Pub Date : 2013-12-10DOI: 10.1109/CDC.2013.6760929
T. N. Dinh, S. Bonnabel, R. Sepulchre
We consider the problem of positive observer design for positive systems. We propose the design of a nonlinear positive observer based on the use of generalized polar coordinates in the positive orthant. The contraction properties of the estimation error are studied thanks to the Hilbert projective metric. The optimization problem of finding the observer gains that maximize the contraction rate is addressed, and the simple two-dimensional case is discussed in detail.
{"title":"Contraction-based design of positive observers","authors":"T. N. Dinh, S. Bonnabel, R. Sepulchre","doi":"10.1109/CDC.2013.6760929","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760929","url":null,"abstract":"We consider the problem of positive observer design for positive systems. We propose the design of a nonlinear positive observer based on the use of generalized polar coordinates in the positive orthant. The contraction properties of the estimation error are studied thanks to the Hilbert projective metric. The optimization problem of finding the observer gains that maximize the contraction rate is addressed, and the simple two-dimensional case is discussed in detail.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127163052","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 : 2013-12-10DOI: 10.1109/CDC.2013.6760698
A. Seuret, P. Menon, C. Edwards
This paper deals with the design of an optimal controller for a set of identical multi-agent systems. The problem under consideration is to examine if there is any benefit to adding to the classical local optimal control law, obtained from solving a Riccati equation, a term which depends on delayed relative information with respect to neighbouring agents. The resulting control law has a local linear feedback term (from solving the Riccati equation) and a consensus-like term which depends on a delayed version of the relative states with respect to its neighbours. The resulting closed loop system at a network level is linear and involves delayed states. A Lyapunov-Krasovskii approach is used to synthesize the gain associated with the consensus term to provide sub-optimal LQR-like performance at a network level. Situations are demonstrated when this approach provides better performance (in terms of the LQR cost) than when a traditional decentralised approach is adopted.
{"title":"LQR performance for multi-agent systems: Benefits of introducing delayed inter-agent measurements","authors":"A. Seuret, P. Menon, C. Edwards","doi":"10.1109/CDC.2013.6760698","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760698","url":null,"abstract":"This paper deals with the design of an optimal controller for a set of identical multi-agent systems. The problem under consideration is to examine if there is any benefit to adding to the classical local optimal control law, obtained from solving a Riccati equation, a term which depends on delayed relative information with respect to neighbouring agents. The resulting control law has a local linear feedback term (from solving the Riccati equation) and a consensus-like term which depends on a delayed version of the relative states with respect to its neighbours. The resulting closed loop system at a network level is linear and involves delayed states. A Lyapunov-Krasovskii approach is used to synthesize the gain associated with the consensus term to provide sub-optimal LQR-like performance at a network level. Situations are demonstrated when this approach provides better performance (in terms of the LQR cost) than when a traditional decentralised approach is adopted.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"119 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131540751","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 : 2013-12-10DOI: 10.1109/CDC.2013.6760990
Sean P. Meyn, P. Barooah, A. Bušić, Jordan Ehren
Renewable energy sources such as wind and solar power have a high degree of unpredictability and time-variation, which makes balancing demand and supply challenging. One possible way to address this challenge is to harness the inherent flexibility in demand of many types of loads. We focus on pool pumps, and how they can be used to provide ancillary service to the grid for maintaining demand-supply balance. A Markovian Decision Process (MDP) model is introduced for an individual pool pump. A randomized control architecture is proposed, motivated by the need for decentralized decision making, and the need to avoid synchronization that can lead to large and detrimental spikes in demand. An aggregate model for a large number of pools is then developed by examining the mean field limit. A key innovation is an LTI-system approximation of the aggregate nonlinear model, with a scalar signal as the input and a measure of the aggregate demand as the output. This makes the approximation particularly convenient for control design at the grid level. Simulations are provided to illustrate the accuracy of the approximations and effectiveness of the proposed control approach.
