Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867779
Mohammed Saad Faizan Bangi, J. Kwon
Modeling a bio-fermentation process accurately is a difficult task given the complex interactions that occur within it. Usually, a first-principles approach is employed to build a model which captures its essential dynamics. But building an accurate model using this approach is time consuming and resource-intensive because it is quite challenging to mathematically quantify all the complex interactions that occur within the process. Therefore, hybrid model wherein a first-principles model is integrated with a data-driven model to achieve greater accuracy and robustness is an appealing alternative. In this manuscript, we develop a hybrid model using a physics-informed machine learning method called Universal Differential Equations (UDEs) for a bio-fermentation process. In this approach a deep neural network (DNN) is utilized to approximate the derivative of the unknown dynamics that occur within the process. The trained DNN is inserted in the ODEs that represent the first-principles model of the process, and the resultant hybrid model is solved using modern ODE solvers. This universal hybrid model gives greater accuracy compared to the original first-principles model.
{"title":"Universal hybrid modeling of batch kinetics of aerobic carotenoid production using Saccharomyces Cerevisiae","authors":"Mohammed Saad Faizan Bangi, J. Kwon","doi":"10.23919/ACC53348.2022.9867779","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867779","url":null,"abstract":"Modeling a bio-fermentation process accurately is a difficult task given the complex interactions that occur within it. Usually, a first-principles approach is employed to build a model which captures its essential dynamics. But building an accurate model using this approach is time consuming and resource-intensive because it is quite challenging to mathematically quantify all the complex interactions that occur within the process. Therefore, hybrid model wherein a first-principles model is integrated with a data-driven model to achieve greater accuracy and robustness is an appealing alternative. In this manuscript, we develop a hybrid model using a physics-informed machine learning method called Universal Differential Equations (UDEs) for a bio-fermentation process. In this approach a deep neural network (DNN) is utilized to approximate the derivative of the unknown dynamics that occur within the process. The trained DNN is inserted in the ODEs that represent the first-principles model of the process, and the resultant hybrid model is solved using modern ODE solvers. This universal hybrid model gives greater accuracy compared to the original first-principles model.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128206804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867786
Jingyi Wang, J. Moreira, Yankai Cao, R. B. Gopaluni
A digital twin is a computer-based digital representation that simulates the behavior of a physical system. Digital twins help users to interact with real-world processes digitally. Time-variant modeling is critical to preserving the accuracy of digital twin models as the process dynamics change with time. Kalman filter is a well-known recursive algorithm that adjusts the process state estimates using real-time measurements. Sparse identification of nonlinear dynamics (SINDy) is an algorithm that automatically identifies system models from large data sets using sparse regression so as to prevent overfitting and find an ideal trade-off between model complexity and accuracy. In this paper, the SINDy approach is first extended to the generalized SINDy (GSINDy). Then, the GSINDy is integrated with Kalman filter to automatically identify time-variant digital twin models for online applications. The effectiveness of the algorithm is revealed through a simulation example based on Lorenz system and an industrial diesel hydrotreating unit example.
{"title":"Time-Variant Digital Twin Modeling through the Kalman-Generalized Sparse Identification of Nonlinear Dynamics","authors":"Jingyi Wang, J. Moreira, Yankai Cao, R. B. Gopaluni","doi":"10.23919/ACC53348.2022.9867786","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867786","url":null,"abstract":"A digital twin is a computer-based digital representation that simulates the behavior of a physical system. Digital twins help users to interact with real-world processes digitally. Time-variant modeling is critical to preserving the accuracy of digital twin models as the process dynamics change with time. Kalman filter is a well-known recursive algorithm that adjusts the process state estimates using real-time measurements. Sparse identification of nonlinear dynamics (SINDy) is an algorithm that automatically identifies system models from large data sets using sparse regression so as to prevent overfitting and find an ideal trade-off between model complexity and accuracy. In this paper, the SINDy approach is first extended to the generalized SINDy (GSINDy). Then, the GSINDy is integrated with Kalman filter to automatically identify time-variant digital twin models for online applications. The effectiveness of the algorithm is revealed through a simulation example based on Lorenz system and an industrial diesel hydrotreating unit example.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128399795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867666
Adeel Akhtar, R. Sanfelice
This paper proposes a hybrid geometric control scheme for the classical problem of globally stabilizing a pointmass system on a unit circle, as it is impossible to design a smooth globally asymptotically stable controller for this problem. Unlike most existing solutions that rely on coordinates and rely on a particular controller construction, our proposed solution is coordinate free (or geometric) and belongs to a class of controllers that we also characterize. Specifically, we propose a geometric hybrid controller that uses a local geometric controller (from the said class) and an open-loop geometric controller. The system achieves global asymptotic stability when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework. Moreover, the hybrid geometric controller guarantees robust asymptotic stability. Simulations validate the stability properties of the proposed hybrid geometric controller.
