We have studied quantum control operations on electrons confined in semiconductor nanostructures using time-dependent spatially uniform electric fields. Our general goal was to manipulate the wave function of one or two electrons and thereby control a certain quantum probability of interest. Since our main interest was in performing certain tasks rather than in developing efficient control methods, we searched relevant parts of our parameter space numerically in a systematic manner. Here we summarize the results of three studies whose common denominator is the fact that the control of the wave function is performed using a uniform electric field, or, in other words, through the electric dipole approximation Hamiltonian H/sub d/= -er/spl middot/E(t). The subjects of these studies are: Coherent control of multisubband wavepackets with terahertz pulses, single-electron turnstile modelled with two interacting electrons, and dynamical localization of two interacting electrons in coupled quantum dots.
{"title":"Quantum control of electrons in semiconductor nanostructures using spatially uniform electric fields","authors":"P. I. Tamborenea, H. Metiu","doi":"10.1109/CDC.2001.980113","DOIUrl":"https://doi.org/10.1109/CDC.2001.980113","url":null,"abstract":"We have studied quantum control operations on electrons confined in semiconductor nanostructures using time-dependent spatially uniform electric fields. Our general goal was to manipulate the wave function of one or two electrons and thereby control a certain quantum probability of interest. Since our main interest was in performing certain tasks rather than in developing efficient control methods, we searched relevant parts of our parameter space numerically in a systematic manner. Here we summarize the results of three studies whose common denominator is the fact that the control of the wave function is performed using a uniform electric field, or, in other words, through the electric dipole approximation Hamiltonian H/sub d/= -er/spl middot/E(t). The subjects of these studies are: Coherent control of multisubband wavepackets with terahertz pulses, single-electron turnstile modelled with two interacting electrons, and dynamical localization of two interacting electrons in coupled quantum dots.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131072861","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}
Addresses and solves model development, simulation, analysis, control, and optimization problems which are critical in synthesis and design of high-performance NEMS and MEMS. It is illustrated that different concepts can be applied in modeling, and novel approaches must be developed in order to guarantee feasibility and applicability of mathematical models for consecutive steps, tasks, and problems. To analyze molecular dynamics and study nanostructures, high-fidelity modeling is approached using the three-dimensional charge density. For electromechanical devices, Maxwell's equations can be used. The lumped-parameter models, which lead to nonlinear differential equations, are applied in the preliminary analysis and design. It is illustrated that three-dimensional in the time domain high-fidelity modeling, simulation, and analysis can be achieved. To demonstrate the results, an illustrative example is provided. In particular, rotational micromotors are studied, modeled, controlled, and tested.
{"title":"Systematic synthesis of nano- and micro-electromechanical systems","authors":"S. Lyshevski, M. Lyshevski","doi":"10.1109/CDC.2001.980138","DOIUrl":"https://doi.org/10.1109/CDC.2001.980138","url":null,"abstract":"Addresses and solves model development, simulation, analysis, control, and optimization problems which are critical in synthesis and design of high-performance NEMS and MEMS. It is illustrated that different concepts can be applied in modeling, and novel approaches must be developed in order to guarantee feasibility and applicability of mathematical models for consecutive steps, tasks, and problems. To analyze molecular dynamics and study nanostructures, high-fidelity modeling is approached using the three-dimensional charge density. For electromechanical devices, Maxwell's equations can be used. The lumped-parameter models, which lead to nonlinear differential equations, are applied in the preliminary analysis and design. It is illustrated that three-dimensional in the time domain high-fidelity modeling, simulation, and analysis can be achieved. To demonstrate the results, an illustrative example is provided. In particular, rotational micromotors are studied, modeled, controlled, and tested.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131081850","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}
Research has, shown that the repetitive control is very efficient in tracking periodic signals. However, the existing repetitive control algorithms require an integer number of samples in each period. In some industry applications where the signal period varies but other requirements on the data acquisition system force a fixed sample rate, the number of samples per period may be a non-integer. To address this problem, the paper presents an adaptive repetitive control, consisting of two portions, the repetitive controller and the nominal controller. The repetitive controller uses a fictitious sampler operating at a variable sample rate maintained at multiple times of the signal frequency, while the nominal controller uses a fixed sampling rate. Interpolations are utilised to generate the fictitious samples required for the repetitive learning. The variation of the repetitive controller's sampling rate is limited to a small value, so that the system stability can be maintained without any changes on the controller parameters. The experimental results on the control of a servomotor demonstrate the effectiveness of the proposed schemes.
