Pub Date : 2022-09-28DOI: 10.1109/OJCSYS.2022.3210453
Mohammadreza Doostmohammadian;Alireza Aghasi;Apostolos I. Rikos;Andreas Grammenos;Evangelia Kalyvianaki;Christoforos N. Hadjicostis;Karl H. Johansson;Themistoklis Charalambous
This paper considers distributed allocation strategies, formulated as a distributed sum-preserving (fixed-sum) allocation of resources over a multi-agent network in the presence of heterogeneous arbitrary time-varying delays. We propose a double time-scale scenario for unknown delays and a faster single time-scale scenario for known delays. Further, the links among the nodes are considered subject to certain nonlinearities (e.g, quantization and saturation/clipping). We discuss different models for nonlinearities and how they may affect the convergence, sum-preserving feasibility constraint, and solution optimality over general weight-balanced uniformly strongly connected networks and, further, time-delayed undirected networks. Our proposed scheme works in a variety of applications with general non-quadratic strongly-convex smooth objective functions. The non-quadratic part, for example, can be due to additive convex penalty or barrier functions to address the local box constraints. The network can change over time, is not necessarily connected at all times, but is only assumed to be uniformly-connected. The novelty of this work is to address all-time feasible Laplacian gradient solutions in presence of nonlinearities, switching digraph topology (not necessarily all-time connected), and heterogeneous time-varying delays.
{"title":"Distributed Anytime-Feasible Resource Allocation Subject to Heterogeneous Time-Varying Delays","authors":"Mohammadreza Doostmohammadian;Alireza Aghasi;Apostolos I. Rikos;Andreas Grammenos;Evangelia Kalyvianaki;Christoforos N. Hadjicostis;Karl H. Johansson;Themistoklis Charalambous","doi":"10.1109/OJCSYS.2022.3210453","DOIUrl":"https://doi.org/10.1109/OJCSYS.2022.3210453","url":null,"abstract":"This paper considers distributed allocation strategies, formulated as a distributed sum-preserving (fixed-sum) allocation of resources over a multi-agent network in the presence of heterogeneous arbitrary time-varying delays. We propose a double time-scale scenario for unknown delays and a faster single time-scale scenario for known delays. Further, the links among the nodes are considered subject to certain nonlinearities (e.g, quantization and saturation/clipping). We discuss different models for nonlinearities and how they may affect the convergence, sum-preserving feasibility constraint, and solution optimality over general weight-balanced uniformly strongly connected networks and, further, time-delayed undirected networks. Our proposed scheme works in a variety of applications with general non-quadratic strongly-convex smooth objective functions. The non-quadratic part, for example, can be due to additive convex penalty or barrier functions to address the local box constraints. The network can change over time, is not necessarily connected at all times, but is only assumed to be uniformly-connected. The novelty of this work is to address all-time feasible Laplacian gradient solutions in presence of nonlinearities, switching digraph topology (not necessarily all-time connected), and heterogeneous time-varying delays.","PeriodicalId":73299,"journal":{"name":"IEEE open journal of control systems","volume":"1 ","pages":"255-267"},"PeriodicalIF":0.0,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/9552933/9683993/09904851.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50348955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-28DOI: 10.1109/OJCSYS.2022.3209945
Zahra Marvi;Bahare Kiumarsi
The satisfaction of the safety and stability properties of reinforcement learning (RL) algorithms has been a long-standing challenge. These properties must be satisfied even during learning, for which exploration is required to collect rich data. However, satisfying the safety of actions when little is known about the system dynamics is a daunting challenge. After all, predicting the consequence of RL actions requires knowing the system dynamics. This paper presents a novel RL scheme that ensures the safety and stability of the linear systems during the exploration and exploitation phases. To do so, a fast and data-efficient model-learning with the convergence guarantee is employed along and simultaneously with an off-policy RL scheme to find the optimal controller. The accurate bound of the model-learning error is derived and its characteristic is employed in the formation of a novel adaptive robustified control barrier function (ARCBF) which guarantees that states of the system remain in the safe set even when the learning is incomplete. Therefore, after satisfaction of a mild rank condition, the noisy input in the exploratory data collection phase and the optimal controller in the exploitation phase are minimally altered such that the ARCBF criterion is satisfied and, therefore, safety is guaranteed in both phases. It is shown that under the proposed RL framework, the model learning error is a vanishing perturbation to the original system. Therefore, a stability guarantee is also provided even in the exploration when noisy random inputs are applied to the system.
