Pub Date : 2014-12-15DOI: 10.1109/CDC.2014.7039825
Ying Tang, C. Prieur, A. Girard
In this paper, we consider the problem of boundary control of a class of linear hyperbolic systems of conservation laws based on the singular perturbation method. The full hyperbolic system is written as two subsystems, namely the reduced system representing the slow dynamics and the boundary-layer system standing for the fast dynamics. By choosing the boundary conditions for the reduced system as zero, the slow dynamics is stabilized in finite time. The main result is illustrated with a design of boundary control for a linearized Saint-Venant-Exner system. The stabilization of the full system is achieved with different boundary conditions for the fast dynamics.
{"title":"Boundary control synthesis for hyperbolic systems: A singular perturbation approach","authors":"Ying Tang, C. Prieur, A. Girard","doi":"10.1109/CDC.2014.7039825","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039825","url":null,"abstract":"In this paper, we consider the problem of boundary control of a class of linear hyperbolic systems of conservation laws based on the singular perturbation method. The full hyperbolic system is written as two subsystems, namely the reduced system representing the slow dynamics and the boundary-layer system standing for the fast dynamics. By choosing the boundary conditions for the reduced system as zero, the slow dynamics is stabilized in finite time. The main result is illustrated with a design of boundary control for a linearized Saint-Venant-Exner system. The stabilization of the full system is achieved with different boundary conditions for the fast dynamics.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121434866","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 : 2014-12-15DOI: 10.1109/CDC.2014.7039994
H. Ríos, D. Efimov, L. Fridman, J. Moreno, W. Perruquetti
The uniform stability notion for a class of nonlinear time-varying systems is studied using the homogeneity framework. It is assumed that the system is weighted homogeneous considering the time variable as a constant parameter, then several conditions of uniform stability for such a class of systems are formulated. The results are applied to the problem of adaptive estimation for a linear system.
{"title":"Uniform stability analysis for time-varying systems applying homogeneity","authors":"H. Ríos, D. Efimov, L. Fridman, J. Moreno, W. Perruquetti","doi":"10.1109/CDC.2014.7039994","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039994","url":null,"abstract":"The uniform stability notion for a class of nonlinear time-varying systems is studied using the homogeneity framework. It is assumed that the system is weighted homogeneous considering the time variable as a constant parameter, then several conditions of uniform stability for such a class of systems are formulated. The results are applied to the problem of adaptive estimation for a linear system.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134435984","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 : 2014-12-15DOI: 10.1109/CDC.2014.7039680
Lichun Li, J. Shamma
This paper provides an efficient linear programming (LP) formulation of asymmetric two player zero-sum stochastic games with finite horizon. In these stochastic games, only one player is informed of the state at each stage, and the transition law is only controlled by the informed player. Compared with the LP formulation of extensive stochastic games whose size grows polynomially with respect to the size of the state and the size of the uninformed player's actions, our proposed LP formulation has its size to be linear with respect to the size of the state and the size of the uninformed player, and hence greatly reduces the computational complexity. A travelling inspector problem is used to demonstrate the efficiency of the proposed LP formulation.
{"title":"LP formulation of asymmetric zero-sum stochastic games","authors":"Lichun Li, J. Shamma","doi":"10.1109/CDC.2014.7039680","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039680","url":null,"abstract":"This paper provides an efficient linear programming (LP) formulation of asymmetric two player zero-sum stochastic games with finite horizon. In these stochastic games, only one player is informed of the state at each stage, and the transition law is only controlled by the informed player. Compared with the LP formulation of extensive stochastic games whose size grows polynomially with respect to the size of the state and the size of the uninformed player's actions, our proposed LP formulation has its size to be linear with respect to the size of the state and the size of the uninformed player, and hence greatly reduces the computational complexity. A travelling inspector problem is used to demonstrate the efficiency of the proposed LP formulation.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129350397","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 : 2014-12-15DOI: 10.1109/CDC.2014.7039423
D. Bresch-Pietri, N. Petit
We investigate the design of a prediction-based controller for a linear system subject to a time-varying input delay, not necessarily causal. This means that the information feeding the system can be older than ones previously received. We propose to use the current delay value in the prediction employed in the control law. Modeling the input delay as a transport Partial Differential Equation, we prove asymptotic tracking of the system state, providing that the average ℒ2-norm of the delay time-derivative is sufficiently small. This result is obtained by generalizing Halanay inequality to time-varying differential inequalities.
