Pub Date : 2014-08-24DOI: 10.3182/20140824-6-ZA-1003.00722
Angiogenic Inhibition, A. Szeles, D. Drexler, Johanna Sápi, I. Harmati, L. Kovács
Abstract Cancer treatment is one of the most important research fields of modern medicine. In the last decades, targeted molecular therapies showed prosperous results. These treatments achieve tumor regression with limited side-effects. Mathematical models were posed which describe the dynamics of tumor regression under the applied control. The current paper investigates antiangiogenic therapy, which inhibits the tumor to grow its own endothelial capillaries and thus inhibits tumor to grow over a certain size. Many different control approaches were elaborated and published since the model formulation was posed. The aim of this paper is to give an overview of these methods and results, and to review the work carried out by the authors.
{"title":"Study of Modern Control Methodologies Applied to Tumor Growth under","authors":"Angiogenic Inhibition, A. Szeles, D. Drexler, Johanna Sápi, I. Harmati, L. Kovács","doi":"10.3182/20140824-6-ZA-1003.00722","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.00722","url":null,"abstract":"Abstract Cancer treatment is one of the most important research fields of modern medicine. In the last decades, targeted molecular therapies showed prosperous results. These treatments achieve tumor regression with limited side-effects. Mathematical models were posed which describe the dynamics of tumor regression under the applied control. The current paper investigates antiangiogenic therapy, which inhibits the tumor to grow its own endothelial capillaries and thus inhibits tumor to grow over a certain size. Many different control approaches were elaborated and published since the model formulation was posed. The aim of this paper is to give an overview of these methods and results, and to review the work carried out by the authors.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"89 1","pages":"9271-9276"},"PeriodicalIF":0.0,"publicationDate":"2014-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84491864","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 : 2014-08-01DOI: 10.3182/20140824-6-ZA-1003.02781
G. Schwartz, H. Tembine, Saurabh Amin, S. Sastry
Abstract In this paper, we develop a novel mechanism for reducing volatility of residential demand for electricity. We construct a reward-based (rebate) mechanism that provides consumers with incentives to shift their demand to off-peak time. In contrast to most other mechanisms proposed in the literature, the key feature of our mechanism is its modest requirements on user preferences, i.e., it does not require exact knowledge of user responsiveness to rewards for shifting their demand from the peak to the off-peak time. Specifically, our mechanism utilizes a probabilistic reward structure for users who shift their demand to the off-peak time, and is robust to incomplete information about user demand and/or risk preferences. We approach the problem from the public good perspective, and demonstrate that the mechanism can be implemented via lottery-like schemes. Our mechanism permits to reduce the distribution losses, and thus improve efficiency of electricity distribution. Finally, the mechanism can be readily incorporated into the emerging demand response schemes (e.g., the time-of-day pricing, and critical peak pricing schemes), and has security and privacy-preserving properties.
{"title":"Demand response scheme based on lottery-like rebates ?","authors":"G. Schwartz, H. Tembine, Saurabh Amin, S. Sastry","doi":"10.3182/20140824-6-ZA-1003.02781","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.02781","url":null,"abstract":"Abstract In this paper, we develop a novel mechanism for reducing volatility of residential demand for electricity. We construct a reward-based (rebate) mechanism that provides consumers with incentives to shift their demand to off-peak time. In contrast to most other mechanisms proposed in the literature, the key feature of our mechanism is its modest requirements on user preferences, i.e., it does not require exact knowledge of user responsiveness to rewards for shifting their demand from the peak to the off-peak time. Specifically, our mechanism utilizes a probabilistic reward structure for users who shift their demand to the off-peak time, and is robust to incomplete information about user demand and/or risk preferences. We approach the problem from the public good perspective, and demonstrate that the mechanism can be implemented via lottery-like schemes. Our mechanism permits to reduce the distribution losses, and thus improve efficiency of electricity distribution. Finally, the mechanism can be readily incorporated into the emerging demand response schemes (e.g., the time-of-day pricing, and critical peak pricing schemes), and has security and privacy-preserving properties.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"30 1","pages":"4584-4588"},"PeriodicalIF":0.0,"publicationDate":"2014-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89491500","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 : 2014-06-30DOI: 10.3182/20140824-6-ZA-1003.01727
Insoon Yang, M. Morzfeld, C. Tomlin, A. Chorin
Abstract Path integral control solves a class of stochastic optimal control problems with a Monte Carlo (MC) method for an associated Hamilton-Jacobi-Bellman (HJB) equation. The MC approach avoids the need for a global grid of the domain of the HJB equation and, therefore, path integral control is in principle applicable to control problems of moderate to large dimension. The class of problems path integral control can solve, however, is defined by requirements on the cost function, the noise covariance matrix and the control input matrix. We relax the requirements on the cost function by introducing a new state that represents an augmented running cost. In our new formulation the cost function can contain stochastic integral terms and linear control costs, which are important in applications in engineering, economics and finance. We find an efficient numerical implementation of our grid-free MC approach and demonstrate its performance and usefulness in examples from hierarchical electric load management. The dimension of one of our examples is large enough to make classical grid-based HJB solvers impractical.
