Pub Date : 2013-12-01DOI: 10.1109/CDC.2013.6761132
D. Nguyen, G. Yin, Qing Zhang
This work develops with trend following trading strategies under a bull-bear market switching model. The asset model is assumed to be geometric Brownian motion type of process, in which drift of the stock price is allowed to switch between two parameters corresponding to an up-trend (bull market) and a downtrend (bear market) corresponding to a partially observable Markov chain. Our objective is to buy and sell the underlying stock to maximize an expected return. It is shown in [6], [7] that an optimal trading strategy can be obtained in terms of two threshold levels, but finding the threshold levels is a difficult task. In this paper, we develop a stochastic approximation algorithm to approximate the threshold levels. The main advantage of our method is that one need not solve the associated HamiltonJacobiBellman (HJB) equations. We establish the convergence of the algorithm and provide numerical examples to illustrate the results.
{"title":"Trend-following trading using recursive stochastic optimization algorithms","authors":"D. Nguyen, G. Yin, Qing Zhang","doi":"10.1109/CDC.2013.6761132","DOIUrl":"https://doi.org/10.1109/CDC.2013.6761132","url":null,"abstract":"This work develops with trend following trading strategies under a bull-bear market switching model. The asset model is assumed to be geometric Brownian motion type of process, in which drift of the stock price is allowed to switch between two parameters corresponding to an up-trend (bull market) and a downtrend (bear market) corresponding to a partially observable Markov chain. Our objective is to buy and sell the underlying stock to maximize an expected return. It is shown in [6], [7] that an optimal trading strategy can be obtained in terms of two threshold levels, but finding the threshold levels is a difficult task. In this paper, we develop a stochastic approximation algorithm to approximate the threshold levels. The main advantage of our method is that one need not solve the associated HamiltonJacobiBellman (HJB) equations. We establish the convergence of the algorithm and provide numerical examples to illustrate the results.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114637569","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 : 2013-12-01DOI: 10.1109/CDC.2013.6760267
J. Shamma
The setup of learning in networked systems is a collection of decision making components with local information and limited communication interacting to balance a collective objective with local incentives. This talk presents a tutorial overview of learning in such settings from a game theoretic perspective. While game theory is well known for its traditional role as a modeling framework in social sciences, it is seeing growing interest as a design approach for distributed architecture control. In game theoretic learning, the focus shifts away from equilibrium solution concepts and towards the dynamics of how decision makers reach equilibrium. This talk presents a sampling of results in game theoretic learning from its origins as a “descriptive” model for social systems to its “prescriptive” role as an approach to designing networked control. The talk presents also presents various examples from distributed coordination.
{"title":"Learning in networked systems","authors":"J. Shamma","doi":"10.1109/CDC.2013.6760267","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760267","url":null,"abstract":"The setup of learning in networked systems is a collection of decision making components with local information and limited communication interacting to balance a collective objective with local incentives. This talk presents a tutorial overview of learning in such settings from a game theoretic perspective. While game theory is well known for its traditional role as a modeling framework in social sciences, it is seeing growing interest as a design approach for distributed architecture control. In game theoretic learning, the focus shifts away from equilibrium solution concepts and towards the dynamics of how decision makers reach equilibrium. This talk presents a sampling of results in game theoretic learning from its origins as a “descriptive” model for social systems to its “prescriptive” role as an approach to designing networked control. The talk presents also presents various examples from distributed coordination.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116293611","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 : 2013-12-01DOI: 10.1109/CDC.2013.6761115
F. D. Brunner, M. Lazar, F. Allgöwer
This paper proposes a method to obtain stabilizing controllers for constrained linear systems with assigned sets of initial conditions. The controller synthesis method is based on invariant tubes and works for linear time-invariant systems and for linear systems with multiplicative uncertainties. Given a compact initial condition set, a sequence of sets and an associated sequence of control laws is computed such that the initial condition set is contained in the first set of the sequence and every state in any set of the sequence is controlled to the next set in the sequence while satisfying state and input constraints. Assumptions on the parameterizations of the sets and the control laws are given that guarantee recursive feasibility of the tube synthesis problem and convergence of the closed-loop trajectories. For a particular type of parameterization it is shown that these assumptions are satisfied. Numerical simulations are presented that illustrate the developed synthesis method.