{"title":"Reinforcement Learning With Safety and Stability Guarantees During Exploration For Linear Systems","authors":"Zahra Marvi;Bahare Kiumarsi","doi":"10.1109/OJCSYS.2022.3209945","DOIUrl":"https://doi.org/10.1109/OJCSYS.2022.3209945","url":null,"abstract":"The satisfaction of the safety and stability properties of reinforcement learning (RL) algorithms has been a long-standing challenge. These properties must be satisfied even during learning, for which exploration is required to collect rich data. However, satisfying the safety of actions when little is known about the system dynamics is a daunting challenge. After all, predicting the consequence of RL actions requires knowing the system dynamics. This paper presents a novel RL scheme that ensures the safety and stability of the linear systems during the exploration and exploitation phases. To do so, a fast and data-efficient model-learning with the convergence guarantee is employed along and simultaneously with an off-policy RL scheme to find the optimal controller. The accurate bound of the model-learning error is derived and its characteristic is employed in the formation of a novel adaptive robustified control barrier function (ARCBF) which guarantees that states of the system remain in the safe set even when the learning is incomplete. Therefore, after satisfaction of a mild rank condition, the noisy input in the exploratory data collection phase and the optimal controller in the exploitation phase are minimally altered such that the ARCBF criterion is satisfied and, therefore, safety is guaranteed in both phases. It is shown that under the proposed RL framework, the model learning error is a vanishing perturbation to the original system. Therefore, a stability guarantee is also provided even in the exploration when noisy random inputs are applied to the system.","PeriodicalId":73299,"journal":{"name":"IEEE open journal of control systems","volume":"1 ","pages":"322-334"},"PeriodicalIF":0.0,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/9552933/9683993/09904857.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50237539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-15DOI: 10.1109/OJCSYS.2022.3206710
Shayok Mukhopadhyay;Hafiz M. Usman;Habibur Rehman
This paper proposes an accurate and efficient Universal Adaptive Stabilizer (UAS) based online parameters estimation technique for a 400 V Li-ion battery bank. The battery open circuit voltage, parameters modeling the transient response, and series resistance are all estimated in a single real-time test. In contrast to earlier UAS based work on individual battery packs, this work does not require prior offline experimentation or any post-processing. Real time fast convergence of parameters' estimates with minimal experimental effort enables update of battery parameters during run-time. The proposed strategy is mathematically validated and its performance is demonstrated on a 400 V, 6.6 Ah Li-ion battery bank powering an induction motor driven prototype electric vehicle (EV) traction system.
{"title":"Real Time Li-Ion Battery Bank Parameters Estimation via Universal Adaptive Stabilization","authors":"Shayok Mukhopadhyay;Hafiz M. Usman;Habibur Rehman","doi":"10.1109/OJCSYS.2022.3206710","DOIUrl":"https://doi.org/10.1109/OJCSYS.2022.3206710","url":null,"abstract":"This paper proposes an accurate and efficient Universal Adaptive Stabilizer (UAS) based online parameters estimation technique for a 400 V Li-ion battery bank. The battery open circuit voltage, parameters modeling the transient response, and series resistance are all estimated in a single real-time test. In contrast to earlier UAS based work on individual battery packs, this work does not require prior offline experimentation or any post-processing. Real time fast convergence of parameters' estimates with minimal experimental effort enables update of battery parameters during run-time. The proposed strategy is mathematically validated and its performance is demonstrated on a 400 V, 6.6 Ah Li-ion battery bank powering an induction motor driven prototype electric vehicle (EV) traction system.","PeriodicalId":73299,"journal":{"name":"IEEE open journal of control systems","volume":"1 ","pages":"268-293"},"PeriodicalIF":0.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/9552933/9683993/09893763.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50348786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-15DOI: 10.1109/OJCSYS.2022.3207108
Yu Wang;Hussein Sibai;Mark Yen;Sayan Mitra;Geir E. Dullerud
Statistical model checking is a class of sequential algorithms that can verify specifications of interest on an ensemble of cyber-physical systems (e.g., whether 99% of cars from a batch meet a requirement on their functionality). These algorithms infer the probability that given specifications are satisfied by the systems with provable statistical guarantees by drawing sufficient numbers of independent and identically distributed samples. During the process of statistical model checking, the values of the samples (e.g., a user's car trajectory) may be inferred by intruders, causing privacy concerns in consumer-level applications (e.g., automobiles and medical devices). This paper addresses the privacy of statistical model checking algorithms from the point of view of differential privacy. These algorithms are sequential, drawing samples until a condition on their values is met. We show that revealing the number of samples drawn can violate privacy. We also show that the standard exponential mechanism that randomizes the output of an algorithm to achieve differential privacy fails to do so in the context of sequential algorithms. Instead, we relax the conservative requirement in differential privacy that the sensitivity of the output of the algorithm should be bounded to any perturbation for any data set. We propose a new notion of differential privacy which we call expected differential privacy (EDP). Then, we propose a novel expected sensitivity analysis for the sequential algorithm and propose a corresponding exponential mechanism that randomizes the termination time to achieve the EDP. We apply the proposed exponential mechanism to statistical model checking algorithms to preserve the privacy of the samples they draw. The utility of the proposed algorithm is demonstrated in a case study.
