Pub Date : 2014-12-01DOI: 10.1109/CDC.2014.7040065
H. Kheloufi, A. Zemouche, F. Bedouhene, H. S. Ali
This note focuses on the design of an observer-based controller for a class of Lipschitz nonlinear discrete-time systems with parameter uncertainties. Thanks to the reformulated Lipschitz property [1] that take into account all the properties of the nonlinearities of the system combined with some mathematical tools, it is shown that the solution of the discrete-time output feedback problem, expressed in term of Linear Matrix Inequality (LMI), is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint. This latter leads to a less restrictive synthesis condition than those available in the literature. A numerical example is provided in order to show the validity and superiority of the proposed method.
{"title":"Robust ℋ∞ observer-based controller for lipschitz nonlinear discrete-time systems with parameter uncertainties","authors":"H. Kheloufi, A. Zemouche, F. Bedouhene, H. S. Ali","doi":"10.1109/CDC.2014.7040065","DOIUrl":"https://doi.org/10.1109/CDC.2014.7040065","url":null,"abstract":"This note focuses on the design of an observer-based controller for a class of Lipschitz nonlinear discrete-time systems with parameter uncertainties. Thanks to the reformulated Lipschitz property [1] that take into account all the properties of the nonlinearities of the system combined with some mathematical tools, it is shown that the solution of the discrete-time output feedback problem, expressed in term of Linear Matrix Inequality (LMI), is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint. This latter leads to a less restrictive synthesis condition than those available in the literature. A numerical example is provided in order to show the validity and superiority of the proposed method.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127607730","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 : 2014-12-01DOI: 10.1109/CDC.2014.7039524
Yun Shen, W. Stannat, K. Obermayer
We introduce a unified framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and behavioral economics. Within the framework, applying weighted norm spaces to incorporate also unbounded costs, we study two types of infinite-horizon risk-sensitive criteria, discounted total risk and average risk, and solve the associated optimization problems by dynamic programming. For the discounted case, we propose a new discount scheme, which is different from the conventional form but consistent with the existing literature, while for the average risk criterion, we state Lyapunov-type stability conditions that generalize known conditions for Markov chains to ensure the existence of solutions to the optimality equation.
{"title":"A unified framework for risk-sensitive Markov control processes","authors":"Yun Shen, W. Stannat, K. Obermayer","doi":"10.1109/CDC.2014.7039524","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039524","url":null,"abstract":"We introduce a unified framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and behavioral economics. Within the framework, applying weighted norm spaces to incorporate also unbounded costs, we study two types of infinite-horizon risk-sensitive criteria, discounted total risk and average risk, and solve the associated optimization problems by dynamic programming. For the discounted case, we propose a new discount scheme, which is different from the conventional form but consistent with the existing literature, while for the average risk criterion, we state Lyapunov-type stability conditions that generalize known conditions for Markov chains to ensure the existence of solutions to the optimality equation.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127607827","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 : 2014-12-01DOI: 10.1109/CDC.2014.7040467
Y. Kantaros, M. Zavlanos
The purpose of this paper is to propose a control scheme to maximize area coverage and at the same time ensure reliable communication in networks of mobile robot sensors. The information that is generated at the sensors depends on the sensing capabilities of the sensors as well as on the frequency at which events occur in their vicinity, captured by appropriate probability density functions. This information is then routed to a fixed set of access points via a multi-hop network whose links model the probability that information packets are correctly decoded at their intended destinations. The proposed hybrid controller simultaneously optimizes coverage and routing of information by decoupling control in the continuous and discrete domains. The robots' motion is performed in continuous time, along the negative gradient of a cost function that combines the coverage objective and a barrier potential used to ensure satisfaction of desired communication rates. On the other hand, the communication variables are updated periodically, in discrete time, by the solution of an optimization problem, and constitute the switching signal in the continuous motion control. Simulation studies are conducted verifying the efficiency of the proposed algorithm.
