Pub Date : 2023-01-01DOI: 10.1016/j.arcontrol.2023.03.009
Alessandro Saviolo, Giuseppe Loianno
This article reviews the state-of-the-art modeling and control techniques for aerial robots such as quadrotor systems and presents several future research directions in this area. The review starts by introducing the benefits and drawbacks of classic physic-based dynamic modeling and control techniques. Subsequently, the manuscript presents the key challenges to augment or replace classic techniques with data-driven approaches that can offer several key benefits in terms of flight precision, safety, adaptation, and agility.
{"title":"Learning quadrotor dynamics for precise, safe, and agile flight control","authors":"Alessandro Saviolo, Giuseppe Loianno","doi":"10.1016/j.arcontrol.2023.03.009","DOIUrl":"https://doi.org/10.1016/j.arcontrol.2023.03.009","url":null,"abstract":"<div><p>This article reviews the state-of-the-art modeling and control techniques for aerial robots such as quadrotor systems and presents several future research directions in this area. The review starts by introducing the benefits and drawbacks of classic physic-based dynamic modeling and control techniques. Subsequently, the manuscript presents the key challenges to augment or replace classic techniques with data-driven approaches that can offer several key benefits in terms of flight precision, safety, adaptation, and agility.</p></div>","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"55 ","pages":"Pages 45-60"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49738908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Active Queue Management (AQM) for mitigating Internet congestion has been addressed via various feedback control syntheses, especially P, PI, and PID regulators, by using a linear approximation where the “round trip time,” i.e., the delay, is assumed to be constant. This constraint is lifted here by using a nonlinear modeling with a variable delay, introduced more than 20 years ago. This delay, intimately linked to the congestion phenomenon, may be viewed as “ a flat output.” All other system variables, especially the control variable, i.e., the packet loss ratio, are expressed as a function of the delay and its derivatives: they are frozen if the delay is kept constant. This flatness-like property, which demonstrates the mathematical discrepancy of the linear approximation adopted until today, yields also our control strategy in two steps: Firstly, designing an open-loop control, thanks to straightforward Flatness-Based Control (FBC) techniques, and secondly, closing the loop via Model-Free Control (MFC) in order to take into account severe model mismatches, like, here, the number of TCP sessions. Several convincing computer simulations, which are easily implementable, are presented and discussed.
{"title":"Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay","authors":"Hugues Mounier , Cédric Join , Emmanuel Delaleau , Michel Fliess","doi":"10.1016/j.arcontrol.2023.02.002","DOIUrl":"https://doi.org/10.1016/j.arcontrol.2023.02.002","url":null,"abstract":"<div><p><span>Active Queue Management (AQM) for mitigating Internet congestion has been addressed via various feedback control syntheses, especially P, PI, and PID regulators, by using a linear approximation where the “round trip time,” i.e., the delay, is assumed to be constant. This constraint is lifted here by using a nonlinear modeling with a variable delay, introduced more than 20 years ago. This delay, intimately linked to the congestion phenomenon, may be viewed as “ a flat output.” All other system variables, especially the control variable, i.e., the </span>packet loss ratio, are expressed as a function of the delay and its derivatives: they are frozen if the delay is kept constant. This flatness-like property, which demonstrates the mathematical discrepancy of the linear approximation adopted until today, yields also our control strategy in two steps: Firstly, designing an open-loop control, thanks to straightforward Flatness-Based Control (FBC) techniques, and secondly, closing the loop via Model-Free Control (MFC) in order to take into account severe model mismatches, like, here, the number of TCP sessions. Several convincing computer simulations, which are easily implementable, are presented and discussed.</p></div>","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"55 ","pages":"Pages 61-69"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49738910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.arcontrol.2022.10.003
Zhe Du, Rudy R. Negenborn, Vasso Reppa
The regulatory endorsement of the International Maritime Organization (IMO) and the support of pivotal shipping market players in recent years motivate the investigation of the potential role that autonomous vessels play in the shipping industry. As the complexity and scale of the envisioned applications increase, research works gradually transform the focus from single-vessel systems to multi-vessel systems. Thus, autonomous multi-vessel systems applied in the shipping industry are becoming a promising research direction. One of the typical research directions is floating object manipulation by multiple tugboats.