{"title":"Differentially Private Algorithms for Statistical Verification of Cyber-Physical Systems","authors":"Yu Wang;Hussein Sibai;Mark Yen;Sayan Mitra;Geir E. Dullerud","doi":"10.1109/OJCSYS.2022.3207108","DOIUrl":"https://doi.org/10.1109/OJCSYS.2022.3207108","url":null,"abstract":"Statistical model checking is a class of sequential algorithms that can verify specifications of interest on an ensemble of cyber-physical systems (e.g., whether 99% of cars from a batch meet a requirement on their functionality). These algorithms infer the probability that given specifications are satisfied by the systems with provable statistical guarantees by drawing sufficient numbers of independent and identically distributed samples. During the process of statistical model checking, the values of the samples (e.g., a user's car trajectory) may be inferred by intruders, causing privacy concerns in consumer-level applications (e.g., automobiles and medical devices). This paper addresses the privacy of statistical model checking algorithms from the point of view of differential privacy. These algorithms are sequential, drawing samples until a condition on their values is met. We show that revealing the number of samples drawn can violate privacy. We also show that the standard exponential mechanism that randomizes the output of an algorithm to achieve differential privacy fails to do so in the context of sequential algorithms. Instead, we relax the conservative requirement in differential privacy that the sensitivity of the output of the algorithm should be bounded to any perturbation for any data set. We propose a new notion of differential privacy which we call \u0000<italic>expected differential privacy</i>\u0000 (EDP). Then, we propose a novel expected sensitivity analysis for the sequential algorithm and propose a corresponding exponential mechanism that randomizes the termination time to achieve the EDP. We apply the proposed exponential mechanism to statistical model checking algorithms to preserve the privacy of the samples they draw. The utility of the proposed algorithm is demonstrated in a case study.","PeriodicalId":73299,"journal":{"name":"IEEE open journal of control systems","volume":"1 ","pages":"294-305"},"PeriodicalIF":0.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/9552933/9683993/09893303.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50381126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or only partially known. In particular, we focus on the design of data-driven controllers to regulate a dynamical system to the solution of a constrained convex optimization problem where: i) the state must be estimated from nonlinear and possibly high-dimensional data; and ii) the cost of the optimization problem – which models control objectives associated with inputs and states of the system – is not available and must be learned from data. We propose a data-driven feedback controller that is based on adaptations of a projected gradient-flow method; the controller includes neural networks as integral components for the estimation of the unknown functions. Leveraging stability theory for perturbed systems, we derive sufficient conditions to guarantee exponential input-to-state stability (ISS) of the control loop. In particular, we show that the interconnected system is ISS with respect to the approximation errors of the neural network and unknown disturbances affecting the system. The transient bounds combine the universal approximation property of deep neural networks with the ISS characterization. Illustrative numerical results are presented in the context of robotics and control of epidemics.