{"title":"Communication-aware coverage control for robotic sensor networks","authors":"Y. Kantaros, M. Zavlanos","doi":"10.1109/CDC.2014.7040467","DOIUrl":"https://doi.org/10.1109/CDC.2014.7040467","url":null,"abstract":"The purpose of this paper is to propose a control scheme to maximize area coverage and at the same time ensure reliable communication in networks of mobile robot sensors. The information that is generated at the sensors depends on the sensing capabilities of the sensors as well as on the frequency at which events occur in their vicinity, captured by appropriate probability density functions. This information is then routed to a fixed set of access points via a multi-hop network whose links model the probability that information packets are correctly decoded at their intended destinations. The proposed hybrid controller simultaneously optimizes coverage and routing of information by decoupling control in the continuous and discrete domains. The robots' motion is performed in continuous time, along the negative gradient of a cost function that combines the coverage objective and a barrier potential used to ensure satisfaction of desired communication rates. On the other hand, the communication variables are updated periodically, in discrete time, by the solution of an optimization problem, and constitute the switching signal in the continuous motion control. Simulation studies are conducted verifying the efficiency of the proposed algorithm.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127625140","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 : 2014-12-01DOI: 10.1109/CDC.2014.7040396
Xiaojing Zhang, M. Kamgarpour, P. Goulart, J. Lygeros
This paper proposes a method for solving robust optimal control problems with modulated uncertainty sets. We consider constrained uncertain linear systems and interpret the uncertainty sets as “robustness margins” or “reserve capacities”. In particular, given a certain reward for offering such a reserve capacity, we address the problem of determining the optimal size and shape of the uncertainty set, i.e. how much reserve capacity our system should offer. By assuming polyhedral constraints, restricting the class of the uncertainty sets and using affine decision rules, we formulate a convex program to solve this problem. We discuss several specific families of uncertainty sets, whose respective constraints can be reformulated as linear constraints, second-order cone constraints, or linear matrix inequalities. A numerical example demonstrates our approach.
{"title":"Selling robustness margins: A framework for optimizing reserve capacities for linear systems","authors":"Xiaojing Zhang, M. Kamgarpour, P. Goulart, J. Lygeros","doi":"10.1109/CDC.2014.7040396","DOIUrl":"https://doi.org/10.1109/CDC.2014.7040396","url":null,"abstract":"This paper proposes a method for solving robust optimal control problems with modulated uncertainty sets. We consider constrained uncertain linear systems and interpret the uncertainty sets as “robustness margins” or “reserve capacities”. In particular, given a certain reward for offering such a reserve capacity, we address the problem of determining the optimal size and shape of the uncertainty set, i.e. how much reserve capacity our system should offer. By assuming polyhedral constraints, restricting the class of the uncertainty sets and using affine decision rules, we formulate a convex program to solve this problem. We discuss several specific families of uncertainty sets, whose respective constraints can be reformulated as linear constraints, second-order cone constraints, or linear matrix inequalities. A numerical example demonstrates our approach.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126339061","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 : 2014-12-01DOI: 10.1109/CDC.2014.7040056
U. Boscain, J. Gauthier, D. Prandi, A. Remizov
We compare the image inpainting results of two models of geometry of vision obtained through control theoretic considerations (the semi-discrete versions of the Citti-Petitot-Sarti and Mumford Elastica models). The main feature described by these models is the lifting of 2D images to the 3D group of translations and discrete rotations on the plane SE(2,N), done by the primary visual cortex. Corrupted images are then reconstructed by minimizing the energy necessary to activate neurons corresponding to the missing regions. This minimization procedure, which gives rise to Dubins/Reed-Shepp-like optimal control problems in the case of corrupted curves, is described by an hypoelliptic diffusion on SE(2,N). We present two numerical algorithms for the resolution of the diffusion equation in both models and then compare the results.