{"title":"An explicit solution to constrained stabilization via polytopic tubes","authors":"F. D. Brunner, M. Lazar, F. Allgöwer","doi":"10.1109/CDC.2013.6761115","DOIUrl":"https://doi.org/10.1109/CDC.2013.6761115","url":null,"abstract":"This paper proposes a method to obtain stabilizing controllers for constrained linear systems with assigned sets of initial conditions. The controller synthesis method is based on invariant tubes and works for linear time-invariant systems and for linear systems with multiplicative uncertainties. Given a compact initial condition set, a sequence of sets and an associated sequence of control laws is computed such that the initial condition set is contained in the first set of the sequence and every state in any set of the sequence is controlled to the next set in the sequence while satisfying state and input constraints. Assumptions on the parameterizations of the sets and the control laws are given that guarantee recursive feasibility of the tube synthesis problem and convergence of the closed-loop trajectories. For a particular type of parameterization it is shown that these assumptions are satisfied. Numerical simulations are presented that illustrate the developed synthesis method.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116357299","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 : 2013-12-01DOI: 10.1109/CDC.2013.6760194
H. Fujioka, H. Kano
In this paper, we develop a method for designing optimal smoothing spline with constraints on its derivatives. A linear control system is used as a spline generator. Employing the results developed in the B-spline approach, we show that equality or inequality constraints on spline and its derivative over interval can be expressed as constraint on the control input and initial state of the linear system. Such constraints are useful in trajectory planning problem and in the shape preserving splines as convex splines. Pointwise constraints can easily be incorporated into the control problem. The problem of optimal smoothing splines with such constraints reduce to convex quadratic programming problems. We demonstrate the effectiveness and usefulness by numerical examples of trajectory planning with the constraints on velocity, acceleration and control input.
{"title":"Control theoretic B-spline smoothing with constraints on derivatives","authors":"H. Fujioka, H. Kano","doi":"10.1109/CDC.2013.6760194","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760194","url":null,"abstract":"In this paper, we develop a method for designing optimal smoothing spline with constraints on its derivatives. A linear control system is used as a spline generator. Employing the results developed in the B-spline approach, we show that equality or inequality constraints on spline and its derivative over interval can be expressed as constraint on the control input and initial state of the linear system. Such constraints are useful in trajectory planning problem and in the shape preserving splines as convex splines. Pointwise constraints can easily be incorporated into the control problem. The problem of optimal smoothing splines with such constraints reduce to convex quadratic programming problems. We demonstrate the effectiveness and usefulness by numerical examples of trajectory planning with the constraints on velocity, acceleration and control input.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121562016","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 : 2013-12-01DOI: 10.1109/CDC.2013.6761074
M. K. Bourdoulis, A. Alexandridis
Doubly-Fed Induction Generators (DFIG) are widely used in wind power systems due to their inherent capability of controlling the produced active and reactive power at desired levels, in a large range of wind speeds. In this paper, a nonconventional modeling approach of a DFIG wind system is introduced that permits to control directly the active and reactive power produced. To this end, first, the complete nonlinear dynamic model that contains as states the stator active and reactive power is extracted in the synchronously rotating dq reference frame. Assuming operation under grid voltage reference frame orientation, it is easily shown that the stator power components can be controlled separately through the d- and q-axis rotor voltage inputs. Hence, unlike the complex conventional cascaded controller designs for DFIGs, in this paper, a simple design of proportional controllers for the stator power components is adopted. For this scheme an advanced, Lyapunov-based, stability analysis is conducted that guarantees stable operation and convergence to the equilibrium. This closed-loop scheme is further completed by an outer PI controller design that tracks the rotor speed to the optimum, providing the active power reference for the maximum power point operation. Finally, the analysis and the performance of the closed-loop DFIG wind system are verified through simulation results.