{"title":"Online Optimization of Dynamical Systems With Deep Learning Perception","authors":"Liliaokeawawa Cothren;Gianluca Bianchin;Emiliano Dall'Anese","doi":"10.1109/OJCSYS.2022.3205871","DOIUrl":"https://doi.org/10.1109/OJCSYS.2022.3205871","url":null,"abstract":"This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or only partially known. In particular, we focus on the design of data-driven controllers to regulate a dynamical system to the solution of a constrained convex optimization problem where: i) the state must be estimated from nonlinear and possibly high-dimensional data; and ii) the cost of the optimization problem – which models control objectives associated with inputs and states of the system – is not available and must be learned from data. We propose a data-driven feedback controller that is based on adaptations of a projected gradient-flow method; the controller includes neural networks as integral components for the estimation of the unknown functions. Leveraging stability theory for perturbed systems, we derive sufficient conditions to guarantee exponential input-to-state stability (ISS) of the control loop. In particular, we show that the interconnected system is ISS with respect to the approximation errors of the neural network and unknown disturbances affecting the system. The transient bounds combine the universal approximation property of deep neural networks with the ISS characterization. Illustrative numerical results are presented in the context of robotics and control of epidemics.","PeriodicalId":73299,"journal":{"name":"IEEE open journal of control systems","volume":"1 ","pages":"306-321"},"PeriodicalIF":0.0,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/9552933/9683993/09891838.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50348787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-12DOI: 10.1109/OJCSYS.2022.3205863
Tenavi Nakamura-Zimmerer;Qi Gong;Wei Kang
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well understood. In particular, some neural networks with high test accuracy can fail to even locally stabilize the dynamic system. To address this challenge we propose several novel neural network architectures, which we show guarantee local asymptotic stability while retaining the approximation capacity to learn the optimal feedback policy semi-globally. The proposed architectures are compared against standard neural network feedback controllers through numerical simulations of two high-dimensional nonlinear optimal control problems: stabilization of an unstable Burgers-type partial differential equation, and altitude and course tracking for an unmanned aerial vehicle. The simulations demonstrate that standard neural networks can fail to stabilize the dynamics even when trained well, while the proposed architectures are always at least locally stabilizing and can achieve near-optimal performance.
{"title":"Neural Network Optimal Feedback Control With Guaranteed Local Stability","authors":"Tenavi Nakamura-Zimmerer;Qi Gong;Wei Kang","doi":"10.1109/OJCSYS.2022.3205863","DOIUrl":"https://doi.org/10.1109/OJCSYS.2022.3205863","url":null,"abstract":"Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well understood. In particular, some neural networks with high test accuracy can fail to even locally stabilize the dynamic system. To address this challenge we propose several novel neural network architectures, which we show guarantee local asymptotic stability while retaining the approximation capacity to learn the optimal feedback policy semi-globally. The proposed architectures are compared against standard neural network feedback controllers through numerical simulations of two high-dimensional nonlinear optimal control problems: stabilization of an unstable Burgers-type partial differential equation, and altitude and course tracking for an unmanned aerial vehicle. The simulations demonstrate that standard neural networks can fail to stabilize the dynamics even when trained well, while the proposed architectures are always at least locally stabilizing and can achieve near-optimal performance.","PeriodicalId":73299,"journal":{"name":"IEEE open journal of control systems","volume":"1 ","pages":"210-222"},"PeriodicalIF":0.0,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/9552933/9683993/09887885.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50348954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-12DOI: 10.1109/OJCSYS.2022.3206083
Michael Enqi Cao;Matthieu Bloch;Samuel Coogan
We present a method for efficiently computing reachable sets and forward invariant sets for continuous-time systems with dynamics that include unknown components. Our main assumption is that, given any hyperrectangle of states, lower and upper bounds for the unknown components are available. With this assumption, the theory of mixed monotone systems allows us to formulate an efficient method for computing a hyperrectangular set that over-approximates the reachable set of the system. We then show a related approach that leads to sufficient conditions for identifying hyperrectangular sets that are forward invariant for the dynamics. We additionally show that set estimates tighten as the bounds on the unknown behavior tighten. Finally, we derive a method for satisfying our main assumption by modeling the unknown components as state-dependent Gaussian processes, providing bounds that are correct with high probability. A key benefit of our approach is to enable tractable computations for systems up to moderately high dimension that are subject to low dimensional uncertainty modeled as Gaussian processes, a class of systems that often appears in practice. We demonstrate our results on several examples, including a case study of a planar multirotor aerial vehicle.