{"title":"Image reconstruction via non-isotropic diffusion in Dubins/Reed-Shepp-like control systems","authors":"U. Boscain, J. Gauthier, D. Prandi, A. Remizov","doi":"10.1109/CDC.2014.7040056","DOIUrl":"https://doi.org/10.1109/CDC.2014.7040056","url":null,"abstract":"We compare the image inpainting results of two models of geometry of vision obtained through control theoretic considerations (the semi-discrete versions of the Citti-Petitot-Sarti and Mumford Elastica models). The main feature described by these models is the lifting of 2D images to the 3D group of translations and discrete rotations on the plane SE(2,N), done by the primary visual cortex. Corrupted images are then reconstructed by minimizing the energy necessary to activate neurons corresponding to the missing regions. This minimization procedure, which gives rise to Dubins/Reed-Shepp-like optimal control problems in the case of corrupted curves, is described by an hypoelliptic diffusion on SE(2,N). We present two numerical algorithms for the resolution of the diffusion equation in both models and then compare the results.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126519143","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 : 2014-12-01DOI: 10.1109/CDC.2014.7040188
Ji Qi, Shin Li
In this paper, we study the control of the class of time-invariant linear ensemble systems, whose natural dynamics vary linearly with the system parameter. This class of ensemble control systems arises from practical engineering and physical applications, such as transport of quantum atoms and steering of uncertain harmonic systems. We, in particular, consider the ensemble systems with strictly positive or negative parameter values and derive explicit necessary and sufficient controllability conditions, which are easy to be checked. Our derivation is based on the notion of polynomial approximation, where the elements of the reachable set are represented in polynomials of the system parameter and used to approximate the desired state of interest. In addition, we highlight the role of the spectra of the system matrices play in the determination of ensemble controllability. Illustrative examples with numerical simulations are provided to demonstrate the tractability of the developed controllability conditions.
{"title":"Controllability characterization of linear ensemble systems","authors":"Ji Qi, Shin Li","doi":"10.1109/CDC.2014.7040188","DOIUrl":"https://doi.org/10.1109/CDC.2014.7040188","url":null,"abstract":"In this paper, we study the control of the class of time-invariant linear ensemble systems, whose natural dynamics vary linearly with the system parameter. This class of ensemble control systems arises from practical engineering and physical applications, such as transport of quantum atoms and steering of uncertain harmonic systems. We, in particular, consider the ensemble systems with strictly positive or negative parameter values and derive explicit necessary and sufficient controllability conditions, which are easy to be checked. Our derivation is based on the notion of polynomial approximation, where the elements of the reachable set are represented in polynomials of the system parameter and used to approximate the desired state of interest. In addition, we highlight the role of the spectra of the system matrices play in the determination of ensemble controllability. Illustrative examples with numerical simulations are provided to demonstrate the tractability of the developed controllability conditions.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127946816","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 : 2014-12-01DOI: 10.1109/CDC.2014.7039500
Masaki Yo, M. Ono, S. Adachi, D. Murayama, N. Okita
Fluctuating wind power must be smoothed before supplied to a power grid in order to prevent potential damages of sensitive electrical devices connected to the grid. This paper considers a hybrid wind-solar thermal plant, where the output from the wind turbine is smoothed by bypassing through the thermal plant. We propose a chance-constrained MPC-based control method that optimally decides the ratio of the wind output that is bypassed through the thermal plant so that the rapid fluctuation of output is suppressed while the direct power output is maximized. The controller's parameters are designed in a way that result in a Pareto-optimal performance. We demonstrate the performance of the proposed method through simulations using real data.
{"title":"Power output smoothing for hybrid wind-solar thermal plant using chance-constrained model predictive control","authors":"Masaki Yo, M. Ono, S. Adachi, D. Murayama, N. Okita","doi":"10.1109/CDC.2014.7039500","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039500","url":null,"abstract":"Fluctuating wind power must be smoothed before supplied to a power grid in order to prevent potential damages of sensitive electrical devices connected to the grid. This paper considers a hybrid wind-solar thermal plant, where the output from the wind turbine is smoothed by bypassing through the thermal plant. We propose a chance-constrained MPC-based control method that optimally decides the ratio of the wind output that is bypassed through the thermal plant so that the rapid fluctuation of output is suppressed while the direct power output is maximized. The controller's parameters are designed in a way that result in a Pareto-optimal performance. We demonstrate the performance of the proposed method through simulations using real data.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115911486","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 : 2014-12-01DOI: 10.1109/CDC.2014.7040185
Lindsey Andrews, Justin R. Klotz, R. Kamalapurkar, W. Dixon
Adaptive dynamic programming is applied to control-affine nonlinear systems with uncertain drift dynamics to obtain a near-optimal solution to a finite-horizon optimal control problem with hard terminal constraints. A reinforcement learning-based actor-critic framework is used to approximately solve the Hamilton-Jacobi-Bellman equation, wherein critic and actor neural networks (NN) are used for approximate learning of the optimal value function and control policy, while enforcing the optimality condition resulting from the hard terminal constraint. Concurrent learning-based update laws relax the restrictive persistence of excitation requirement. A Lyapunov-based stability analysis guarantees uniformly ultimately bounded convergence of the enacted control policy to the optimal control policy.