{"title":"Path Integral Formulation of Stochastic Optimal Control with Generalized Costs","authors":"Insoon Yang, M. Morzfeld, C. Tomlin, A. Chorin","doi":"10.3182/20140824-6-ZA-1003.01727","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.01727","url":null,"abstract":"Abstract Path integral control solves a class of stochastic optimal control problems with a Monte Carlo (MC) method for an associated Hamilton-Jacobi-Bellman (HJB) equation. The MC approach avoids the need for a global grid of the domain of the HJB equation and, therefore, path integral control is in principle applicable to control problems of moderate to large dimension. The class of problems path integral control can solve, however, is defined by requirements on the cost function, the noise covariance matrix and the control input matrix. We relax the requirements on the cost function by introducing a new state that represents an augmented running cost. In our new formulation the cost function can contain stochastic integral terms and linear control costs, which are important in applications in engineering, economics and finance. We find an efficient numerical implementation of our grid-free MC approach and demonstrate its performance and usefulness in examples from hierarchical electric load management. The dimension of one of our examples is large enough to make classical grid-based HJB solvers impractical.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"80 1","pages":"6994-7000"},"PeriodicalIF":0.0,"publicationDate":"2014-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79360624","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 : 2014-06-14DOI: 10.3182/20140824-6-ZA-1003.01525
Yunlei Zou, Jiandong Zhu
Abstract This paper investigates the decomposition with respect to outputs for Boolean control networks (BCNs). Firstly, based on the linear representation of BCNs, some algebraic equivalent conditions are obtained. Secondly, the concept of perfect equal vertex partition (PEVP) is proposed for BCNs. Thirdly, a necessary and sufficient graphical condition based on the PEVP for the decomposability with respect to outputs is obtained. Finally, an equivalent condition of PEVP is derived to help to calculate a PEVP for a BCN.
{"title":"Decomposition with Respect to Outputs for Boolean Control Networks","authors":"Yunlei Zou, Jiandong Zhu","doi":"10.3182/20140824-6-ZA-1003.01525","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.01525","url":null,"abstract":"Abstract This paper investigates the decomposition with respect to outputs for Boolean control networks (BCNs). Firstly, based on the linear representation of BCNs, some algebraic equivalent conditions are obtained. Secondly, the concept of perfect equal vertex partition (PEVP) is proposed for BCNs. Thirdly, a necessary and sufficient graphical condition based on the PEVP for the decomposability with respect to outputs is obtained. Finally, an equivalent condition of PEVP is derived to help to calculate a PEVP for a BCN.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"47 1","pages":"10331-10336"},"PeriodicalIF":0.0,"publicationDate":"2014-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74159143","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 : 2014-04-01DOI: 10.3182/20140824-6-ZA-1003.00341
A. Bishop, A. Doucet
Abstract Distributed consensus in the Wasserstein metric space of probability measures is introduced for the first time in this work. It is shown that convergence of the individual agents' measures to a common measure value is guaranteed so long as a weak network connectivity condition is satisfied asymptotically. The common measure achieved asymptotically at each agent is the one closest simultaneously to all initial agent measures in the sense that it minimises a weighted sum of Wasserstein distances between it and all the initial measures. This algorithm has applicability in the field of distributed estimation.
