Synthesis of Stabilizing Recurrent Equilibrium Network Controllers

Junnarkar, Neelay; Yin, He; Gu, Fangda; Arcak, Murat; Seiler, Peter

doi:10.1109/cdc51059.2022.9992684

Cited by 3 publications

(7 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Notice that the satisfaction of the LMI (20) can be enforced via adding penalty terms in the objective function [3], [16] or projection techniques [4], [5] during the learning process, which can be an improvement of this work. For further details, readers are referred to [3], [4], [5], [16].…”

Section: Resultsmentioning

confidence: 99%

“…To simplify the RNN analysis, we then perform a loop transformation that shifts and scales the activation function Φ to a new activation function Φ sector-bounded by sec[−1 nΦ×1 , 1 nΦ×1 ] [4], [5], such that the following QC is satisfied:…”

Section: Preliminaries a Problem Formulationmentioning

confidence: 99%

“…In general, it is difficult for Neural Network (NN)-based controllers to provide guaranteed stability due to the complex structures with nonlinearites [1], [2]. In the recent literature, classical robust control methods-based analysis and synthesis of NNs have been actively discussed, where Quadratic Constraint (QC) multipliers are employed to overapproximate the dynamics of nonlinear activation functions of NNs [1], [2], [3], [4], [5]. The QC-based methods enable the robustness analysis of the NN-controlled system through Linear Matrix Inequality (LMI) optimization.…”

Section: Introductionmentioning

confidence: 99%

“…Bounds on the Lipschitz constant of feedforward NNs and Recurrent Neural Networks (RNNs) are guaranteed in [1], [3]. [2], [4], [5] provide robust stability conditions for partially observed systems stabilized by NN and RNN controllers.…”

Section: Introductionmentioning

confidence: 99%

“…Studies have focused on handling perturbations such as noises and adversarial attacks [1]. However, there is still a lot of potential for exploring the incorporation of dynamic uncertainties, especially when using RNN as a controller [4], [5]. To explicitly analyze the dynamic uncertainties, a commonly applied technique in classical robust control theory is the Linear Fractional Transformation (LFT) method, which provides a convenient means to capture the system uncertainty and represent it in the form of state-space systems [6].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Robust Model Predictive Control for Adaptive Cruise Control with Model Uncertainties

Quan

Kim

Lee

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

This paper proposes a Recurrent Neural Network (RNN) controller for lane-keeping systems, effectively handling model uncertainties and disturbances. First, quadratic constraints cover the nonlinearities brought by the RNN controller, and the linear fractional transformation method models the dynamics of system uncertainties. Second, we prove the robust stability of the lane-keeping system in the presence of uncertain vehicle speed using a linear matrix inequality. Then, we define a reachable set for the lane-keeping system. Finally, to confirm the safety of the lane-keeping system with tracking error bound, we formulate semidefinite programming to approximate the outer set of the reachable set. Numerical experiments demonstrate that this approach confirms the stabilizing RNN controller and validates the safety with an untrained dataset with untrained varying road curvatures.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Preliminaries a Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust Model Predictive Control for Adaptive Cruise Control with Model Uncertainties

Quan

Kim

Lee

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

Learning Over Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems

Barbara,

Wang,

Manchester

2023

2023 62nd IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

Strengthened Circle and Popov Criteria for the Stability Analysis of Feedback Systems With ReLU Neural Networks

Richardson

Turner

Gunn

2023

IEEE Control Syst. Lett.

View full text Add to dashboard Cite

This paper considers the stability analysis of a Lurie system with a static repeated ReLU (rectified linear unit) nonlinearity. Properties of the ReLU function are leveraged to derive new tailored quadratic constraints (QCs) which are satisfied by the repeated ReLU. These QCs are used to strengthen the Circle and Popov Criteria for this specialised Lurie system. It is shown that the criteria can be cast as a set of linear matrix inequalities (LMIs) with less restrictive conditions on the matrix variables. Many systems involving a neural network (NN) with ReLU activations are important instances of this specialised Lurie system; for example, a continuous time recurrent neural network (RNN) or the interconnection of a linear system with a feedforward NN. Numerical examples show the strengthened criteria strike an appealing balance between reduced conservatism and complexity, compared to existing criteria.

show abstract

Synthesis of Stabilizing Recurrent Equilibrium Network Controllers

Cited by 3 publications

References 16 publications

Robust Model Predictive Control for Adaptive Cruise Control with Model Uncertainties

Robust Model Predictive Control for Adaptive Cruise Control with Model Uncertainties

Learning Over Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems

Strengthened Circle and Popov Criteria for the Stability Analysis of Feedback Systems With ReLU Neural Networks

Contact Info

Product

Resources

About