This paper offers a comprehensive literature review of the existing research on floating object manipulation by autonomous multi-vessel systems. Based on the prior knowledge of object manipulation problems in multi-robot systems, four typical ways of maritime object manipulation are summarized: attaching, caging, pushing, and towing. The advantages and disadvantages of each manipulation way are discussed, including its typical floating object and application scenarios. Moreover, the aspects of control objective, control architecture, collision avoidance operation, disturbances consideration, and role of each involved vessel are analyzed for gaining insight into the approaches for solving these problems. Finally, challenges and future directions are highlighted to give possible inspiration.
{"title":"Review of floating object manipulation by autonomous multi-vessel systems","authors":"Zhe Du, Rudy R. Negenborn, Vasso Reppa","doi":"10.1016/j.arcontrol.2022.10.003","DOIUrl":"https://doi.org/10.1016/j.arcontrol.2022.10.003","url":null,"abstract":"<div><p>The regulatory endorsement of the International Maritime Organization (IMO) and the support of pivotal shipping market players in recent years motivate the investigation of the potential role that autonomous vessels play in the shipping industry. As the complexity and scale of the envisioned applications increase, research works gradually transform the focus from single-vessel systems to multi-vessel systems. Thus, autonomous multi-vessel systems applied in the shipping industry are becoming a promising research direction. One of the typical research directions is floating object manipulation by multiple tugboats.</p><p>This paper offers a comprehensive literature review of the existing research on floating object manipulation by autonomous multi-vessel systems. Based on the prior knowledge of object manipulation problems in multi-robot systems, four typical ways of maritime object manipulation are summarized: attaching, caging, pushing, and towing. The advantages and disadvantages of each manipulation way are discussed, including its typical floating object and application scenarios. Moreover, the aspects of control objective, control architecture, collision avoidance operation, disturbances consideration, and role of each involved vessel are analyzed for gaining insight into the approaches for solving these problems. Finally, challenges and future directions are highlighted to give possible inspiration.</p></div>","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"55 ","pages":"Pages 255-278"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49739029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.arcontrol.2023.03.001
Anup Biswas , Vivek S. Borkar
Risk-sensitive control has received considerable interest since the seminal work of Howard and Matheson (Howard and Matheson, 1971/72) because of its ability to account for fluctuations about the mean, its connection with control, and its application to financial mathematics. In this article we attempt to put together a comprehensive survey on the research done on ergodic risk-sensitive control over the last four decades.
自Howard和Matheson(Howard and Matheson,1971/72)的开创性工作以来,风险敏感控制因其能够解释平均值的波动、与H∞控制的联系以及在金融数学中的应用而引起了人们的极大兴趣。在这篇文章中,我们试图对过去四十年来对遍历风险敏感控制的研究进行全面的调查。
{"title":"Ergodic risk-sensitive control—A survey","authors":"Anup Biswas , Vivek S. Borkar","doi":"10.1016/j.arcontrol.2023.03.001","DOIUrl":"https://doi.org/10.1016/j.arcontrol.2023.03.001","url":null,"abstract":"<div><p>Risk-sensitive control has received considerable interest since the seminal work of Howard and Matheson (Howard and Matheson, 1971/72) because of its ability to account for fluctuations about the mean, its connection with <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> control, and its application to financial mathematics. In this article we attempt to put together a comprehensive survey on the research done on ergodic risk-sensitive control over the last four decades.</p></div>","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"55 ","pages":"Pages 118-141"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49739390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.arcontrol.2022.12.002
Bernard Brogliato
So-called robot–object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an “object” and a “robot”. Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, robotic systems that manipulate objects, tapping, pushing systems, kinematic chains with joint clearance, crawling, climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot–object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article.