{"title":"An alternative modeling and controller design guaranteeing power stability for DFIG wind systems","authors":"M. K. Bourdoulis, A. Alexandridis","doi":"10.1109/CDC.2013.6761074","DOIUrl":"https://doi.org/10.1109/CDC.2013.6761074","url":null,"abstract":"Doubly-Fed Induction Generators (DFIG) are widely used in wind power systems due to their inherent capability of controlling the produced active and reactive power at desired levels, in a large range of wind speeds. In this paper, a nonconventional modeling approach of a DFIG wind system is introduced that permits to control directly the active and reactive power produced. To this end, first, the complete nonlinear dynamic model that contains as states the stator active and reactive power is extracted in the synchronously rotating dq reference frame. Assuming operation under grid voltage reference frame orientation, it is easily shown that the stator power components can be controlled separately through the d- and q-axis rotor voltage inputs. Hence, unlike the complex conventional cascaded controller designs for DFIGs, in this paper, a simple design of proportional controllers for the stator power components is adopted. For this scheme an advanced, Lyapunov-based, stability analysis is conducted that guarantees stable operation and convergence to the equilibrium. This closed-loop scheme is further completed by an outer PI controller design that tracks the rotor speed to the optimum, providing the active power reference for the maximum power point operation. Finally, the analysis and the performance of the closed-loop DFIG wind system are verified through simulation results.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121574860","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 : 2013-12-01DOI: 10.1109/CDC.2013.6760795
Seung-Hi Lee, C. Chung
An innovative approximate explicit model predictive control strategy is proposed. A multilevel approximation scheme for state space partitioning is applied, which relies on an adaptive domain decomposition strategy using multidimensional tree techniques. Polytopes are generated from such state space partitioning, for which equivalent state feedback gains are computed such that approximate explicit controls can be simply computed. The proposed scheme requires no online optimization and thus computing control using pre-computed control gains is extremely fast. Through an application to autonomous vehicle lateral control, it is shown that the proposed method can achieve a significant improvement of computation time and approximation quality over other approximate predictive control methods.
{"title":"Multilevel approximate model predictive control and its application to autonomous vehicle active steering","authors":"Seung-Hi Lee, C. Chung","doi":"10.1109/CDC.2013.6760795","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760795","url":null,"abstract":"An innovative approximate explicit model predictive control strategy is proposed. A multilevel approximation scheme for state space partitioning is applied, which relies on an adaptive domain decomposition strategy using multidimensional tree techniques. Polytopes are generated from such state space partitioning, for which equivalent state feedback gains are computed such that approximate explicit controls can be simply computed. The proposed scheme requires no online optimization and thus computing control using pre-computed control gains is extremely fast. Through an application to autonomous vehicle lateral control, it is shown that the proposed method can achieve a significant improvement of computation time and approximation quality over other approximate predictive control methods.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"2018 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121576773","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 : 2013-12-01DOI: 10.1109/CDC.2013.6761097
Xavier David-Henriet, L. Hardouin, J. Raisch, Bertrand Cottenceau
Timed event graphs (TEGs) are a subclass of timed Petri nets suitable to model decision-free timed discrete event systems. In classical TEGs, exact synchronization of two transitions T1 and T2 is available by requiring that transitions T1 and T2 fire simultaneously. In this paper, a new sort of synchronization, namely partial synchronization, is introduced: transition T2 has to fire when transition T1 fires, but transition T1 is not influenced by transition T2. Under some assumptions, optimal control, already available for classical TEGs, is extended to TEGs under partial synchronization.
{"title":"Optimal control for timed event graphs under partial synchronization","authors":"Xavier David-Henriet, L. Hardouin, J. Raisch, Bertrand Cottenceau","doi":"10.1109/CDC.2013.6761097","DOIUrl":"https://doi.org/10.1109/CDC.2013.6761097","url":null,"abstract":"Timed event graphs (TEGs) are a subclass of timed Petri nets suitable to model decision-free timed discrete event systems. In classical TEGs, exact synchronization of two transitions T<sub>1</sub> and T<sub>2</sub> is available by requiring that transitions T<sub>1</sub> and T<sub>2</sub> fire simultaneously. In this paper, a new sort of synchronization, namely partial synchronization, is introduced: transition T<sub>2</sub> has to fire when transition T<sub>1</sub> fires, but transition T<sub>1</sub> is not influenced by transition T<sub>2</sub>. Under some assumptions, optimal control, already available for classical TEGs, is extended to TEGs under partial synchronization.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121740954","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 : 2013-12-01DOI: 10.1109/CDC.2013.6760213
D. Tavernini, E. Velenis, R. Lot, M. Massaro
The aim of this paper is to investigate the optimality of the handbrake cornering technique for a Front Wheel Drive vehicle. Nonlinear Optimal Control theory is used to formulate the problem of optimal cornering and to simulate manoeuvres used by race drivers. Handbrake cornering is optimal with an appropriate selection of the minimization cost. The optimal solution is validated against data collected during the execution of the technique by an expert race driver on a loose off-road surface. Further optimization results considering high adhesion road surface are obtained to show that the optimality of the technique is not affected by the road conditions.
