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Aguiar, M. (2024). Learning flow functions: architectures, universal approximation and applications to spiking systems. (Licentiate dissertation). Stockholm: KTH Royal Institute of Technology
Open this publication in new window or tab >>Learning flow functions: architectures, universal approximation and applications to spiking systems
2024 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

Learning flow functions of continuous-time control systems is considered in this thesis. The flow function is the operator mapping initial states and control inputs to the state trajectories, and the problem is to find a suitable neural network architecture to learn this infinite-dimensional operator from measurements of state trajectories. The main motivation is the construction of continuous-time simulation models for such systems. The contribution is threefold.

We first study the design of neural network architectures for this problem, when the control inputs have a certain discrete-time structure, inspired by the classes of control inputs commonly used in applications. We provide a mathematical formulation of the problem and show that, under the considered input class, the flow function can be represented exactly in discrete time. Based on this representation, we propose a discrete-time recurrent neural network architecture. We evaluate the architecture experimentally on data from models of two nonlinear oscillators, namely the Van der Pol oscillator and the FitzHugh-Nagumo oscillator. In both cases, we show that we can train models which closely reproduce the trajectories of the two systems.

Secondly, we consider an application to spiking systems. Conductance-based models of biological neurons are the prototypical examples of this type of system. Because of their multi-timescale dynamics and high-frequency response, continuous-time representations which are efficient to simulate are desirable. We formulate a framework for surrogate modelling of spiking systems from trajectory data, based on learning the flow function of the system. The framework is demonstrated on data from models of a single biological neuron and of the interconnection of two neurons. The results show that we are able to accurately replicate the spiking behaviour.

Finally, we prove an universal approximation theorem for the proposed recurrent neural network architecture. First, general conditions are given on the flow function and the control inputs which guarantee that the architecture is able to approximate the flow function of any control system with arbitrary accuracy. Then, we specialise to systems with dynamics given by a controlled ordinary differential equation, showing that the conditions are satisfied whenever the equation has a continuously differentiable right-hand side, for the control input classes of interest.

Abstract [sv]

Denna avhandling studerar maskininlärningsmetoder för tidskontinuerliga reglersystem. Vi utgår från en abstrakt systemrepresentation med en lösningsoperator, som avbildar systemets initialtillstånd och insignal på motsvarande tillståndstrajektorian. Målet är att undersöka inlärning av tidskontinuerliga simuleringsmodeller utifrån tillståndsmätningar. Avhandlingen består av tre huvudbidrag.

Vi undersöker först arkitekturer baserade på neurala nätverk, för klasser av insignaler som är brukliga i tillämpningar och har en viss tidsdiskret struktur. Vi formulerar problemet matematiskt, och visar att lösningsoperatorn kan representeras exakt av ett tidsdiskret system. Detta leder till en arkitektur baserad på ett återkopplande neuralt nätverk (RNN), som vi utförligt beskriver, analyserar och validerar med hjälp av data från två modeller av icke-linjära oscillatorer, nämligen Van der Pol oscillatorn och FitzHugh-Nagumo oscillatorn. I båda fall visar vi att vi kan träna modeller som noggrant reproducerar systemens lösningsbanor.

Därefter studerar vi en tillämpning på system vars tillståndstrajektorier kännetecknas av förekomsten av snabba oscillationer i form av impulser, såsom modeller av biologiska neuroner. Denna klass av system karakteriseras av ett flerskaligt och högfrekvent tidssvar, vilket gör det önskvärt att ta fram tidskontinuerliga modeller som är lätta att simulera. Vi lägger fram ett ramverk för inlärning av surrogatmodeller av sådana system från data. Ramverket demonstreras med hjälp av data från en modell av en biologisk neuron och en modell av två kopplade biologiska neuroner, och resultaten visar att våra modeller noggrant reproducerar systemens beteende.