{"title":"Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives","authors":"Bernard Brogliato","doi":"10.1016/j.arcontrol.2022.12.002","DOIUrl":"https://doi.org/10.1016/j.arcontrol.2022.12.002","url":null,"abstract":"<div><p><span>So-called robot–object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an “object” and a “robot”. Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, </span>robotic systems<span><span><span> that manipulate objects, tapping, pushing systems, </span>kinematic chains<span> with joint clearance, crawling, </span></span>climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot–object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article.</span></p></div>","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"55 ","pages":"Pages 297-337"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49762809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.arcontrol.2023.100912
Erick Mejia Uzeda, Mohamed A. Hafez, Mireille E. Broucke
A longstanding open problem of systems neuroscience is to understand how the brain calibrates thousands of reflexes to achieve near instantaneous disturbance rejection. While reflexes typically act locally at the site of sensory measurements, the adaptation of reflex gains is the result of an ingenious architecture in which knowledge of disturbances is transferred from the cerebellum to the deep cerebellar nuclei or the brainstem. This paper investigates the use of control theory as the mathematical foundation to explain the mechanisms by which such forms of learning, as well as forgetting, manifest themselves in systems neuroscience. Particularly, we use adaptive control and averaging theory to model the computations performed in learning appropriate reflex gains. While forgetting is perceived as counter-productive to learning, we show that if incorporated correctly, it can endow the much needed robustness to train thousands of reflexes without interfering with their adaptation. This is accomplished using the -modification which achieves robustness of adaptive schemes through the estimation of exciting subspaces. Our techniques are combined in a comprehensive model, with simulations illustrating their effectiveness.
{"title":"Learning and forgetting in systems neuroscience: A control perspective","authors":"Erick Mejia Uzeda, Mohamed A. Hafez, Mireille E. Broucke","doi":"10.1016/j.arcontrol.2023.100912","DOIUrl":"10.1016/j.arcontrol.2023.100912","url":null,"abstract":"<div><p>A longstanding open problem of systems neuroscience is to understand how the brain calibrates thousands of reflexes to achieve near instantaneous disturbance rejection. While reflexes typically act locally at the site of sensory measurements, the adaptation of reflex gains is the result of an ingenious architecture in which knowledge of disturbances is transferred from the cerebellum to the deep cerebellar nuclei or the brainstem. This paper investigates the use of control theory as the mathematical foundation to explain the mechanisms by which such forms of learning, as well as forgetting, manifest themselves in systems neuroscience. Particularly, we use adaptive control and averaging theory to model the computations performed in learning appropriate reflex gains. While forgetting is perceived as counter-productive to learning, we show that if incorporated correctly, it can endow the much needed robustness to train thousands of reflexes without interfering with their adaptation. This is accomplished using the <span><math><mi>μ</mi></math></span>-modification which achieves robustness of adaptive schemes through the estimation of exciting subspaces. Our techniques are combined in a comprehensive model, with simulations illustrating their effectiveness.</p></div>","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"56 ","pages":"Article 100912"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.arcontrol.2023.100917
Alan Yang, Stephen Boyd
We propose a method for designing policies for convex stochastic control problems characterized by random linear dynamics and convex stage cost. We consider policies that employ quadratic approximate value functions as a substitute for the true value function. Evaluating the associated control policy involves solving a convex problem, typically a quadratic program, which can be carried out reliably in real-time. Such policies often perform well even when the approximate value function is not a particularly good approximation of the true value function. We propose value-gradient iteration, which fits the gradient of value function, with regularization that can include constraints reflecting known bounds on the true value function. Our value-gradient iteration method can yield a good approximate value function with few samples, and little hyperparameter tuning. We find that the method can find a good policy with computational effort comparable to that required to just evaluate a control policy via simulation.