{"title":"Distributed nonlinear consensus in the space of probability measures","authors":"A. Bishop, A. Doucet","doi":"10.3182/20140824-6-ZA-1003.00341","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.00341","url":null,"abstract":"Abstract Distributed consensus in the Wasserstein metric space of probability measures is introduced for the first time in this work. It is shown that convergence of the individual agents' measures to a common measure value is guaranteed so long as a weak network connectivity condition is satisfied asymptotically. The common measure achieved asymptotically at each agent is the one closest simultaneously to all initial agent measures in the sense that it minimises a weighted sum of Wasserstein distances between it and all the initial measures. This algorithm has applicability in the field of distributed estimation.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"57 1","pages":"8662-8668"},"PeriodicalIF":0.0,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83977804","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 : 2014-03-20DOI: 10.3182/20140824-6-ZA-1003.00632
D. Dolz, D. Quevedo, Ignacio Peñarrocha-Alós, R. Sanchis
This paper addresses the design of a state observer for networked systems with random delays and dropouts. The model of plant and network covers the cases of multiple sensors, out-of-sequence and buffered measurements. The measurement outcomes over a finite interval model the network measurement reception scenarios, which follow a Markov distribution. We present a tractable optimization problem to precalculate off-line a finite set of gains of jump observers. The proposed procedure allows us to trade the complexity of the observer implementation for achieved performance. Several examples illustrate that the on-line computational cost of the observer implementation is lower than that of the Kalman filter, whilst the performance is similar.
{"title":"Performance vs complexity trade-offs for Markovian networked jump estimators","authors":"D. Dolz, D. Quevedo, Ignacio Peñarrocha-Alós, R. Sanchis","doi":"10.3182/20140824-6-ZA-1003.00632","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.00632","url":null,"abstract":"This paper addresses the design of a state observer for networked systems with random delays and dropouts. The model of plant and network covers the cases of multiple sensors, out-of-sequence and buffered measurements. The measurement outcomes over a finite interval model the network measurement reception scenarios, which follow a Markov distribution. We present a tractable optimization problem to precalculate off-line a finite set of gains of jump observers. The proposed procedure allows us to trade the complexity of the observer implementation for achieved performance. Several examples illustrate that the on-line computational cost of the observer implementation is lower than that of the Kalman filter, whilst the performance is similar.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"15 1","pages":"7412-7417"},"PeriodicalIF":0.0,"publicationDate":"2014-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85132838","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 : 2014-03-17DOI: 10.3182/20140824-6-ZA-1003.00361
P. E. Valenzuela, J. Dahlin, C. Rojas, T. Schon
Abstract We propose an extended method for experiment design in nonlinear state space models. The proposed input design technique optimizes a scalar cost function of the information matrix, by computing the optimal stationary probability mass function (pmf) from which an input sequence is sampled. The feasible set of the stationary pmf is a polytope, allowing it to be expressed as a convex combination of its extreme points. The extreme points in the feasible set of pmf's can be computed using graph theory. Therefore, the final information matrix can be approximated as a convex combination of the information matrices associated with each extreme point. For nonlinear systems, the information matrices for each extreme point can be computed by using particle methods. Numerical examples show that the proposed technique can be successfully employed for experiment design in nonlinear systems.
{"title":"A graph/particle-based method for experiment design in nonlinear systems","authors":"P. E. Valenzuela, J. Dahlin, C. Rojas, T. Schon","doi":"10.3182/20140824-6-ZA-1003.00361","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.00361","url":null,"abstract":"Abstract We propose an extended method for experiment design in nonlinear state space models. The proposed input design technique optimizes a scalar cost function of the information matrix, by computing the optimal stationary probability mass function (pmf) from which an input sequence is sampled. The feasible set of the stationary pmf is a polytope, allowing it to be expressed as a convex combination of its extreme points. The extreme points in the feasible set of pmf's can be computed using graph theory. Therefore, the final information matrix can be approximated as a convex combination of the information matrices associated with each extreme point. For nonlinear systems, the information matrices for each extreme point can be computed by using particle methods. Numerical examples show that the proposed technique can be successfully employed for experiment design in nonlinear systems.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"74 1","pages":"1404-1409"},"PeriodicalIF":0.0,"publicationDate":"2014-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80897802","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 : 2014-02-10DOI: 10.3182/20140824-6-ZA-1003.01649
S. Pakazad, A. Hansson, Martin S. Andersen, A. Rantzer
Abstract Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of performing robust stability analysis in a centralized manner, privacy requirements in the network can also introduce further issues. In this paper, we utilize IQC analysis for analyzing large-scale interconnected uncertain systems and we evade these issues by describing a decomposition scheme that is based on the interconnection structure of the system. This scheme is based on the so-called chordal decomposition and does not add any conservativeness to the analysis approach. The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit. We further discuss the merits of the proposed analysis approach using a numerical experiment.