{"title":"Efficient Learning of Hyperrectangular Invariant Sets Using Gaussian Processes","authors":"Michael Enqi Cao;Matthieu Bloch;Samuel Coogan","doi":"10.1109/OJCSYS.2022.3206083","DOIUrl":"https://doi.org/10.1109/OJCSYS.2022.3206083","url":null,"abstract":"We present a method for efficiently computing reachable sets and forward invariant sets for continuous-time systems with dynamics that include unknown components. Our main assumption is that, given any hyperrectangle of states, lower and upper bounds for the unknown components are available. With this assumption, the theory of mixed monotone systems allows us to formulate an efficient method for computing a hyperrectangular set that over-approximates the reachable set of the system. We then show a related approach that leads to sufficient conditions for identifying hyperrectangular sets that are forward invariant for the dynamics. We additionally show that set estimates tighten as the bounds on the unknown behavior tighten. Finally, we derive a method for satisfying our main assumption by modeling the unknown components as state-dependent Gaussian processes, providing bounds that are correct with high probability. A key benefit of our approach is to enable tractable computations for systems up to moderately high dimension that are subject to low dimensional uncertainty modeled as Gaussian processes, a class of systems that often appears in practice. We demonstrate our results on several examples, including a case study of a planar multirotor aerial vehicle.","PeriodicalId":73299,"journal":{"name":"IEEE open journal of control systems","volume":"1 ","pages":"223-236"},"PeriodicalIF":0.0,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/9552933/9683993/09888053.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50381124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-31DOI: 10.1109/OJCSYS.2022.3200015
Yue Sun;Samet Oymak;Maryam Fazel
This paper studies the problem of identifying low-order linear time-invariant systems via Hankel nuclear norm (HNN) regularization. This regularization encourages the Hankel matrix to be low-rank, which corresponds to the dynamical system being of low order. We provide novel statistical analysis for this regularization, and contrast it with the unregularized ordinary least-squares (OLS) estimator. Our analysis leads to new finite-sample error bounds on estimating the impulse response and the Hankel matrix associated with the linear system using HNN regularization. We design a suitable input excitation, and show that we can recover the system using a number of observations that scales optimally with the true system order and achieves strong statistical estimation rates. Complementing these, we also demonstrate that the input design indeed matters by proving that intuitive choices, such as i.i.d. Gaussian input, lead to sub-optimal sample complexity. To better understand the benefits of regularization, we also revisit the OLS estimator. Besides refining existing bounds, we experimentally identify when HNN regularization improves over OLS: (1) For low-order systems with slow impulse-response decay, OLS method performs poorly in terms of sample complexity, (2) the Hankel matrix returned by regularization has a more clear singular value gap that makes determining the system order easier, (3) HNN regularization is less sensitive to hyperparameter choice. To choose the regularization parameter, we also outline a simple joint train-validation procedure.
{"title":"Finite Sample Identification of Low-Order LTI Systems via Nuclear Norm Regularization","authors":"Yue Sun;Samet Oymak;Maryam Fazel","doi":"10.1109/OJCSYS.2022.3200015","DOIUrl":"https://doi.org/10.1109/OJCSYS.2022.3200015","url":null,"abstract":"This paper studies the problem of identifying low-order linear time-invariant systems via Hankel nuclear norm (HNN) regularization. This regularization encourages the Hankel matrix to be low-rank, which corresponds to the dynamical system being of low order. We provide novel statistical analysis for this regularization, and contrast it with the unregularized ordinary least-squares (OLS) estimator. Our analysis leads to new finite-sample error bounds on estimating the impulse response and the Hankel matrix associated with the linear system using HNN regularization. We design a suitable input excitation, and show that we can recover the system using a number of observations that scales optimally with the true system order and achieves strong statistical estimation rates. Complementing these, we also demonstrate that the input design indeed matters by proving that intuitive choices, such as i.i.d. Gaussian input, lead to sub-optimal sample complexity. To better understand the benefits of regularization, we also revisit the OLS estimator. Besides refining existing bounds, we experimentally identify when HNN regularization improves over OLS: (1) For low-order systems with slow impulse-response decay, OLS method performs poorly in terms of sample complexity, (2) the Hankel matrix returned by regularization has a more clear singular value gap that makes determining the system order easier, (3) HNN regularization is less sensitive to hyperparameter choice. To choose the regularization parameter, we also outline a simple joint train-validation procedure.","PeriodicalId":73299,"journal":{"name":"IEEE open journal of control systems","volume":"1 ","pages":"237-254"},"PeriodicalIF":0.0,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/9552933/9683993/09870857.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50381125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Sherrit, M. Badescu, John B. Steeves, William E. Krieger, Clifford A. Klein, Otto R. Polanco, C. Weisberg, D. Van Buren, J. Sauvageau, K. Coste
A variety of applications require precision control at cryogenic temperatures. The next-generation of telescopes are looking to increase apertures in space telescopes and observations in the mid through far infrared regions enabling new science ranging from exoplanet characterization to precision astronomical observations to further refine astrophysics models. Concepts include segmented telescopes which are capable of observations in UV through IR bands, thus driving the need for UV surface performance at cryogenic temperatures. These telescope’s segments will require actuators for controlled surface displacements capable of operation at cryogenic temperatures ( $le 150text{K}$ ). The work reported in this paper is directed at understanding piezoelectric stack actuator operation down to cryogenic temperatures (100 K) which will provide actuator designers the needed information to model and predict performance. The data reported down to 100 K includes; resonance data, displacement voltage (S vs E) and capacitor voltage (D vs E) curves, stiffness, hysteresis, blocking force, DC resistance measurements, thermal strains and the coefficients of thermal expansion as a function of the electrical boundary conditions. Open-loop control drive strategies and errors are also reported. We apply this data to a surface parallel actuator mirror design.