{"title":"Ancillary service to the grid from deferrable loads: The case for intelligent pool pumps in Florida","authors":"Sean P. Meyn, P. Barooah, A. Bušić, Jordan Ehren","doi":"10.1109/CDC.2013.6760990","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760990","url":null,"abstract":"Renewable energy sources such as wind and solar power have a high degree of unpredictability and time-variation, which makes balancing demand and supply challenging. One possible way to address this challenge is to harness the inherent flexibility in demand of many types of loads. We focus on pool pumps, and how they can be used to provide ancillary service to the grid for maintaining demand-supply balance. A Markovian Decision Process (MDP) model is introduced for an individual pool pump. A randomized control architecture is proposed, motivated by the need for decentralized decision making, and the need to avoid synchronization that can lead to large and detrimental spikes in demand. An aggregate model for a large number of pools is then developed by examining the mean field limit. A key innovation is an LTI-system approximation of the aggregate nonlinear model, with a scalar signal as the input and a measure of the aggregate demand as the output. This makes the approximation particularly convenient for control design at the grid level. Simulations are provided to illustrate the accuracy of the approximations and effectiveness of the proposed control approach.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"113 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129381893","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 : 2013-12-10DOI: 10.1109/CDC.2013.6760064
A. Kibangou, C. Commault
In this paper, we study the observability issue in consensus networks modeled with strongly regular graphs or distance regular graphs. We derive a Kalman-like simple algebraic criterion for observability in distance regular graphs. This criterion consists in evaluating the rank of a matrix built with the components of the Bose-Mesner algebra associated with the considered graph. Then, we state a simple necessary condition of observability based on parameters of the graph, namely the diameter, the degree, and the number of vertices of the graph.
{"title":"Algebraic characterization of observability in distance-regular consensus networks","authors":"A. Kibangou, C. Commault","doi":"10.1109/CDC.2013.6760064","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760064","url":null,"abstract":"In this paper, we study the observability issue in consensus networks modeled with strongly regular graphs or distance regular graphs. We derive a Kalman-like simple algebraic criterion for observability in distance regular graphs. This criterion consists in evaluating the rank of a matrix built with the components of the Bose-Mesner algebra associated with the considered graph. Then, we state a simple necessary condition of observability based on parameters of the graph, namely the diameter, the degree, and the number of vertices of the graph.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"45 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120998324","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 : 2013-12-10DOI: 10.1109/CDC.2013.6761112
U. Khan, Harold M. H. Chong, M. French
Atomic Force Microscopes (AFMs) generate topographic images with nanometer resolution and need little or no sample preparation, however typical operation depends on the proper tuning of a PI controller for vertical nanopositioning. Currently these controllers need to be tuned manually by the end user which reduces their ease of use. Here we develop an automated online Proportional Integral (PI) controller tuning procedure for the control of vertical loop using a multiple model adaptive control (MMAC) approach. The approach is suitable for retro-fitting around an existing PI controller. Preliminary experimental results are presented.
{"title":"Automated controller tuning for Atomic Force Microscopes using Estimation Based Multiple Model Switched Adaptive Control","authors":"U. Khan, Harold M. H. Chong, M. French","doi":"10.1109/CDC.2013.6761112","DOIUrl":"https://doi.org/10.1109/CDC.2013.6761112","url":null,"abstract":"Atomic Force Microscopes (AFMs) generate topographic images with nanometer resolution and need little or no sample preparation, however typical operation depends on the proper tuning of a PI controller for vertical nanopositioning. Currently these controllers need to be tuned manually by the end user which reduces their ease of use. Here we develop an automated online Proportional Integral (PI) controller tuning procedure for the control of vertical loop using a multiple model adaptive control (MMAC) approach. The approach is suitable for retro-fitting around an existing PI controller. Preliminary experimental results are presented.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"222 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122763060","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 : 2013-12-10DOI: 10.1109/CDC.2013.6760094
M. Mahyuddin, G. Herrmann, F. Lewis
A robust distributed adaptive leader-following control for multi-degree-of-freedom (multi-DOF) robot manipulator-type agents is proposed to guarantee finite-time convergence for leader-following tracking and parameter estimation via agent-based estimation and control algorithms. The dynamics of each manipulator agent system of n degrees including the leader agent are assumed unknown. For a specific leader-following network Laplacian, the agents' position, velocity and some switched control information can be fed back to the communication network. In contrast to the current multi-agent literature for robotic manipulators, the proposed approach does not require a priori information of the leader's joint velocity and acceleration to be available to all agents due to the use of agent-based robust adaptive control elements. Due to the multi-DOF character of each agent, matrix theoretical results related to M-matrix theory used for multi-agent systems needs to be extended to the multi-degree context in contrast to recent scalar double integrator results. A simulation example of two-degree of freedom manipulators exemplifies the effectiveness of the approach.
