Lyapunov-stable neural-network control

Dai, Hongkai; Benoit, Landry; Yang, Lujie; Pavone, Marco; Tedrake, Russ

doi:10.48550/arxiv.2109.14152

Cited by 12 publications

(19 citation statements)

References 36 publications

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“…Optimization and verification techniques might also be useful for obtaining safety guarantees for ANNs in process control applications. For example, Dai et al (2021) guarantee Lyapunov stability of ANN controllers during training by also learning a Lyapunov function as an ANN, while Paulson and Mesbah (2020) propose a projection operator for guaranteeing feasibility and constraint satisfaction.…”

Section: How Restricted Data Challenges Are Addressed In the Literaturementioning

confidence: 99%

Maximizing information from chemical engineering data sets: Applications to machine learning

Thebelt,

Wiebe,

Kronqvist

et al. 2022

Preprint

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It is well-documented how artificial intelligence can have (and already is having) a big impact on chemical engineering. But classical machine learning approaches may be weak for many chemical engineering applications. This review discusses how challenging data characteristics arise in chemical engineering applications. We identify four characteristics of data arising in chemical engineering applications that make applying classical artificial intelligence approaches difficult: (1) high variance, low volume data, (2) low variance, high volume data, (3) noisy/corrupt/missing data, and (4) restricted data with physics-based limitations. For each of these four data characteristics, we discuss applications where these data characteristics arise and show how current chemical engineering research is extending the fields of data science and machine learning to incorporate these challenges. Finally, we identify several challenges for future research.

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Section: How Restricted Data Challenges Are Addressed In the Literaturementioning

confidence: 99%

Maximizing information from chemical engineering data sets: Applications to machine learning

Thebelt,

Wiebe,

Kronqvist

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…By combining these constraints with a mixed integer encoding of the control network π using the techniques of Tjeng et al [24], we obtain a set of mixed integer constraints corresponding to the abstract closed-loop system f . The optimization problem in (18) then becomes a MILP and can be solved using a MILP solver to obtain an over-approximated BP set.…”

Section: Nonlinear Dynamics: Over-approximation Of Bp Setsmentioning

confidence: 99%

“…The second source of over-approximation error is present in both algorithms and results from (18), which produces axis-aligned, hyper-rectangular BP sets. The use of hyper-rectanglar sets can result in large over-approximation errors if the true BP sets are not well-represented by axis-aligned hyper-rectangles.…”

Section: E Sources Of Over-approximation Errormentioning

confidence: 99%

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

Rober¹,

Katz²,

Sidrane³

et al. 2022

Preprint

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The increasing prevalence of neural networks (NNs) in safety-critical applications calls for methods to certify safe behavior. This paper presents a backward reachability approach for safety verification of neural feedback loops (NFLs), i.e., closed-loop systems with NN control policies. While recent works have focused on forward reachability as a strategy for safety certification of NFLs, backward reachability offers advantages over the forward strategy, particularly in obstacle avoidance scenarios. Prior works have developed techniques for backward reachability analysis for systems without NNs, but the presence of NNs in the feedback loop presents a unique set of problems due to the nonlinearities in their activation functions and because NN models are generally not invertible. To overcome these challenges, we use existing forward NN analysis tools to efficiently find an over-approximation of the backprojection (BP) set, i.e., the set of states for which the NN control policy will drive the system to a given target set. We present frameworks for calculating BP over-approximations for both linear and nonlinear systems with control policies represented by feedforward NNs and propose computationally efficient strategies. We use numerical results from a variety of models to showcase the proposed algorithms, including a demonstration of safety certification for a 6D system.

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“…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%

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

Havens¹,

Keivan²,

Seiler³

et al. 2022

Preprint

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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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Lyapunov-stable neural-network control

Cited by 12 publications

References 36 publications

Maximizing information from chemical engineering data sets: Applications to machine learning

Maximizing information from chemical engineering data sets: Applications to machine learning

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

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

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