各种应用需要在低温下进行精确控制。下一代望远镜正在寻求增加太空望远镜的孔径，并在中红外到远红外区域进行观测，从而实现从系外行星表征到精确天文观测的新科学，以进一步完善天体物理学模型。概念包括能够在紫外线到红外波段进行观测的分段望远镜，从而推动了对低温下紫外线表面性能的需求。这些望远镜的部分将需要能够在低温（$le 150text｛K｝$）下运行的可控表面位移的致动器。本文报道的工作旨在了解压电堆致动器在低温（100K）下的操作，这将为致动器设计者提供建模和预测性能所需的信息。报告的低至100K的数据包括：；谐振数据、位移电压（S vs E）和电容器电压（D vs E）曲线、刚度、磁滞、阻塞力、直流电阻测量、热应变和热膨胀系数作为电边界条件的函数。还报告了开环控制驱动策略和错误。我们将这些数据应用于表面平行致动器反射镜的设计。
{"title":"Characterization of Multilayer Piezoelectric Stacks Down to 100K","authors":"S. Sherrit, M. Badescu, John B. Steeves, William E. Krieger, Clifford A. Klein, Otto R. Polanco, C. Weisberg, D. Van Buren, J. Sauvageau, K. Coste","doi":"10.1117/12.2634962","DOIUrl":"https://doi.org/10.1117/12.2634962","url":null,"abstract":"A variety of applications require precision control at cryogenic temperatures. The next-generation of telescopes are looking to increase apertures in space telescopes and observations in the mid through far infrared regions enabling new science ranging from exoplanet characterization to precision astronomical observations to further refine astrophysics models. Concepts include segmented telescopes which are capable of observations in UV through IR bands, thus driving the need for UV surface performance at cryogenic temperatures. These telescope’s segments will require actuators for controlled surface displacements capable of operation at cryogenic temperatures ( $le 150text{K}$ ). The work reported in this paper is directed at understanding piezoelectric stack actuator operation down to cryogenic temperatures (100 K) which will provide actuator designers the needed information to model and predict performance. The data reported down to 100 K includes; resonance data, displacement voltage (S vs E) and capacitor voltage (D vs E) curves, stiffness, hysteresis, blocking force, DC resistance measurements, thermal strains and the coefficients of thermal expansion as a function of the electrical boundary conditions. Open-loop control drive strategies and errors are also reported. We apply this data to a surface parallel actuator mirror design.","PeriodicalId":73299,"journal":{"name":"IEEE open journal of control systems","volume":"2 1","pages":"65-82"},"PeriodicalIF":0.0,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47036631","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 : 2022-08-29DOI: 10.1109/OJCSYS.2022.3202202
Yan Jiang;Wenqi Cui;Baosen Zhang;Jorge Cortés
Frequency control plays a pivotal role in reliable power system operations. It is conventionally performed in a hierarchical way that first rapidly stabilizes the frequency deviations and then slowly recovers the nominal frequency. However, as the generation mix shifts from synchronous generators to renewable resources, power systems experience larger and faster frequency fluctuations due to the loss of inertia, which adversely impacts the frequency stability. This has motivated active research in algorithms that jointly address frequency degradation and economic efficiency in a fast timescale, among which the distributed averaging-based integral (DAI) control is a notable one that sets controllable power injections directly proportional to the integrals of frequency deviation and economic inefficiency signals. Nevertheless, DAI does not typically consider the transient performance of the system following power disturbances and has been restricted to quadratic operational cost functions. This paper aims to leverage nonlinear optimal controllers to simultaneously achieve optimal transient frequency control and find the most economic power dispatch for frequency restoration. To this end, we integrate reinforcement learning (RL) to the classic DAI, which results in RL-DAI control. Specifically, we use RL to learn a neural network-based control policy mapping from the integral variables of DAI to the controllable power injections which provides optimal transient frequency control, while DAI inherently ensures the frequency restoration and optimal economic dispatch. Compared to existing methods, we provide provable guarantees on the stability of the learned controllers and extend the set of allowable cost functions to a much larger class. Simulations on the 39-bus New England system illustrate our results.
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