{"title":"On the optimality of handbrake cornering","authors":"D. Tavernini, E. Velenis, R. Lot, M. Massaro","doi":"10.1109/CDC.2013.6760213","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760213","url":null,"abstract":"The aim of this paper is to investigate the optimality of the handbrake cornering technique for a Front Wheel Drive vehicle. Nonlinear Optimal Control theory is used to formulate the problem of optimal cornering and to simulate manoeuvres used by race drivers. Handbrake cornering is optimal with an appropriate selection of the minimization cost. The optimal solution is validated against data collected during the execution of the technique by an expert race driver on a loose off-road surface. Further optimization results considering high adhesion road surface are obtained to show that the optimality of the technique is not affected by the road conditions.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114701907","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 : 2013-12-01DOI: 10.1109/CDC.2013.6760644
S. Ahuja, S. Peles
Energy efficient retrofits of existing buildings present an immediate and large opportunity to reduce the energy footprint of the built infrastructure, which consumes nearly 40% of primary energy consumption in the U.S. and worldwide. Whole building energy modeling and simulation tools are increasingly being used for detailed performance analysis and for evaluation of multiple retrofit design options. However, the models typically involve several hundreds of input parameters and processes (e.g. weather and occupancy schedules) that are uncertain in early stages of design, and are not fully understood until after retrofit installation and commissioning. We present tools for sensitivity analysis and uncertainty quantification of such building energy models that help designers understand the key drivers to energy consumption and estimate error bounds on predicted energy savings. The focus is on quantifying uncertainties due to stochastic processes, such as weather conditions and schedules of occupants, which are modeled using a Karhunen-Loève expansion.
{"title":"Building energy models: Quantifying uncertainties due to stochastic processes","authors":"S. Ahuja, S. Peles","doi":"10.1109/CDC.2013.6760644","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760644","url":null,"abstract":"Energy efficient retrofits of existing buildings present an immediate and large opportunity to reduce the energy footprint of the built infrastructure, which consumes nearly 40% of primary energy consumption in the U.S. and worldwide. Whole building energy modeling and simulation tools are increasingly being used for detailed performance analysis and for evaluation of multiple retrofit design options. However, the models typically involve several hundreds of input parameters and processes (e.g. weather and occupancy schedules) that are uncertain in early stages of design, and are not fully understood until after retrofit installation and commissioning. We present tools for sensitivity analysis and uncertainty quantification of such building energy models that help designers understand the key drivers to energy consumption and estimate error bounds on predicted energy savings. The focus is on quantifying uncertainties due to stochastic processes, such as weather conditions and schedules of occupants, which are modeled using a Karhunen-Loève expansion.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114717638","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 : 2013-12-01DOI: 10.1109/CDC.2013.6761104
J. Tani, Sandipan Mishra, J. Wen
This paper demonstrates the use of a slow-rate image sensor for control of a fast-rate beam steering system. The image sensor is modeled as an integrative intensity sensor, from which fast-rate dynamics may be estimated by appropriate motion-field extraction. These fast-rate state estimates obtained from the slow-rate image sensor are then used for a multirate model-following controller that achieves desired performance through state-matching. This is in contrast to traditional control schemes for fast-rate systems with image sensors, which rely on the slow-rate time-averaged output measurement during the exposure time of the image sensor (i.e., the first spatial moment of the acquired image), discarding the image blur as noise. We demonstrate that the proposed multirate feedback controller, which uses the entire intensity distribution at the image sensor, provides superior tracking performance than a similar multirate controller that uses only the first moment of the image (time-averaged output) as feedback measurements.
{"title":"On multirate control of a fast-rate beam steering system using slow-rate image sensor feedback","authors":"J. Tani, Sandipan Mishra, J. Wen","doi":"10.1109/CDC.2013.6761104","DOIUrl":"https://doi.org/10.1109/CDC.2013.6761104","url":null,"abstract":"This paper demonstrates the use of a slow-rate image sensor for control of a fast-rate beam steering system. The image sensor is modeled as an integrative intensity sensor, from which fast-rate dynamics may be estimated by appropriate motion-field extraction. These fast-rate state estimates obtained from the slow-rate image sensor are then used for a multirate model-following controller that achieves desired performance through state-matching. This is in contrast to traditional control schemes for fast-rate systems with image sensors, which rely on the slow-rate time-averaged output measurement during the exposure time of the image sensor (i.e., the first spatial moment of the acquired image), discarding the image blur as noise. We demonstrate that the proposed multirate feedback controller, which uses the entire intensity distribution at the image sensor, provides superior tracking performance than a similar multirate controller that uses only the first moment of the image (time-averaged output) as feedback measurements.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"182 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114742032","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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