{"title":"Robust compensation of a chattering time-varying input delay","authors":"D. Bresch-Pietri, N. Petit","doi":"10.1109/CDC.2014.7039423","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039423","url":null,"abstract":"We investigate the design of a prediction-based controller for a linear system subject to a time-varying input delay, not necessarily causal. This means that the information feeding the system can be older than ones previously received. We propose to use the current delay value in the prediction employed in the control law. Modeling the input delay as a transport Partial Differential Equation, we prove asymptotic tracking of the system state, providing that the average ℒ2-norm of the delay time-derivative is sufficiently small. This result is obtained by generalizing Halanay inequality to time-varying differential inequalities.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"597 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116238389","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 : 2014-12-15DOI: 10.1109/CDC.2014.7040071
Olivier Huber, Vincent Acary, B. Brogliato, F. Plestan
In this note, we present an implementation of the twisting controller on an electropneumatic plant for a tracking control problem. Implicit and explicit discrete-time twisting controllers are considered, and some implementation details are provided. Experimental results are provided and analyzed. They sustain the theoretical superiority of the implicitly discretized version, as shown in previous work. The main advantages of the implicit method are better tracking and drastic reduction in the input and output chattering. This is achieved without modifying the controller structure compared to its continuous-time version.
{"title":"Discrete-time twisting controller without numerical chattering: analysis and experimental results with an implicit method","authors":"Olivier Huber, Vincent Acary, B. Brogliato, F. Plestan","doi":"10.1109/CDC.2014.7040071","DOIUrl":"https://doi.org/10.1109/CDC.2014.7040071","url":null,"abstract":"In this note, we present an implementation of the twisting controller on an electropneumatic plant for a tracking control problem. Implicit and explicit discrete-time twisting controllers are considered, and some implementation details are provided. Experimental results are provided and analyzed. They sustain the theoretical superiority of the implicitly discretized version, as shown in previous work. The main advantages of the implicit method are better tracking and drastic reduction in the input and output chattering. This is achieved without modifying the controller structure compared to its continuous-time version.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123547976","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 : 2014-12-15DOI: 10.1109/CDC.2014.7039682
K. K. Kim, J. Shamma
This paper considers multi-agent sequential hypothesis testing and presents a framework for strategic learning in sequential games with explicit consideration of both temporal and spatial coordination. The associated Bayes risk functions explicitly incorporate costs of taking private/public measurements, costs of time-difference and disagreement in actions of agents, and costs of false declaration/choices in the sequential hypothesis testing. The corresponding sequential decision processes have well-defined value functions with respect to (a) the belief states for the case of conditional independent private noisy measurements that are also assumed to be independent identically distributed over time, and (b) the information states for the case of correlated private noisy measurements. A sequential investment game of strategic coordination and delay is also discussed as an application of the proposed strategic learning rules.
{"title":"Multi-agent sequential hypothesis testing","authors":"K. K. Kim, J. Shamma","doi":"10.1109/CDC.2014.7039682","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039682","url":null,"abstract":"This paper considers multi-agent sequential hypothesis testing and presents a framework for strategic learning in sequential games with explicit consideration of both temporal and spatial coordination. The associated Bayes risk functions explicitly incorporate costs of taking private/public measurements, costs of time-difference and disagreement in actions of agents, and costs of false declaration/choices in the sequential hypothesis testing. The corresponding sequential decision processes have well-defined value functions with respect to (a) the belief states for the case of conditional independent private noisy measurements that are also assumed to be independent identically distributed over time, and (b) the information states for the case of correlated private noisy measurements. A sequential investment game of strategic coordination and delay is also discussed as an application of the proposed strategic learning rules.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"324 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130004132","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 : 2014-12-15DOI: 10.1109/CDC.2014.7039356
D. Efimov, A. Polyakov, W. Perruquetti, J. Richard
Global delay independent stability is analyzed for nonlinear time-delay systems applying homogeneity theory. The results of [1] are extended to the case of non-zero degree of homogeneity. Several tools for stability analysis in time-delay systems using homogeneity are presented: in particular, it is shown that if a time-delay system is homogeneous with nonzero degree and it is globally asymptotically stable for some delay, then this property is preserved for any delay value, which is known as the independent of delay (IOD) stability. The results are illustrated by numerical experiments.