{"title":"Value-gradient iteration with quadratic approximate value functions","authors":"Alan Yang, Stephen Boyd","doi":"10.1016/j.arcontrol.2023.100917","DOIUrl":"10.1016/j.arcontrol.2023.100917","url":null,"abstract":"<div><p>We propose a method for designing policies for convex stochastic control problems characterized by random linear dynamics and convex stage cost. We consider policies that employ quadratic approximate value functions as a substitute for the true value function. Evaluating the associated control policy involves solving a convex problem<span>, typically a quadratic program, which can be carried out reliably in real-time. Such policies often perform well even when the approximate value function is not a particularly good approximation of the true value function. We propose value-gradient iteration, which fits the gradient of value function, with regularization that can include constraints reflecting known bounds on the true value function. Our value-gradient iteration method can yield a good approximate value function with few samples, and little hyperparameter tuning. We find that the method can find a good policy with computational effort comparable to that required to just evaluate a control policy via simulation.</span></p></div>","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"56 ","pages":"Article 100917"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135609020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.arcontrol.2023.100925
Lucrezia Manieri, Alessandro Falsone, Maria Prandini
In this paper, we focus on the optimal operation of a multi-agent system affected by uncertainty. In particular, we consider a cooperative setting where agents jointly optimize a performance index compatibly with individual constraints on their discrete and continuous decision variables and with coupling global constraints. We assume that individual constraints are affected by uncertainty, which is known to each agent via a private set of data that cannot be shared with others. Exploiting tools from statistical learning theory, we provide data-based probabilistic feasibility guarantees for a (possibly sub-optimal) solution of the multi-agent problem that is obtained via a decentralized/distributed scheme that preserves the privacy of the local information. The generalization properties of the data-based solution are shown to depend on the size of each local dataset and on the complexity of the uncertain individual constraint sets. Explicit bounds are derived in the case of linear individual constraints. A comparative analysis with the cases of a common dataset and of local uncertainties that are independent is performed.
{"title":"Probabilistic feasibility in data-driven multi-agent non-convex optimization","authors":"Lucrezia Manieri, Alessandro Falsone, Maria Prandini","doi":"10.1016/j.arcontrol.2023.100925","DOIUrl":"https://doi.org/10.1016/j.arcontrol.2023.100925","url":null,"abstract":"<div><p>In this paper, we focus on the optimal operation of a multi-agent system affected by uncertainty. In particular, we consider a cooperative setting where agents jointly optimize a performance index compatibly with individual constraints on their discrete and continuous decision variables and with coupling global constraints. We assume that individual constraints are affected by uncertainty, which is known to each agent via a private set of data that cannot be shared with others. Exploiting tools from statistical learning theory, we provide data-based probabilistic feasibility guarantees for a (possibly sub-optimal) solution of the multi-agent problem that is obtained via a decentralized/distributed scheme that preserves the privacy of the local information. The generalization properties of the data-based solution are shown to depend on the size of each local dataset and on the complexity of the uncertain individual constraint sets. Explicit bounds are derived in the case of linear individual constraints. A comparative analysis with the cases of a common dataset and of local uncertainties that are independent is performed.</p></div>","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"56 ","pages":"Article 100925"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1367578823000895/pdfft?md5=400ea0f3b2244fc3aeddd15afd97f00f&pid=1-s2.0-S1367578823000895-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136697008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.arcontrol.2023.02.001
Alain Oustaloup , François Levron , Stéphane Victor , Luc Dugard