Slutligen tar vi fram ett bevis för ett approximationsteorem för inlärning av lösningsoperatorer av tidskontinuerliga system. Vi visar att den RNN- arkitektur som vi har tagit fram kan approximera godtyckliga reglersystem under vissa villkor som vi först formulerar abstrakt. Sedan bevisar att reglersystem som beskrivs av ordinära differentialekvationer uppfyller dessa villkor, vilket betyder att de kan approximeras av den studerade arkitekturen.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2024. p. 80
Series
TRITA-EECS-AVL ; 2024:20
National Category
Control Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-343571 (URN)978-91-8040-852-3 (ISBN)
Presentation
2024-03-15, D3, Lindstedtsvägen 9, Join Zoom Meeting https://kth-se.zoom.us/j/62682986918?pwd=NTFxcVovZnY2MkUrbWFaYjB6MXNudz09 Meeting ID: 626 8298 6918 Password: 462187, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20240220

Available from: 2024-02-20 Created: 2024-02-20 Last updated: 2024-03-12Bibliographically approved
Fonseca, J., Rocha, A., Aguiar, M. & Johansson, K. H. (2023). Adaptive Sampling of Algal Blooms Using an Autonomous Underwater Vehicle and Satellite Imagery. In: 2023 IEEE Conference on Control Technology and Applications, CCTA 2023: . Paper presented at 2023 IEEE Conference on Control Technology and Applications, CCTA 2023, Bridgetown, Barbados, Aug 16 2023 - Aug 18 2023 (pp. 638-644). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Adaptive Sampling of Algal Blooms Using an Autonomous Underwater Vehicle and Satellite Imagery
2023 (English)In: 2023 IEEE Conference on Control Technology and Applications, CCTA 2023, Institute of Electrical and Electronics Engineers (IEEE) , 2023, p. 638-644Conference paper, Published paper (Refereed)
Abstract [en]

This paper proposes a method that uses satellite data to improve adaptive sampling missions. We find and track algal bloom fronts using an autonomous underwater vehicle (AUV) equipped with a sensor that measures the concentration of chlorophyll a. Chlorophyll a concentration indicates the presence of algal blooms. The proposed method learns the kernel parameters of a Gaussian process model using satellite images of chlorophyll a from previous days. The AUV estimates the chlorophyll a concentration online using locally collected data. The algal bloom front estimate is fed to the motion control algorithm. The performance of this method is evaluated through simulations using a real dataset of an algal bloom front in the Baltic. We consider a real-world scenario with sensor and localization noise and with a detailed AUV model.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2023
National Category
Oceanography, Hydrology and Water Resources
Identifiers
urn:nbn:se:kth:diva-338992 (URN)10.1109/CCTA54093.2023.10252251 (DOI)2-s2.0-85173889475 (Scopus ID)
Conference
2023 IEEE Conference on Control Technology and Applications, CCTA 2023, Bridgetown, Barbados, Aug 16 2023 - Aug 18 2023
Note

Part of ISBN 9798350335446

QC 20231123

Available from: 2023-11-01 Created: 2023-11-01 Last updated: 2023-11-23Bibliographically approved
Aguiar, M., Das, A. & Johansson, K. H. (2023). Learning Flow Functions from Data with Applications to Nonlinear Oscillators. In: 22nd IFAC World CongressYokohama, Japan, July 9-14, 2023: . Paper presented at 22nd IFAC World Congress, Yokohama, Japan, Jul 9 2023 - Jul 14 2023 (pp. 4088-4093). Elsevier BV, 56
Open this publication in new window or tab >>Learning Flow Functions from Data with Applications to Nonlinear Oscillators
2023 (English)In: 22nd IFAC World CongressYokohama, Japan, July 9-14, 2023, Elsevier BV , 2023, Vol. 56, p. 4088-4093Conference paper, Published paper (Refereed)
Abstract [en]

We describe a recurrent neural network (RNN) based architecture to learn the flow function of a causal, time-invariant and continuous-time control system from trajectory data. By restricting the class of control inputs to piecewise constant functions, we show that learning the flow function is equivalent to learning the input-to-state map of a discrete-time dynamical system. This motivates the use of an RNN together with encoder and decoder networks which map the state of the system to the hidden state of the RNN and back. We show that the proposed architecture is able to approximate the flow function by exploiting the system's causality and time-invariance. The output of the learned flow function model can be queried at any time instant. We experimentally validate the proposed method using models of the Van der Pol and FitzHugh-Nagumo oscillators. In both cases, the results demonstrate that the architecture is able to closely reproduce the trajectories of these two systems. For the Van der Pol oscillator, we further show that the trained model generalises to the system's response with a prolonged prediction time horizon as well as control inputs outside the training distribution. For the FitzHugh-Nagumo oscillator, we show that the model accurately captures the input-dependent phenomena of excitability.

