Stability Analysis Using Quadratic Constraints for Systems With Neural Network Controllers

Yin, He; Seiler, Peter; Arcak, Murat

doi:10.1109/tac.2021.3069388

Cited by 81 publications

(65 citation statements)

References 23 publications

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“…The polices for these problems are parameterized using large-scale NNs, and our results show that our PGD approach is highly-flexible and effective for perception-based control. As a sanity check, for the inverted pendulum problem, we have also included some analysis results for the relatively simple state-feedback setting where our approach can be justified via a comparison with the Lyapunov-based inner approximation approach developed in Yin et al (2021).…”

Section: Resultsmentioning

confidence: 99%

“…Sanity check: Comparison with the quadratic constraint approach. As a sanity check, we first provide some results for the state-feedback setting where our approach can be justified via a comparison with the quadratic constraint approach developed in Yin et al (2021). The experimental setup is identical to Example IV.A in Yin et al (2021), and we adopt the same policy for the purpose of comparison.…”

Section: Inverted-pendulummentioning

confidence: 99%

“…As a sanity check, we first provide some results for the state-feedback setting where our approach can be justified via a comparison with the quadratic constraint approach developed in Yin et al (2021). The experimental setup is identical to Example IV.A in Yin et al (2021), and we adopt the same policy for the purpose of comparison. In Yin et al (2021), quadratic constraints and semidefinite programs are leveraged to obtain provable inner ROA estimations for feedback systems with NN controllers.…”

Section: Inverted-pendulummentioning

confidence: 99%

“…The experimental setup is identical to Example IV.A in Yin et al (2021), and we adopt the same policy for the purpose of comparison. In Yin et al (2021), quadratic constraints and semidefinite programs are leveraged to obtain provable inner ROA estimations for feedback systems with NN controllers. This approach amounts to isolating the nonlinearity of the NN policies with local sector constraints which are next used to formulate ROA analysis conditions in the form of linear matrix inequalities (LMIs).…”

Section: Inverted-pendulummentioning

confidence: 99%

“…Third, in general, the control action may not just be a function of the current state, and the coupling of system states at different time steps can be complicated. The first two issues will cause trouble for existing Lyapunov-based ROA analysis methods using semidefinite programming (Yin et al, 2021;Hu et al, 2020;Jin and Lavaei, 2020;Aydinoglu et al, 2021) or mixed-integer programs (Chen et al, 2020(Chen et al, , 2021Dai et al, 2021). Due to the last issue, the methods of Lyapunov neural networks (Richards et al, 2018;Chang et al, 2019; or other stability certificate learning methods (Kenanian et al, 2019;Giesl et al, 2020;Ravanbakhsh and Sankaranarayanan, 2019) may also be not applicable since these methods typically require the control action to depend on the current state.…”

Section: Introductionmentioning

confidence: 99%

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Revisiting PGD Attacks for Stability Analysis of Large-Scale Nonlinear Systems and Perception-Based Control

Havens¹,

Keivan²,

Seiler³

et al. 2022

Preprint

Self Cite

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Many existing region-of-attraction (ROA) analysis tools find difficulty in addressing feedback systems with large-scale neural network (NN) policies and/or high-dimensional sensing modalities such as cameras. In this paper, we tailor the projected gradient descent (PGD) attack method developed in the adversarial learning community as a general-purpose ROA analysis tool for large-scale nonlinear systems and end-to-end perception-based control. We show that the ROA analysis can be approximated as a constrained maximization problem whose goal is to find the worst-case initial condition which shifts the terminal state the most. Then we present two PGD-based iterative methods which can be used to solve the resultant constrained maximization problem. Our analysis is not based on Lyapunov theory, and hence requires minimum information of the problem structures. In the model-based setting, we show that the PGD updates can be efficiently performed using backpropagation. In the model-free setting (which is more relevant to ROA analysis of perception-based control), we propose a finite-difference PGD estimate which is general and only requires a blackbox simulator for generating the trajectories of the closed-loop system given any initial state. We demonstrate the scalability and generality of our analysis tool on several numerical examples with large-scale NN policies and high-dimensional image observations. We believe that our proposed analysis serves as a meaningful initial step toward further understanding of closed-loop stability of large-scale nonlinear systems and perception-based control.

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Section: Resultsmentioning

confidence: 99%

Section: Inverted-pendulummentioning

confidence: 99%

Section: Inverted-pendulummentioning

confidence: 99%

Section: Inverted-pendulummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Revisiting PGD Attacks for Stability Analysis of Large-Scale Nonlinear Systems and Perception-Based Control

Havens¹,

Keivan²,

Seiler³

et al. 2022

Preprint

Self Cite

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show abstract

Computation of invariant sets for discrete‐time uncertain systems

Khalife

Jaoude

Farhood

et al. 2023

Intl J Robust & Nonlinear

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This article proposes novel methods for the computation of state and output bounding sets for discrete‐time uncertain systems. The systems under consideration are formed from the interconnection of a nominal linear time‐invariant system and an uncertainty operator that is known to lie within a prespecified set. The set of allowable uncertainties is described by a pointwise integral quadratic constraint (IQC), that is, a quadratic constraint that holds for all time‐steps. Examples of pointwise IQCs characterizing common uncertainty sets are provided. The exogenous input to the system is assumed to lie in a given polytope or ellipsoid for all time‐steps. The proposed methods are illustrated via an example.

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Improved Data-driven Adaptive Control Structure Against Input and Output Saturation

Asadi,

Farsangi,

Rezaei

2024

Int. J. Control Autom. Syst.

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Stability Analysis Using Quadratic Constraints for Systems With Neural Network Controllers

Cited by 81 publications

References 23 publications

Revisiting PGD Attacks for Stability Analysis of Large-Scale Nonlinear Systems and Perception-Based Control

Revisiting PGD Attacks for Stability Analysis of Large-Scale Nonlinear Systems and Perception-Based Control

Computation of invariant sets for discrete‐time uncertain systems

Improved Data-driven Adaptive Control Structure Against Input and Output Saturation

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