{"title":"Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition","authors":"S. Pakazad, A. Hansson, Martin S. Andersen, A. Rantzer","doi":"10.3182/20140824-6-ZA-1003.01649","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.01649","url":null,"abstract":"Abstract Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of performing robust stability analysis in a centralized manner, privacy requirements in the network can also introduce further issues. In this paper, we utilize IQC analysis for analyzing large-scale interconnected uncertain systems and we evade these issues by describing a decomposition scheme that is based on the interconnection structure of the system. This scheme is based on the so-called chordal decomposition and does not add any conservativeness to the analysis approach. The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit. We further discuss the merits of the proposed analysis approach using a numerical experiment.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"70 1","pages":"2594-2599"},"PeriodicalIF":0.0,"publicationDate":"2014-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90284670","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 : 2014-02-06DOI: 10.3182/20140824-6-ZA-1003.02157
Niklas Wahlstrom, P. Axelsson, F. Gustafsson
Abstract Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems. Discretization of continuous-time models is hence fundamental. We present a novel algorithm using a combination of Lyapunov equations and analytical solutions, enabling efficient implementation in software. The proposed method circumvents numerical problems exhibited by standard algorithms in the literature. Both theoretical and simulation results are provided.
{"title":"Discretizing stochastic dynamical systems using Lyapunov equations","authors":"Niklas Wahlstrom, P. Axelsson, F. Gustafsson","doi":"10.3182/20140824-6-ZA-1003.02157","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.02157","url":null,"abstract":"Abstract Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems. Discretization of continuous-time models is hence fundamental. We present a novel algorithm using a combination of Lyapunov equations and analytical solutions, enabling efficient implementation in software. The proposed method circumvents numerical problems exhibited by standard algorithms in the literature. Both theoretical and simulation results are provided.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"9 1","pages":"3726-3731"},"PeriodicalIF":0.0,"publicationDate":"2014-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90963604","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 : 2014-01-30DOI: 10.3182/20140824-6-ZA-1003.01577
Isak Nielsen, Daniel Axehill
The use of Model Predictive Control is steadily increasing in industry as more complicated problems can be addressed. Due to that online optimization is usually performed, the main bottleneck with Model Predictive Control is the relatively high computational complexity. Hence, much research has been performed to find efficient algorithms that solve the optimization problem. As parallel hardware is becoming more commonly available, the demand of efficient parallel solvers for Model Predictive Control has increased. In this paper, a tailored parallel algorithm that can adopt different levels of parallelism for solving the Newton step is presented. With sufficiently many processing units, it is capable of reducing the computational growth to logarithmic in the prediction horizon. Since the Newton step computation is where most computational effort is spent in both interior-point and active-set solvers, this new algorithm can significantly reduce the computational complexity of highly relevant solvers for Model Predictive Control.
{"title":"An O(log N) Parallel Algorithm for Newton Step Computation in Model Predictive Control","authors":"Isak Nielsen, Daniel Axehill","doi":"10.3182/20140824-6-ZA-1003.01577","DOIUrl":"https://doi.org/10.3182/20140824-6-ZA-1003.01577","url":null,"abstract":"The use of Model Predictive Control is steadily increasing in industry as more complicated problems can be addressed. Due to that online optimization is usually performed, the main bottleneck with Model Predictive Control is the relatively high computational complexity. Hence, much research has been performed to find efficient algorithms that solve the optimization problem. As parallel hardware is becoming more commonly available, the demand of efficient parallel solvers for Model Predictive Control has increased. In this paper, a tailored parallel algorithm that can adopt different levels of parallelism for solving the Newton step is presented. With sufficiently many processing units, it is capable of reducing the computational growth to logarithmic in the prediction horizon. Since the Newton step computation is where most computational effort is spent in both interior-point and active-set solvers, this new algorithm can significantly reduce the computational complexity of highly relevant solvers for Model Predictive Control.","PeriodicalId":13260,"journal":{"name":"IFAC Proceedings Volumes","volume":"21 1","pages":"10505-10511"},"PeriodicalIF":0.0,"publicationDate":"2014-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79208835","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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