Place, publisher, year, edition, pages
Elsevier BV, 2023
Series
IFAC-PapersOnLine, ISSN 2405-8963 ; 56
Keywords
Excitability, Learning, Oscillator, Recurrent Neural Network
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-343165 (URN)10.1016/j.ifacol.2023.10.1738 (DOI)2-s2.0-85183634393 (Scopus ID)
Conference
22nd IFAC World Congress, Yokohama, Japan, Jul 9 2023 - Jul 14 2023
Note

QC 20240209

Part of ISBN 9781713872344

Available from: 2024-02-08 Created: 2024-02-08 Last updated: 2024-02-09Bibliographically approved
Aguiar, M., Das, A. & Johansson, K. H. (2023). Universal Approximation of Flows of Control Systems by Recurrent Neural Networks. In: 2023 62nd IEEE Conference on Decision and Control, CDC 2023: . Paper presented at 62nd IEEE Conference on Decision and Control, CDC 2023, Singapore, Singapore, Dec 13 2023 - Dec 15 2023 (pp. 2320-2327). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Universal Approximation of Flows of Control Systems by Recurrent Neural Networks
2023 (English)In: 2023 62nd IEEE Conference on Decision and Control, CDC 2023, Institute of Electrical and Electronics Engineers (IEEE) , 2023, p. 2320-2327Conference paper, Published paper (Refereed)
Abstract [en]

We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we prove that an architecture based on discrete-time recurrent neural networks universally approximates flows of continuous-time dynamical systems with inputs. The required assumptions are shown to hold for systems whose dynamics are well-behaved ordinary differential equations and with practically relevant classes of input signals. This enables the use of off-the-shelf solutions for learning such flow functions in continuous-time from sampled trajectory data.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2023
Keywords
Machine learning, Neural networks, Nonlinear systems
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-343710 (URN)10.1109/CDC49753.2023.10383457 (DOI)001166433801150 ()2-s2.0-85184831372 (Scopus ID)
Conference
62nd IEEE Conference on Decision and Control, CDC 2023, Singapore, Singapore, Dec 13 2023 - Dec 15 2023
Note

QC 20240222

Part of ISBN  979-8-3503-0124-3

Available from: 2024-02-22 Created: 2024-02-22 Last updated: 2024-03-26Bibliographically approved
Rocha, A., Aguiar, M., Lima, K., Mendes, R., Dias, J. M., Sousa, M. C. & De Sousa, J. B. (2021). Optimal AUV trajectory planning and execution control for maritime pollution incident response. In: Oceans Conference Record (IEEE): . Paper presented at OCEANS 2021: San Diego - Porto, Portugal, 20 September - 23 September, 2021. Institute of Electrical and Electronics Engineers Inc.
Open this publication in new window or tab >>Optimal AUV trajectory planning and execution control for maritime pollution incident response
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2021 (English)In: Oceans Conference Record (IEEE), Institute of Electrical and Electronics Engineers Inc. , 2021Conference paper, Published paper (Refereed)
Abstract [en]

Marine pollution incidents can have a huge impact on different ecosystems, with unpredictable short- and long-term consequences. Once the pollutant is detected, it is critical to quickly understand its characteristics so that authorities can lay out an adequate response. In parallel to the time- and cost-constrained traditional operational means, this paper suggests the use of AUVs for the sampling procedures of marine pollution incidents, to increase the speed and efficiency of operations. A new software architecture is developed, integrating trajectory optimization for AUVs into a software toolchain that allows human operators to plan, simulate, and control multiple vehicles deployments. A method to optimize AUVs deployment position and time is also presented. The overall architecture is simulated using high-resolution hydrodynamic data from the Ria de Aveiro lagoon and the adjacent coastal area, in Aveiro, Portugal. 