{"title":"A Class of Hybrid Geometric Controllers for Robust Global Asymptotic Stabilization on S1","authors":"Adeel Akhtar, R. Sanfelice","doi":"10.23919/ACC53348.2022.9867666","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867666","url":null,"abstract":"This paper proposes a hybrid geometric control scheme for the classical problem of globally stabilizing a pointmass system on a unit circle, as it is impossible to design a smooth globally asymptotically stable controller for this problem. Unlike most existing solutions that rely on coordinates and rely on a particular controller construction, our proposed solution is coordinate free (or geometric) and belongs to a class of controllers that we also characterize. Specifically, we propose a geometric hybrid controller that uses a local geometric controller (from the said class) and an open-loop geometric controller. The system achieves global asymptotic stability when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework. Moreover, the hybrid geometric controller guarantees robust asymptotic stability. Simulations validate the stability properties of the proposed hybrid geometric controller.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128362590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867250
Dan Wu, P. Bharadwaj, Premila Rowles, M. Ilic
In this paper we introduce the objectives and design principles of corrective control under cyber-physical attacks. We propose two types of observer-based corrective control for both the open-loop stable and the open-loop unstable LTI systems. The basic idea of our corrective control design is to use the observer as the ground-truth during the attack, making the plant dynamics follow the observer behavior. This is the opposite to the no-attack-detected period in which the observer is designed to follow the plant dynamics. We show stability of the proposed control under compromised sensor measurements, and quantify the effects of the discrepancy between the observer and the plant. Numerical examples, with illustrations using microgrid energy dynamics, are presented to show benefits of the proposed corrective control.
{"title":"Cyber-Physical Secure Observer-Based Corrective Control under Compromised Sensor Measurements","authors":"Dan Wu, P. Bharadwaj, Premila Rowles, M. Ilic","doi":"10.23919/ACC53348.2022.9867250","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867250","url":null,"abstract":"In this paper we introduce the objectives and design principles of corrective control under cyber-physical attacks. We propose two types of observer-based corrective control for both the open-loop stable and the open-loop unstable LTI systems. The basic idea of our corrective control design is to use the observer as the ground-truth during the attack, making the plant dynamics follow the observer behavior. This is the opposite to the no-attack-detected period in which the observer is designed to follow the plant dynamics. We show stability of the proposed control under compromised sensor measurements, and quantify the effects of the discrepancy between the observer and the plant. Numerical examples, with illustrations using microgrid energy dynamics, are presented to show benefits of the proposed corrective control.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128379671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867710
Duc M. Le, O. Patil, Patrick M. Amy, W. Dixon
Recent results in the adaptive control literature have made connections to methods in optimization and have led to new adaptive update laws based on accelerated gradient methods. Accelerated gradient methods such as Nesterov’s accelerated gradient in numerical optimization have been shown to yield faster convergence than standard gradient methods. However, these results either assume available measurements of the regression error or do not guarantee convergence of the parameter estimation error unless the restrictive persistence of excitation condition is satisfied. In this paper, a new integral concurrent learning (ICL)-based accelerated gradient adaptive update law is developed to achieve trajectory tracking and real-time parameter identification for general uncertain Euler-Lagrange systems. The accelerated gradient adaptation is a higher-order scheme composed of two coupled adaptation laws. A Lyapunov-based method is used to guarantee the closed-loop error system yields global exponential stability under a less restrictive finite excitation condition. A comparative simulation study is performed on a two-link robot manipulator to demonstrate the efficacy of the developed method. Results show the higher-order scheme outperforms standard and ICL-based adaption by 19.6% and 11.1%, respectively, in terms of the root mean squared parameter estimation errors.
{"title":"Integral Concurrent Learning-Based Accelerated Gradient Adaptive Control of Uncertain Euler-Lagrange Systems","authors":"Duc M. Le, O. Patil, Patrick M. Amy, W. Dixon","doi":"10.23919/ACC53348.2022.9867710","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867710","url":null,"abstract":"Recent results in the adaptive control literature have made connections to methods in optimization and have led to new adaptive update laws based on accelerated gradient methods. Accelerated gradient methods such as Nesterov’s accelerated gradient in numerical optimization have been shown to yield faster convergence than standard gradient methods. However, these results either assume available measurements of the regression error or do not guarantee convergence of the parameter estimation error unless the restrictive persistence of excitation condition is satisfied. In this paper, a new integral concurrent learning (ICL)-based accelerated gradient adaptive update law is developed to achieve trajectory tracking and real-time parameter identification for general uncertain Euler-Lagrange systems. The accelerated gradient adaptation is a higher-order scheme composed of two coupled adaptation laws. A Lyapunov-based method is used to guarantee the closed-loop error system yields global exponential stability under a less restrictive finite excitation condition. A comparative simulation study is performed on a two-link robot manipulator to demonstrate the efficacy of the developed method. Results show the higher-order scheme outperforms standard and ICL-based adaption by 19.6% and 11.1%, respectively, in terms of the root mean squared parameter estimation errors.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129684497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867597
Junsoo Lee, W. Haddad, Manuel Lanchares
In this paper, we address finite time stabilization in probability of discrete-time stochastic dynamical systems. Specifically, a stochastic finite-time optimal control framework is developed by exploiting connections between stochastic Lyapunov theory for finite time stability in probability and stochastic Bellman theory. In particular, we show that finite time stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that can clearly be seen to be the solution to the steady state form of the stochastic Bellman equation, and hence, guaranteeing both stochastic finite time stability and optimality.