<div><p>The article Oustaloup et al. (2021) has shown that the Fractional Power Model (FPM), <span><math><mrow><mi>A</mi><mo>+</mo><mi>B</mi><msup><mrow><mi>t</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span>, enables well representing the cumulated data of COVID infections, thanks to a nonlinear identification technique. Beyond this identification interval, the article has also shown that the model enables predicting the future values on an unusual prediction horizon as for its range. The objective of this addendum is to explain, via an autoregressive form, why this model intrinsically benefits from such a predictivity property, the idea being to show the interest of the FPM model by highlighting its <em>predictive specificity</em>, inherent to non-integer integration that conditions the model. More precisely, this addendum establishes a <em>predictive form with long memory</em><span> of the FPM model. This form corresponds to an autoregressive (AR) filter of infinite order. Taking into account the whole past through an indefinite linear combination of past values, a first predictive form, said to be with </span><em>long memory</em>, results from an approach using one of the formulations of non-integer differentiation. Actually, as this first predictive form is the one of the power-law, <span><math><msup><mrow><mi>t</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, its adaptation to the FPM model, <span><math><mrow><mi>A</mi><mo>+</mo><mi>B</mi><msup><mrow><mi>t</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span>, which generalizes the linear regression, <span><math><mrow><mi>A</mi><mo>+</mo><mi>B</mi><mi>t</mi></mrow></math></span>, is then straightforward: it leads to the <em>predictive form of the FPM model</em> that specifies the model in prediction. This predictive form with long memory shows that the <em>predictivity</em> of the FPM model is such that <em>any predicted value takes into account the whole past</em>, according to a weighted sum of all the past values. These values are taken into account through weighting coefficients, that, for <span><math><mrow><mi>m</mi><mo>></mo><mo>−</mo><mn>1</mn></mrow></math></span> and <em>a fortiori</em> for <span><math><mrow><mi>m</mi><mo>></mo><mn>0</mn></mrow></math></span>, correspond to an <em>attenuation of the past</em>, that the non-integer power, <span><math><mi>m</mi></math></span><span>, determines by itself. To confirm the specificity of the FPM model in considering the past, this model is compared with a model of another nature, also having three parameters, namely an exponential model (Liu et al. (2020); Sallahi et al. (2021)): whereas, for the FPM model, the past is taken into account </span><em>globally</em> through <em>all past instants</em>, for the exponential model, the past is taken into account only <em>locally</em> through <em>one single past instant</em>, the predictive form of the model having a <em>short memory</em> and corresponding to a
Oustaloup等人。(2021)已经表明,由于非线性识别技术,分数幂模型(FPM)A+Btm能够很好地表示新冠病毒感染的累积数据。除了这个识别区间,文章还表明,该模型能够在不寻常的预测范围内预测未来的值。本附录的目的是通过自回归形式解释为什么该模型本质上受益于这种预测性,其思想是通过强调其预测特异性来显示FPM模型的兴趣,这是制约模型的非整数积分所固有的。更准确地说,本附录建立了FPM模型的长记忆预测形式。这种形式对应于无限阶的自回归(AR)滤波器。通过对过去值的不确定线性组合来考虑整个过去,据说具有长记忆的第一种预测形式来自于使用非整数微分公式之一的方法。事实上,由于第一种预测形式是幂律的一种,tm,它对FPM模型A+Btm的适应,推广了线性回归A+Bt,因此是直接的:它导致了FPM模型的预测形式,在预测中指定了模型。这种具有长记忆的预测形式表明,FPM模型的预测性使得根据所有过去值的加权和,任何预测值都考虑了整个过去。通过加权系数来考虑这些值,即对于m>;−1,更进一步的是m>;0,对应于过去的衰减,该衰减由非整数幂m自己确定。为了证实FPM模型在考虑过去时的特异性,将该模型与另一种性质的模型进行了比较,该模型也有三个参数,即指数模型(Liu et al.(2020);Sallahi等人。(2021)):而对于FPM模型,过去通过所有过去瞬间被全局考虑,对于指数模型,过去仅通过一个过去瞬间被局部考虑,该模型的预测形式具有短记忆,对应于1阶AR滤波器。在这两个模型的预测中获得的比较结果显示了FPM模型的预测兴趣。
{"title":"Addendum: Predictive form of the FPM model","authors":"Alain Oustaloup , François Levron , Stéphane Victor , Luc Dugard","doi":"10.1016/j.arcontrol.2023.02.001","DOIUrl":"https://doi.org/10.1016/j.arcontrol.2023.02.001","url":null,"abstract":"<div><p>The article Oustaloup et al. (2021) has shown that the Fractional Power Model (FPM), <span><math><mrow><mi>A</mi><mo>+</mo><mi>B</mi><msup><mrow><mi>t</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span>, enables well representing the cumulated data of COVID infections, thanks to a nonlinear identification technique. Beyond this identification interval, the article has also shown that the model enables predicting the future values on an unusual prediction horizon as for its range. The objective of this addendum is to explain, via an autoregressive form, why this model intrinsically benefits from such a predictivity property, the idea being to show the interest of the FPM model by highlighting its <em>predictive specificity</em>, inherent to non-integer integration that conditions the model. More precisely, this addendum establishes a <em>predictive form with long memory</em><span> of the FPM model. This form corresponds