Pub Date : 1900-01-01DOI: 10.1137/1.9781611974072.6
M. Cantoni, Chung-Yao Kao
The stability and performance of distributed-parameter systems operating under periodic sampled-data feedback control is studied via integral-quadratic constraint (IQC) based analysis. Sufficient frequency-domain conditions are derived for verifying a specified bound on the L2-gain of the feedback interconnection of a plant with (irrational) Callier-Desoer class transfer function and a feedback controller obtained via the periodic sample-and-hold discretization of a finitedimensional LTI controller. The analysis is underpinned by a time-varying delay model of the sample-and-hold operation and IQC characterizations of a related system. An illustrative numerial example involving the control of a linear system of hyperbolic conservation laws is presented.
{"title":"Frequency-domain performance analysis of distributed-parameter systems under periodic sampled-data feedback control","authors":"M. Cantoni, Chung-Yao Kao","doi":"10.1137/1.9781611974072.6","DOIUrl":"https://doi.org/10.1137/1.9781611974072.6","url":null,"abstract":"The stability and performance of distributed-parameter systems operating under periodic sampled-data feedback control is studied via integral-quadratic constraint (IQC) based analysis. Sufficient frequency-domain conditions are derived for verifying a specified bound on the L2-gain of the feedback interconnection of a plant with (irrational) Callier-Desoer class transfer function and a feedback controller obtained via the periodic sample-and-hold discretization of a finitedimensional LTI controller. The analysis is underpinned by a time-varying delay model of the sample-and-hold operation and IQC characterizations of a related system. An illustrative numerial example involving the control of a linear system of hyperbolic conservation laws is presented.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131734450","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 : 1900-01-01DOI: 10.1137/1.9781611974072.40
A. Cherukuri, Enrique Mallada, J. Cortés
This paper characterizes the asymptotic convergence properties of the primal-dual dynamics to the solutions of a constrained concave optimization problem using classical notions from stability analysis. We motivate our study by providing an example which rules out the possibility of employing the invariance principle for hybrid automata to analyze the asymptotic convergence. We understand the solutions of the primal-dual dynamics in the Caratheodory sense and establish their existence, uniqueness, and continuity with respect to the initial conditions. We employ the invariance principle for Caratheodory solutions of a discontinuous dynamical system to show that the primal-dual optimizers are globally asymptotically stable under the primal-dual dynamics and that each solution of the dynamics converges to an optimizer.
{"title":"Convergence of Caratheodory solutions for primal-dual dynamics in constrained concave optimization","authors":"A. Cherukuri, Enrique Mallada, J. Cortés","doi":"10.1137/1.9781611974072.40","DOIUrl":"https://doi.org/10.1137/1.9781611974072.40","url":null,"abstract":"This paper characterizes the asymptotic convergence properties of the primal-dual dynamics to the solutions of a constrained concave optimization problem using classical notions from stability analysis. We motivate our study by providing an example which rules out the possibility of employing the invariance principle for hybrid automata to analyze the asymptotic convergence. We understand the solutions of the primal-dual dynamics in the Caratheodory sense and establish their existence, uniqueness, and continuity with respect to the initial conditions. We employ the invariance principle for Caratheodory solutions of a discontinuous dynamical system to show that the primal-dual optimizers are globally asymptotically stable under the primal-dual dynamics and that each solution of the dynamics converges to an optimizer.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"71 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120851983","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 : 1900-01-01DOI: 10.1137/1.9781611974072.23
Tao Pang, Azmat Hussain
We consider a stochastic portfolio optimization model in which the returns of risky asset depend on its past performance. The price of the risky asset is described by a stochastic delay differential equation. The investor’s goal is to maximize the expected discounted utility by choosing optimal investment and consumption as controls. We use the functional Ito’s formula to derive the associated HamiltonJacobi-Bellman equation. For logarithmic and exponential utility functions, we can obtain explicit solutions in a finite dimensional space.
{"title":"An Application of Functional Ito's Formula to Stochastic Portfolio Optimization with Bounded Memory","authors":"Tao Pang, Azmat Hussain","doi":"10.1137/1.9781611974072.23","DOIUrl":"https://doi.org/10.1137/1.9781611974072.23","url":null,"abstract":"We consider a stochastic portfolio optimization model in which the returns of risky asset depend on its past performance. The price of the risky asset is described by a stochastic delay differential equation. The investor’s goal is to maximize the expected discounted utility by choosing optimal investment and consumption as controls. We use the functional Ito’s formula to derive the associated HamiltonJacobi-Bellman equation. For logarithmic and exponential utility functions, we can obtain explicit solutions in a finite dimensional space.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132324291","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 : 1900-01-01DOI: 10.1137/1.9781611974072.16
A. Cortés, S. Martínez
We present a novel algorithm for the computation of optimal predictive storage and reactive power control in microgrids. This algorithm is based on the dual decomposition approach, but takes care of the local constraints by means of primal projections. This significantly increases the speed of convergence. Further, we show the convergence of the algorithm to an optimizer for a more general class of quadratic programs that includes the storage and reactive power control problem Then, we present a distributed way of implementing the algorithm which is based on the Jacobi overrelaxation. Simulations compare the algorithm performance with that of a purely dual decomposition approach, in a set of different microgrid testbeds.