{"title":"Optimal Finite Time Control for Discrete-Time Stochastic Dynamical Systems","authors":"Junsoo Lee, W. Haddad, Manuel Lanchares","doi":"10.23919/ACC53348.2022.9867597","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867597","url":null,"abstract":"In this paper, we address finite time stabilization in probability of discrete-time stochastic dynamical systems. Specifically, a stochastic finite-time optimal control framework is developed by exploiting connections between stochastic Lyapunov theory for finite time stability in probability and stochastic Bellman theory. In particular, we show that finite time stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that can clearly be seen to be the solution to the steady state form of the stochastic Bellman equation, and hence, guaranteeing both stochastic finite time stability and optimality.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130234078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867765
Juyeong Jung, Hyun-Kyu Choi, S. Son, Joseph Sang-Il Kwon, J. Lee
As the reduction of greenhouse gas emissions is an imperative issue due to global warming, the technologies of lightweight packaging have become an emerging field in the pulp and paper industry. Efficient use of pulp is one challenge while being comparable to conventional packaging materials. During Kraft cooking, both the chemical and physical changes on the wood fibers occur, causing strength properties changes in end-use papers. Accordingly, in this study, the fiber deformation in a pulp digester is elucidated by developing the multiscale model with the classical column buckling theory. Subsequently, in order to regulate the fiber deformation during pulping, a model predictive control system is designed by utilizing an approximate model taken from the high-fidelity model. In the end, the multiscale model-based control system accomplished suppressing fiber deformations compared to the conventional pulping manufacturing, which signifies the achievement of improved tensile strength on end-use paper.
{"title":"Model predictive control of fiber deformation in a batch pulp digester","authors":"Juyeong Jung, Hyun-Kyu Choi, S. Son, Joseph Sang-Il Kwon, J. Lee","doi":"10.23919/ACC53348.2022.9867765","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867765","url":null,"abstract":"As the reduction of greenhouse gas emissions is an imperative issue due to global warming, the technologies of lightweight packaging have become an emerging field in the pulp and paper industry. Efficient use of pulp is one challenge while being comparable to conventional packaging materials. During Kraft cooking, both the chemical and physical changes on the wood fibers occur, causing strength properties changes in end-use papers. Accordingly, in this study, the fiber deformation in a pulp digester is elucidated by developing the multiscale model with the classical column buckling theory. Subsequently, in order to regulate the fiber deformation during pulping, a model predictive control system is designed by utilizing an approximate model taken from the high-fidelity model. In the end, the multiscale model-based control system accomplished suppressing fiber deformations compared to the conventional pulping manufacturing, which signifies the achievement of improved tensile strength on end-use paper.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126903588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867419
S. Sarna, Nikesh Patel, P. Mhaskar, Brandon Corbett, Christopher R Mccready
This manuscript focuses on data driven modeling and control of an industrial bioreactor used by Sartorius to grow cells to produce monoclonal antibodies, demonstrated using a high fidelity simulation test bed. The contribution of this paper is the development of a subspace model based model predictive controller (MPC) for the bioreactor with constraints in place to manage the delicate cell health and growth. Subspace identification is first utilized for developing a linear model, and utilized, along with a state observer, to formulate and implement the Model Predictive Controller. Three implementations are shown, the first which simply tracks a desired trajectory of the viable cell density while maximizing the total product, the second maximizing the total product, and finally a formulation to enable trajectory tracking of titer. In each case the MPC is able to successfully operate the bioreactor and show improvements compared to the existing proportional-integral controller. The success of the MPC implementation on the simulation test bed paves the way for implementation on the bioreactor, as well as the development much more ambitious MPC designs.
