Predictive Control with Input-to-State Stability

Cited by 10 publications

References 25 publications

An Incremental Input-to-State Stability Condition for a Class of Recurrent Neural Networks

An Incremental Input-to-State Stability Condition for a Class of Recurrent Neural Networks

Emerging methodologies in stability and optimization problems of learning‐based nonlinear model predictive control: A survey

Convex Neural Network-Based Cost Modifications for Learning Model Predictive Control

Contact Info

Product

Resources

About