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers Inc., 2021
Keywords
Marine pollution, Networked vehicle system, Ocean sampling, Trajectory optimization, Autonomous underwater vehicles, Networked control systems, Oil spills, Pollution control, Trajectories, Execution control, Networked vehicles, Planning and execution, Planning controls, Pollution incidents, Trajectory Planning, Vehicle system, Aerodynamics
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-316282 (URN)10.23919/OCEANS44145.2021.9705986 (DOI)000947273302147 ()2-s2.0-85125886907 (Scopus ID)
Conference
OCEANS 2021: San Diego - Porto, Portugal, 20 September - 23 September, 2021
Note

Part of proceedings: ISBN 978-0-692-93559-0

QC 20230921

Available from: 2022-08-15 Created: 2022-08-15 Last updated: 2023-09-21Bibliographically approved
Barreau, M., Aguiar, M., Liu, J. & Johansson, K. H. (2021). Physics-informed Learning for Identification and State Reconstruction of Traffic Density. In: 2021 60thIEEE conference on decision and control (CDC): . Paper presented at 60th IEEE Conference on Decision and Control (CDC), DEC 13-17, 2021, ELECTR NETWORK (pp. 2653-2658). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Physics-informed Learning for Identification and State Reconstruction of Traffic Density
2021 (English)In: 2021 60thIEEE conference on decision and control (CDC), Institute of Electrical and Electronics Engineers (IEEE) , 2021, p. 2653-2658Conference paper, Published paper (Refereed)
Abstract [en]

We consider the problem of traffic density reconstruction using measurements from probe vehicles (PVs) with a low penetration rate. In other words, the number of sensors is small compared to the number of vehicles on the road. The model used assumes noisy measurements and a partially unknown first-order model. All these considerations make the use of machine learning to reconstruct the state the only applicable solution. We first investigate how the identification and reconstruction processes can be merged and how a sparse dataset can still enable a good identification. Secondly, we propose a pre-training procedure that aids the hyperparameter tuning, preventing the gradient descent algorithm from getting stuck at saddle points. Examples using numerical simulations and the SUMO traffic simulator show that the reconstructions are close to the real density in all cases.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2021
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Reliability and Maintenance
Identifiers
urn:nbn:se:kth:diva-312982 (URN)10.1109/CDC45484.2021.9683295 (DOI)000781990302064 ()2-s2.0-85126011066 (Scopus ID)
Conference
60th IEEE Conference on Decision and Control (CDC), DEC 13-17, 2021, ELECTR NETWORK
Note

QC 20220530

Part of proceedings ISBN 978-1-6654-3659-5

Available from: 2022-05-30 Created: 2022-05-30 Last updated: 2024-03-18Bibliographically approved
Aguiar, M., Estrela da Silva, J. & Borges de Sousa, J. (2020). Minimal time delivery of multiple robots. In: 2020 59th IEEE Conference on Decision and Control (CDC): . Paper presented at 2020 59th IEEE Conference on Decision and Control (CDC).
Open this publication in new window or tab >>Minimal time delivery of multiple robots
2020 (English)In: 2020 59th IEEE Conference on Decision and Control (CDC), 2020Conference paper, Published paper (Refereed)
Abstract [en]

Consider a set of autonomous vehicles, each one with a preassigned task to start at a given region. Due to energy constraints, and in order to minimize the overall task completion time, these vehicles are deployed from a faster carrier vehicle. This paper develops a dynamic programming (DP) based solution for the problem of finding the optimal deployment location and time for each vehicle, and for a given sequence of deployments, so that the global mission duration is minimal. The problem is specialized for ocean-going vehicles operating under time-varying currents. The solution approach involves solving a sequence of optimal stopping problems that are transformed into a set variational inequalities through the application of the dynamic programming principle (DPP). The optimal trajectory for the carrier and the optimal deployment location and time for each vehicle to be deployed are obtained in feedback-form from the numerical solution of the variational inequalities. The solution is computed with our open source parallel implementation of the fast sweeping method. The approach is illustrated with two numerical examples.

National Category
Robotics
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-293529 (URN)10.1109/CDC42340.2020.9304510 (DOI)2-s2.0-85099878863 (Scopus ID)
Conference
2020 59th IEEE Conference on Decision and Control (CDC)
Note

QC 20210521

Available from: 2021-04-28 Created: 2021-04-28 Last updated: 2024-03-18Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0009-0006-0657-4103

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