{"title":"Distributed adaptive leader-following control for multi-agent multi-degree manipulators with finite-time guarantees","authors":"M. Mahyuddin, G. Herrmann, F. Lewis","doi":"10.1109/CDC.2013.6760094","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760094","url":null,"abstract":"A robust distributed adaptive leader-following control for multi-degree-of-freedom (multi-DOF) robot manipulator-type agents is proposed to guarantee finite-time convergence for leader-following tracking and parameter estimation via agent-based estimation and control algorithms. The dynamics of each manipulator agent system of n degrees including the leader agent are assumed unknown. For a specific leader-following network Laplacian, the agents' position, velocity and some switched control information can be fed back to the communication network. In contrast to the current multi-agent literature for robotic manipulators, the proposed approach does not require a priori information of the leader's joint velocity and acceleration to be available to all agents due to the use of agent-based robust adaptive control elements. Due to the multi-DOF character of each agent, matrix theoretical results related to M-matrix theory used for multi-agent systems needs to be extended to the multi-degree context in contrast to recent scalar double integrator results. A simulation example of two-degree of freedom manipulators exemplifies the effectiveness of the approach.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"167 10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125974381","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 : 2013-12-10DOI: 10.1109/CDC.2013.6760942
S. Tarbouriech, I. Queinnec, C. Prieur
This paper deals with the stability analysis problem for linear systems with saturation and backlash in the loop. The resulting system controlled by a static output feedback is a dynamical model with nested backlash and saturation operators. Uniform ultimate boundedness stability is tackled in a regional (local) or global context depending on the stability property of the open-loop system. Suitable regions of the state space in which the closed-loop trajectories can be captured are characterized, together with estimates of the basin of attraction of such regions. Convex optimization problems are proposed in order to give a constructive solution (in the sense of theoretical conditions associated to numerical procedures).
{"title":"Stability analysis for systems with saturation and backlash in the loop","authors":"S. Tarbouriech, I. Queinnec, C. Prieur","doi":"10.1109/CDC.2013.6760942","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760942","url":null,"abstract":"This paper deals with the stability analysis problem for linear systems with saturation and backlash in the loop. The resulting system controlled by a static output feedback is a dynamical model with nested backlash and saturation operators. Uniform ultimate boundedness stability is tackled in a regional (local) or global context depending on the stability property of the open-loop system. Suitable regions of the state space in which the closed-loop trajectories can be captured are characterized, together with estimates of the basin of attraction of such regions. Convex optimization problems are proposed in order to give a constructive solution (in the sense of theoretical conditions associated to numerical procedures).","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130042614","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 : 2013-12-10DOI: 10.1109/CDC.2013.6760348
Abeer Al-Gburi, M. French, C. Freeman
Based on the nonlinear gap metric robustness analysis, a study is undertaken for nonlinear systems with input-output linearizing controllers to derive and validate theoretical robustness and performance margins for these systems.
{"title":"Robustness analysis of nonlinear systems with feedback linearizing control","authors":"Abeer Al-Gburi, M. French, C. Freeman","doi":"10.1109/CDC.2013.6760348","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760348","url":null,"abstract":"Based on the nonlinear gap metric robustness analysis, a study is undertaken for nonlinear systems with input-output linearizing controllers to derive and validate theoretical robustness and performance margins for these systems.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125440783","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 : 2013-12-10DOI: 10.1109/CDC.2013.6760004
A. Seuret, F. Gouaisbaut, E. Fridman
This paper considers the stability of systems with fast-varying delay. The novelty of the paper comes from the consideration of a new integral inequality which is proved to be less conservative than the celebrated Jensen's inequality. Based on this new inequality, a dedicated construction of Lyapunov-Krasovskii functionals is proposed and is showed to have a great potential in practice. The method is also combined with an efficient representation of the improved reciprocally convex combination inequality, recently provided in the literature, in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.
{"title":"Stability of systems with fast-varying delay using improved Wirtinger's inequality","authors":"A. Seuret, F. Gouaisbaut, E. Fridman","doi":"10.1109/CDC.2013.6760004","DOIUrl":"https://doi.org/10.1109/CDC.2013.6760004","url":null,"abstract":"This paper considers the stability of systems with fast-varying delay. The novelty of the paper comes from the consideration of a new integral inequality which is proved to be less conservative than the celebrated Jensen's inequality. Based on this new inequality, a dedicated construction of Lyapunov-Krasovskii functionals is proposed and is showed to have a great potential in practice. The method is also combined with an efficient representation of the improved reciprocally convex combination inequality, recently provided in the literature, in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117204700","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 : 2013-12-10DOI: 10.1109/CDC.2013.6759850
D. Boutat, J. Barbot, M. Darouach
This paper supplies a new algorithms to compute the internal dynamics (or inversion dynamics) of affine MIMO control nonlinear systems. This algorithm consider both cases regular or singular characteristic matrix. Furthermore, it provides an extension to a class of nonlinear descriptor systems.
{"title":"A new algorithm to compute inverse dynamic of a class of nonlinear systems","authors":"D. Boutat, J. Barbot, M. Darouach","doi":"10.1109/CDC.2013.6759850","DOIUrl":"https://doi.org/10.1109/CDC.2013.6759850","url":null,"abstract":"This paper supplies a new algorithms to compute the internal dynamics (or inversion dynamics) of affine MIMO control nonlinear systems. This algorithm consider both cases regular or singular characteristic matrix. Furthermore, it provides an extension to a class of nonlinear descriptor systems.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121113687","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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