{"title":"Stability analysis for nonlinear time-delay systems applying homogeneity","authors":"D. Efimov, A. Polyakov, W. Perruquetti, J. Richard","doi":"10.1109/CDC.2014.7039356","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039356","url":null,"abstract":"Global delay independent stability is analyzed for nonlinear time-delay systems applying homogeneity theory. The results of [1] are extended to the case of non-zero degree of homogeneity. Several tools for stability analysis in time-delay systems using homogeneity are presented: in particular, it is shown that if a time-delay system is homogeneous with nonzero degree and it is globally asymptotically stable for some delay, then this property is preserved for any delay value, which is known as the independent of delay (IOD) stability. The results are illustrated by numerical experiments.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"427 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121577672","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 : 2014-12-15DOI: 10.1109/CDC.2014.7039616
M. Fiacchini, I. Morǎrescu
In this paper we give tractable necessary and sufficient condition for the global exponential stability of a linear impulsive system. The reset rule considered in the paper is quasi-periodic and the stability analysis is based on a standard tool in set theory that is Minkowski functional. Firstly, we reformulate the problem in term of discrete-time parametric uncertain system with the state matrix belonging to a compact but non-convex set. Secondly, we provide a tractable algorithm for testing the stability and computing the associated polyhedral Lyapunov function when the system is stable. The main result is an algorithm whose computational effort is analogous to that of classical algorithms for contractive polytopes computation for discrete-time parametric uncertain systems with the state matrix belonging to a polytopic set.
{"title":"Set theory conditions for stability of linear impulsive systems","authors":"M. Fiacchini, I. Morǎrescu","doi":"10.1109/CDC.2014.7039616","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039616","url":null,"abstract":"In this paper we give tractable necessary and sufficient condition for the global exponential stability of a linear impulsive system. The reset rule considered in the paper is quasi-periodic and the stability analysis is based on a standard tool in set theory that is Minkowski functional. Firstly, we reformulate the problem in term of discrete-time parametric uncertain system with the state matrix belonging to a compact but non-convex set. Secondly, we provide a tractable algorithm for testing the stability and computing the associated polyhedral Lyapunov function when the system is stable. The main result is an algorithm whose computational effort is analogous to that of classical algorithms for contractive polytopes computation for discrete-time parametric uncertain systems with the state matrix belonging to a polytopic set.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117253939","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 : 2014-12-15DOI: 10.1109/CDC.2014.7040369
G. Battistelli, Daniele Mari, D. Selvi, A. Tesi, P. Tesi
In this paper, an algorithm combining switching and tuning is proposed as a solution to the problem of adaptive disturbance attenuation. A high-level switching logic selects the controller providing the best potential performance within a pre-designed family; then a tuning procedure aims at finding a local refinement of the selected controller in order to improve its attenuation capabilities, and a low-level switching logic is used to decide whether to substitute the controller with its refinement or not. The control architecture is designed by adopting a particular implementation which ensures stability under any arbitrary switching sequence. It is shown that an arbitrary attenuation level can be achieved by adopting appropriately defined functionals. Simulation results are provided to show the validity of the proposed algorithm.
{"title":"A hierarchical approach to adaptive disturbance attenuation combining switching and tuning","authors":"G. Battistelli, Daniele Mari, D. Selvi, A. Tesi, P. Tesi","doi":"10.1109/CDC.2014.7040369","DOIUrl":"https://doi.org/10.1109/CDC.2014.7040369","url":null,"abstract":"In this paper, an algorithm combining switching and tuning is proposed as a solution to the problem of adaptive disturbance attenuation. A high-level switching logic selects the controller providing the best potential performance within a pre-designed family; then a tuning procedure aims at finding a local refinement of the selected controller in order to improve its attenuation capabilities, and a low-level switching logic is used to decide whether to substitute the controller with its refinement or not. The control architecture is designed by adopting a particular implementation which ensures stability under any arbitrary switching sequence. It is shown that an arbitrary attenuation level can be achieved by adopting appropriately defined functionals. Simulation results are provided to show the validity of the proposed algorithm.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121973179","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 : 2014-12-15DOI: 10.1109/CDC.2014.7039863
A. Tanwani, B. Brogliato, C. Prieur
We consider the problem of designing state feedback control laws for output regulation in a class of dynamical systems which are described by variational inequalities and ordinary differential equations. In our setup, these variational inequalities are used to model state trajectories constrained to evolve within time-varying, closed, and convex sets, and systems with complementarity relations. We first derive conditions to study the existence and uniqueness of solutions in such systems. The derivation of control laws for output regulation is based on the use of internal model principle, and two cases are treated: First, a static feedback control law is derived when full state feedback is available; In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed.
{"title":"On output regulation in systems with differential variational inequalities","authors":"A. Tanwani, B. Brogliato, C. Prieur","doi":"10.1109/CDC.2014.7039863","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039863","url":null,"abstract":"We consider the problem of designing state feedback control laws for output regulation in a class of dynamical systems which are described by variational inequalities and ordinary differential equations. In our setup, these variational inequalities are used to model state trajectories constrained to evolve within time-varying, closed, and convex sets, and systems with complementarity relations. We first derive conditions to study the existence and uniqueness of solutions in such systems. The derivation of control laws for output regulation is based on the use of internal model principle, and two cases are treated: First, a static feedback control law is derived when full state feedback is available; In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116110946","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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