{"title":"A Projection-based Dual Algorithm for Fast Computation of Control in Microgrids","authors":"A. Cortés, S. Martínez","doi":"10.1137/1.9781611974072.16","DOIUrl":"https://doi.org/10.1137/1.9781611974072.16","url":null,"abstract":"We present a novel algorithm for the computation of optimal predictive storage and reactive power control in microgrids. This algorithm is based on the dual decomposition approach, but takes care of the local constraints by means of primal projections. This significantly increases the speed of convergence. Further, we show the convergence of the algorithm to an optimizer for a more general class of quadratic programs that includes the storage and reactive power control problem Then, we present a distributed way of implementing the algorithm which is based on the Jacobi overrelaxation. Simulations compare the algorithm performance with that of a purely dual decomposition approach, in a set of different microgrid testbeds.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113954127","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 : 1900-01-01DOI: 10.1137/1.9781611974072.5
P. Gutman, I. Ioslovich, Shai Moshenberg
Optimal control problems of rigid body precise movement minimal time optimality and minimal energy optimality are considered as competing approaches for trajectory planning. We investigate here theoretical and simulation results showing that, with appropriate choice of constraints, these approaches are equivalent in the sense that they produce the same trajectory. The optimal control solver DIDO was used as a numerical tool.
{"title":"On the Optimal Control of the Rigid Body Precise Movement: Is Energy Optimality the Same As Time Optimality?","authors":"P. Gutman, I. Ioslovich, Shai Moshenberg","doi":"10.1137/1.9781611974072.5","DOIUrl":"https://doi.org/10.1137/1.9781611974072.5","url":null,"abstract":"Optimal control problems of rigid body precise movement minimal time optimality and minimal energy optimality are considered as competing approaches for trajectory planning. We investigate here theoretical and simulation results showing that, with appropriate choice of constraints, these approaches are equivalent in the sense that they produce the same trajectory. The optimal control solver DIDO was used as a numerical tool.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134014794","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 : 1900-01-01DOI: 10.1137/1.9781611973273.18
C. Somarakis, J. Baras
The problem of continuous linear time varying consensus dynamics is addressed in the presence of constant communication delays. We make a Fixed Point Theory argument with the use of contraction mappings and we state sufficient conditions for exponential convergence to a consensus value with prescribed convergence rate.
{"title":"Fixed Point Theory Approach to Exponential Convergence in LTV Continuous Time Consensus Dynamics with Delays","authors":"C. Somarakis, J. Baras","doi":"10.1137/1.9781611973273.18","DOIUrl":"https://doi.org/10.1137/1.9781611973273.18","url":null,"abstract":"The problem of continuous linear time varying consensus dynamics is addressed in the presence of constant communication delays. We make a Fixed Point Theory argument with the use of contraction mappings and we state sufficient conditions for exponential convergence to a consensus value with prescribed convergence rate.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124681479","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 : 1900-01-01DOI: 10.1137/1.9781611973273.17
Solmaz S. Kia, J. Cortés, S. Martínez
This paper considers the static average consensus problem for a multi-agent system and proposes a distributed algorithm that enables individual agents to set their own rate of convergence. The algorithm has a two-time scale structure and is constructed using a singular perturbation approach. A fast information processing state uses a Laplacian consensus strategy to calculate the agreement value in a distributed manner. The slow-time dynamic part, termed motion phase, allows each agent to move towards the agreement point at its own desired speed. We provide a complete analysis of the proposed consensus algorithm. This covers the rate of convergence of individual agents, effects of communication delays, robustness to changes in the network topology, implementation in discrete time, and performance guarantees under limited control authority. Our analysis is based on tools from matrix theory, algebraic graph theory and stability analysis. Numerical examples illustrate the benefits of the proposed algorithm.
{"title":"Saturation-tolerant average consensus with controllable rates of convergence","authors":"Solmaz S. Kia, J. Cortés, S. Martínez","doi":"10.1137/1.9781611973273.17","DOIUrl":"https://doi.org/10.1137/1.9781611973273.17","url":null,"abstract":"This paper considers the static average consensus problem for a multi-agent system and proposes a distributed algorithm that enables individual agents to set their own rate of convergence. The algorithm has a two-time scale structure and is constructed using a singular perturbation approach. A fast information processing state uses a Laplacian consensus strategy to calculate the agreement value in a distributed manner. The slow-time dynamic part, termed motion phase, allows each agent to move towards the agreement point at its own desired speed. We provide a complete analysis of the proposed consensus algorithm. This covers the rate of convergence of individual agents, effects of communication delays, robustness to changes in the network topology, implementation in discrete time, and performance guarantees under limited control authority. Our analysis is based on tools from matrix theory, algebraic graph theory and stability analysis. Numerical examples illustrate the benefits of the proposed algorithm.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127291544","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 : 1900-01-01DOI: 10.1137/1.9781611974072.61
Xiaowei Zhao, G. Weiss
We study the vibration reduction of the non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) model representing a vertical beam clamped at the bottom, with a rigid body having a large mass on top, using a Tuned Mass Damper (TMD). The TMD is a heavy trolley mounted on top of the rigid body, connected to the rigid body via a spring and a damper. Such an arrangement is used to stabilize tall buildings. Using our recent well-posedness and strong stabilization results for coupled impedance passive linear time-invariant systems (possibly infinite-dimensional), we show the following: The SCOLE system with the trolley is well-posed and regular on the energy state space with the force or torque acting on the rigid body as input and with the speed or angular velocity of the rigid body as output, and this system is strongly stable on the energy state space.