{"title":"Data Driven Modeling and Model Predictive Control of Bioreactor for Production of Monoclonal Antibodies","authors":"S. Sarna, Nikesh Patel, P. Mhaskar, Brandon Corbett, Christopher R Mccready","doi":"10.23919/ACC53348.2022.9867419","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867419","url":null,"abstract":"This manuscript focuses on data driven modeling and control of an industrial bioreactor used by Sartorius to grow cells to produce monoclonal antibodies, demonstrated using a high fidelity simulation test bed. The contribution of this paper is the development of a subspace model based model predictive controller (MPC) for the bioreactor with constraints in place to manage the delicate cell health and growth. Subspace identification is first utilized for developing a linear model, and utilized, along with a state observer, to formulate and implement the Model Predictive Controller. Three implementations are shown, the first which simply tracks a desired trajectory of the viable cell density while maximizing the total product, the second maximizing the total product, and finally a formulation to enable trajectory tracking of titer. In each case the MPC is able to successfully operate the bioreactor and show improvements compared to the existing proportional-integral controller. The success of the MPC implementation on the simulation test bed paves the way for implementation on the bioreactor, as well as the development much more ambitious MPC designs.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129075404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867441
C. Yilmaz, M. Krstić
We introduce a prescribed–time extremum seeking (PT-ES) design for a PDE-ODE cascade of a heat PDE feeding into an integrator, which in turn feeds into an unknown map. Leveraging the integrator in the PDE-ODE plant, and employing “chirpy” probing and demodulation signals designed by PDE motion planning methods, we achieve convergence to the extremum in a user-prescribed time independent of the distance of the initial estimate from the optimizer. Although this PDE-ODE cascade is defined on a fixed spatial domain, it is inspired by free boundary models such as the Stefan model of phase change dynamics. The design is based on the time-varying backstepping approach, which transforms the PDE-ODE cascade into a suitable prescribed-time stable target system, and the averaging-based estimations of the gradient as well as the Hessian of the map. By means of Lyapunov method, it is shown that the average closed-loop dynamics are prescribed-time stable. This Part II paper is companion to a Part I paper which introduces PT-ES for two problems that are less challenging than here: a static map and a map with an input delay.
{"title":"Prescribed-Time Extremum Seeking with Chirpy Probing for PDEs—Part II: Heat PDE","authors":"C. Yilmaz, M. Krstić","doi":"10.23919/ACC53348.2022.9867441","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867441","url":null,"abstract":"We introduce a prescribed–time extremum seeking (PT-ES) design for a PDE-ODE cascade of a heat PDE feeding into an integrator, which in turn feeds into an unknown map. Leveraging the integrator in the PDE-ODE plant, and employing “chirpy” probing and demodulation signals designed by PDE motion planning methods, we achieve convergence to the extremum in a user-prescribed time independent of the distance of the initial estimate from the optimizer. Although this PDE-ODE cascade is defined on a fixed spatial domain, it is inspired by free boundary models such as the Stefan model of phase change dynamics. The design is based on the time-varying backstepping approach, which transforms the PDE-ODE cascade into a suitable prescribed-time stable target system, and the averaging-based estimations of the gradient as well as the Hessian of the map. By means of Lyapunov method, it is shown that the average closed-loop dynamics are prescribed-time stable. This Part II paper is companion to a Part I paper which introduces PT-ES for two problems that are less challenging than here: a static map and a map with an input delay.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130608924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.23919/ACC53348.2022.9867147
Hesameddin Mohammadi, M. Jovanović
In this paper, we examine amplification of additive stochastic disturbances to primal-dual gradient flow dynamics based on proximal augmented Lagrangian. These dynamics can be used to solve a class of non-smooth composite optimization problems and are convenient for distributed implementation. We utilize the theory of integral quadratic constraints to show that the upper bound on noise amplification is inversely proportional to the strong-convexity module of the smooth part of the objective function. Furthermore, to demonstrate tightness of these upper bounds, we exploit the structure of quadratic optimization problems and derive analytical expressions in terms of the eigenvalues of the corresponding dynamical generators. We further specialize our results to a distributed optimization framework and discuss the impact of network topology on the noise amplification.
{"title":"On the noise amplification of primal-dual gradient flow dynamics based on proximal augmented Lagrangian","authors":"Hesameddin Mohammadi, M. Jovanović","doi":"10.23919/ACC53348.2022.9867147","DOIUrl":"https://doi.org/10.23919/ACC53348.2022.9867147","url":null,"abstract":"In this paper, we examine amplification of additive stochastic disturbances to primal-dual gradient flow dynamics based on proximal augmented Lagrangian. These dynamics can be used to solve a class of non-smooth composite optimization problems and are convenient for distributed implementation. We utilize the theory of integral quadratic constraints to show that the upper bound on noise amplification is inversely proportional to the strong-convexity module of the smooth part of the objective function. Furthermore, to demonstrate tightness of these upper bounds, we exploit the structure of quadratic optimization problems and derive analytical expressions in terms of the eigenvalues of the corresponding dynamical generators. We further specialize our results to a distributed optimization framework and discuss the impact of network topology on the noise amplification.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130665698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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