{"title":"Adaptive dynamic programming for terminally constrained finite-horizon optimal control problems","authors":"Lindsey Andrews, Justin R. Klotz, R. Kamalapurkar, W. Dixon","doi":"10.1109/CDC.2014.7040185","DOIUrl":"https://doi.org/10.1109/CDC.2014.7040185","url":null,"abstract":"Adaptive dynamic programming is applied to control-affine nonlinear systems with uncertain drift dynamics to obtain a near-optimal solution to a finite-horizon optimal control problem with hard terminal constraints. A reinforcement learning-based actor-critic framework is used to approximately solve the Hamilton-Jacobi-Bellman equation, wherein critic and actor neural networks (NN) are used for approximate learning of the optimal value function and control policy, while enforcing the optimality condition resulting from the hard terminal constraint. Concurrent learning-based update laws relax the restrictive persistence of excitation requirement. A Lyapunov-based stability analysis guarantees uniformly ultimately bounded convergence of the enacted control policy to the optimal control policy.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115954551","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 : 2014-12-01DOI: 10.1109/CDC.2014.7040222
Lara Briñón-Arranz, A. Pascoal, Antonio Pedro Aguiar
This paper addresses the problem of adaptive leader-follower formation control (ALFC) of autonomous marine vehicles. The rationale for this study can be found in a number of challenging geotechnical surveying missions aimed at mapping geological structures under the seabed. Mission specifications require that a group of surface vehicles equipped with acoustic receivers (hydrophones) maneuver in formation and acquire acoustic data emitted by one or more vehicles that carry acoustic emitters. To this effect, we adopt a basic set-up for ALFC previously proposed for mobile robots modeled as single integrators and extend it to include explicitly the full dynamic equations of a representative type of marine vehicles. The paper offers a formal proof of convergence of the resulting formation control system. Results of simulations illustrate the performance that can be obtained with the control law proposed.
{"title":"Adaptive leader-follower formation control of autonomous marine vehicles","authors":"Lara Briñón-Arranz, A. Pascoal, Antonio Pedro Aguiar","doi":"10.1109/CDC.2014.7040222","DOIUrl":"https://doi.org/10.1109/CDC.2014.7040222","url":null,"abstract":"This paper addresses the problem of adaptive leader-follower formation control (ALFC) of autonomous marine vehicles. The rationale for this study can be found in a number of challenging geotechnical surveying missions aimed at mapping geological structures under the seabed. Mission specifications require that a group of surface vehicles equipped with acoustic receivers (hydrophones) maneuver in formation and acquire acoustic data emitted by one or more vehicles that carry acoustic emitters. To this effect, we adopt a basic set-up for ALFC previously proposed for mobile robots modeled as single integrators and extend it to include explicitly the full dynamic equations of a representative type of marine vehicles. The paper offers a formal proof of convergence of the resulting formation control system. Results of simulations illustrate the performance that can be obtained with the control law proposed.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131365367","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 : 2014-12-01DOI: 10.1109/CDC.2014.7039866
W. Heemels, Valentina Sessa, F. Vasca, M. Camlibel
In this paper we study a class of set-valued dynamical systems that satisfy maximal monotonicity properties. This class includes linear relay systems, linear complementarity systems, and linear mechanical systems with dry friction under certain conditions. We discuss two numerical time-stepping schemes for the computation of periodic solutions of these systems when being periodically excited. For these two schemes we will provide formal mathematical justifications and compare them in terms of approximation accuracy and computation time using a numerical example.
{"title":"Time-stepping methods for constructing periodic solutions in maximally monotone set-valued dynamical systems","authors":"W. Heemels, Valentina Sessa, F. Vasca, M. Camlibel","doi":"10.1109/CDC.2014.7039866","DOIUrl":"https://doi.org/10.1109/CDC.2014.7039866","url":null,"abstract":"In this paper we study a class of set-valued dynamical systems that satisfy maximal monotonicity properties. This class includes linear relay systems, linear complementarity systems, and linear mechanical systems with dry friction under certain conditions. We discuss two numerical time-stepping schemes for the computation of periodic solutions of these systems when being periodically excited. For these two schemes we will provide formal mathematical justifications and compare them in terms of approximation accuracy and computation time using a numerical example.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131396546","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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