{"title":"Strong stabilization of the SCOLE model using a tuned mass damper","authors":"Xiaowei Zhao, G. Weiss","doi":"10.1137/1.9781611974072.61","DOIUrl":"https://doi.org/10.1137/1.9781611974072.61","url":null,"abstract":"We study the vibration reduction of the non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) model representing a vertical beam clamped at the bottom, with a rigid body having a large mass on top, using a Tuned Mass Damper (TMD). The TMD is a heavy trolley mounted on top of the rigid body, connected to the rigid body via a spring and a damper. Such an arrangement is used to stabilize tall buildings. Using our recent well-posedness and strong stabilization results for coupled impedance passive linear time-invariant systems (possibly infinite-dimensional), we show the following: The SCOLE system with the trolley is well-posed and regular on the energy state space with the force or torque acting on the rigid body as input and with the speed or angular velocity of the rigid body as output, and this system is strongly stable on the energy state space.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115683791","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 : 1900-01-01DOI: 10.1137/1.9781611974072.66
A. Murray, A. MacIsaac
In this paper, a model is formulated that modifies the Sethi model of advertising optimization to incorporate unique features present in the mobile game space. Although the optimization of advertising in traditional industries has been thoroughly studied, the optimization models used lack sufficient predictive power for several emerging market sectors. For the free-to-play video game industry in particular, there are issues that arise in the form of uncertain revenue from users and the effect of the ranking systems used for these games. This paper compares the modified and original Sethi models and it is shown how little or no advertising in the video game industry can still result in a large market share given sufficient virality parameters for the game.
{"title":"Extension of the Sethi Model to the Advertising of Digital Products","authors":"A. Murray, A. MacIsaac","doi":"10.1137/1.9781611974072.66","DOIUrl":"https://doi.org/10.1137/1.9781611974072.66","url":null,"abstract":"In this paper, a model is formulated that modifies the Sethi model of advertising optimization to incorporate unique features present in the mobile game space. Although the optimization of advertising in traditional industries has been thoroughly studied, the optimization models used lack sufficient predictive power for several emerging market sectors. For the free-to-play video game industry in particular, there are issues that arise in the form of uncertain revenue from users and the effect of the ranking systems used for these games. This paper compares the modified and original Sethi models and it is shown how little or no advertising in the video game industry can still result in a large market share given sufficient virality parameters for the game.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115395185","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 : 1900-01-01DOI: 10.1137/1.9781611974072.32
C. Ho, P. Parpas
Multiscale Markov processes are used to model and control stochastic dynamics across different scales in many applications areas such as electrical engineering, finance, and material science. A commonly used mathematical representation that captures multiscale stochastic dynamics is that of singularly perturbed Markov processes. Dimensionality reductions techniques for this class of stochastic optimal control problems have been studied for many years. However, it is typically assumed that the structure of perturbed process and its dynamics are known. In this paper, we show how to infer the structure of a singularly perturbed Markov process from data. We propose a measure of similarity for the different states of the Markov process and then use techniques from spectral graph theory to show that the perturbed structure can be obtained by looking at the spectrum of a graph defined on the proposed similarity matrix.
{"title":"On Using Spectral Graph Theory to Infer the Structure of Multiscale Markov Processes","authors":"C. Ho, P. Parpas","doi":"10.1137/1.9781611974072.32","DOIUrl":"https://doi.org/10.1137/1.9781611974072.32","url":null,"abstract":"Multiscale Markov processes are used to model and control stochastic dynamics across different scales in many applications areas such as electrical engineering, finance, and material science. A commonly used mathematical representation that captures multiscale stochastic dynamics is that of singularly perturbed Markov processes. Dimensionality reductions techniques for this class of stochastic optimal control problems have been studied for many years. However, it is typically assumed that the structure of perturbed process and its dynamics are known. In this paper, we show how to infer the structure of a singularly perturbed Markov process from data. We propose a measure of similarity for the different states of the Markov process and then use techniques from spectral graph theory to show that the perturbed structure can be obtained by looking at the spectrum of a graph defined on the proposed similarity matrix.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122108446","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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