to an autoregressive (AR) filter of infinite order. Taking into account the whole past through an indefinite linear combination of past values, a first predictive form, said to be with </span><em>long memory</em>, results from an approach using one of the formulations of non-integer differentiation. Actually, as this first predictive form is the one of the power-law, <span><math><msup><mrow><mi>t</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, its adaptation to the FPM model, <span><math><mrow><mi>A</mi><mo>+</mo><mi>B</mi><msup><mrow><mi>t</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span>, which generalizes the linear regression, <span><math><mrow><mi>A</mi><mo>+</mo><mi>B</mi><mi>t</mi></mrow></math></span>, is then straightforward: it leads to the <em>predictive form of the FPM model</em> that specifies the model in prediction. This predictive form with long memory shows that the <em>predictivity</em> of the FPM model is such that <em>any predicted value takes into account the whole past</em>, according to a weighted sum of all the past values. These values are taken into account through weighting coefficients, that, for <span><math><mrow><mi>m</mi><mo>></mo><mo>−</mo><mn>1</mn></mrow></math></span> and <em>a fortiori</em> for <span><math><mrow><mi>m</mi><mo>></mo><mn>0</mn></mrow></math></span>, correspond to an <em>attenuation of the past</em>, that the non-integer power, <span><math><mi>m</mi></math></span><span>, determines by itself. To confirm the specificity of the FPM model in considering the past, this model is compared with a model of another nature, also having three parameters, namely an exponential model (Liu et al. (2020); Sallahi et al. (2021)): whereas, for the FPM model, the past is taken into account </span><em>globally</em> through <em>all past instants</em>, for the exponential model, the past is taken into account only <em>locally</em> through <em>one single past instant</em>, the predictive form of the model having a <em>short memory</em> and corresponding to a","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"55 ","pages":"Pages 291-296"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49762799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.arcontrol.2023.03.006
Amirhossein Taghvaei , Prashant G. Mehta
In this survey, we describe controlled interacting particle systems (CIPS) to approximate the solution of the optimal filtering and the optimal control problems. Part I of the survey is focussed on the feedback particle filter (FPF) algorithm, its derivation based on optimal transportation theory, and its relationship to the ensemble Kalman filter (EnKF) and the conventional sequential importance sampling–resampling (SIR) particle filters. The central numerical problem of FPF—to approximate the solution of the Poisson equation—is described together with the main solution approaches. An analytical and numerical comparison with the SIR particle filter is given to illustrate the advantages of the CIPS approach. Part II of the survey is focussed on adapting these algorithms for the problem of reinforcement learning. The survey includes several remarks that describe extensions as well as open problems in this subject.
{"title":"A survey of feedback particle filter and related controlled interacting particle systems (CIPS)","authors":"Amirhossein Taghvaei , Prashant G. Mehta","doi":"10.1016/j.arcontrol.2023.03.006","DOIUrl":"https://doi.org/10.1016/j.arcontrol.2023.03.006","url":null,"abstract":"<div><p><span>In this survey, we describe controlled interacting particle systems (CIPS) to approximate the solution of the optimal filtering and the optimal control problems. Part I of the survey is focussed on the feedback particle filter (FPF) algorithm, its derivation based on optimal transportation theory, and its relationship to the ensemble </span>Kalman filter (EnKF) and the conventional sequential importance sampling–resampling (SIR) particle filters. The central numerical problem of FPF—to approximate the solution of the Poisson equation—is described together with the main solution approaches. An analytical and numerical comparison with the SIR particle filter is given to illustrate the advantages of the CIPS approach. Part II of the survey is focussed on adapting these algorithms for the problem of reinforcement learning. The survey includes several remarks that describe extensions as well as open problems in this subject.</p></div>","PeriodicalId":50750,"journal":{"name":"Annual Reviews in Control","volume":"55 ","pages":"Pages 356-378"},"PeriodicalIF":9.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49762819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}