{"title":"Tracking variable periodic signals with fixed sampling rate","authors":"Z. Cao, G. Ledwich","doi":"10.1109/CDC.2001.980982","DOIUrl":"https://doi.org/10.1109/CDC.2001.980982","url":null,"abstract":"Research has, shown that the repetitive control is very efficient in tracking periodic signals. However, the existing repetitive control algorithms require an integer number of samples in each period. In some industry applications where the signal period varies but other requirements on the data acquisition system force a fixed sample rate, the number of samples per period may be a non-integer. To address this problem, the paper presents an adaptive repetitive control, consisting of two portions, the repetitive controller and the nominal controller. The repetitive controller uses a fictitious sampler operating at a variable sample rate maintained at multiple times of the signal frequency, while the nominal controller uses a fixed sampling rate. Interpolations are utilised to generate the fictitious samples required for the repetitive learning. The variation of the repetitive controller's sampling rate is limited to a small value, so that the system stability can be maintained without any changes on the controller parameters. The experimental results on the control of a servomotor demonstrate the effectiveness of the proposed schemes.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131136440","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}
It is shown how the geometric framework for distributed-parameter port-controlled Hamiltonian systems can be adapted to formulate ideal isentropic compressible fluids with nonzero energy flow through the boundary of the spatial domain as Hamiltonian boundary control systems. The key ingredient is the modification of the Stokes-Dirac structure to a Dirac structure defined on the space of mass density 3-forms and velocity 1-forms, incorporating three-dimensional convection. Some initial steps towards stabilization of these boundary control systems, based on the generation of Casimir functions for the closed-loop Hamiltonian system, are discussed.
{"title":"Fluid dynamical systems as Hamiltonian boundary control systems","authors":"A. Schaft, B. Maschke","doi":"10.1109/CDC.2001.980911","DOIUrl":"https://doi.org/10.1109/CDC.2001.980911","url":null,"abstract":"It is shown how the geometric framework for distributed-parameter port-controlled Hamiltonian systems can be adapted to formulate ideal isentropic compressible fluids with nonzero energy flow through the boundary of the spatial domain as Hamiltonian boundary control systems. The key ingredient is the modification of the Stokes-Dirac structure to a Dirac structure defined on the space of mass density 3-forms and velocity 1-forms, incorporating three-dimensional convection. Some initial steps towards stabilization of these boundary control systems, based on the generation of Casimir functions for the closed-loop Hamiltonian system, are discussed.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130917147","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}
Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Previously, we (2001) have extended MPC to a class of discrete event systems that can be described by a model that is "linear" in the (max, +) algebra. In our previous work we have only considered MPC for the perturbations-free case and for the case with bounded noise and/or modeling errors. We extend our previous results on MPC for perturbed max-plus-linear systems to a stochastic setting. We show that under quite general conditions the resulting optimization problems turn out to be convex and can be solved very efficiently.
{"title":"Model predictive control for perturbed max-plus-linear systems: a stochastic approach","authors":"T. Boom, B. Schutter","doi":"10.1109/CDC.2001.980918","DOIUrl":"https://doi.org/10.1109/CDC.2001.980918","url":null,"abstract":"Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Previously, we (2001) have extended MPC to a class of discrete event systems that can be described by a model that is \"linear\" in the (max, +) algebra. In our previous work we have only considered MPC for the perturbations-free case and for the case with bounded noise and/or modeling errors. We extend our previous results on MPC for perturbed max-plus-linear systems to a stochastic setting. We show that under quite general conditions the resulting optimization problems turn out to be convex and can be solved very efficiently.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131204896","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}
M. Dymkov, I. Gaishun, E. Rogers, K. Gałkowski, D. Owens
Repetitive processes are a distinct class of 2D systems of both theoretical and applications interest. They arise, for example, in the modeling of industrial processes such as long-wall coal cutting and are the essential starting point for the study of classes of linear iterative learning control schemes. The development of a 'mature' systems theory for these processes is the subject of the paper. In particular, a Volterra operator setting is used to produce the first significant results on an observability theory for so-called discrete linear repetitive processes which are of particular interest in a number of areas, e.g. the modeling and analysis of a wide class of linear iterative learning control schemes.
{"title":"On the observability properties of a class of 2D discrete linear systems","authors":"M. Dymkov, I. Gaishun, E. Rogers, K. Gałkowski, D. Owens","doi":"10.1109/CDC.2001.980423","DOIUrl":"https://doi.org/10.1109/CDC.2001.980423","url":null,"abstract":"Repetitive processes are a distinct class of 2D systems of both theoretical and applications interest. They arise, for example, in the modeling of industrial processes such as long-wall coal cutting and are the essential starting point for the study of classes of linear iterative learning control schemes. The development of a 'mature' systems theory for these processes is the subject of the paper. In particular, a Volterra operator setting is used to produce the first significant results on an observability theory for so-called discrete linear repetitive processes which are of particular interest in a number of areas, e.g. the modeling and analysis of a wide class of linear iterative learning control schemes.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133022939","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}
Link layer error control is one of the important technologies in mobile systems. In this paper, adaptive error control investigated using a modified Markov decision process (MDP) model is discussed. An adaptive error control strategy, where the MAC frame length adapts to the varying channel condition, was developed. The proposed algorithm implemented online, achieves better average link layer throughput in a dynamic data channel. The simulation example provided shows that the algorithm can improve the throughput of the wireless data channel by 23%.
{"title":"Adaptive error control for mobile networks: on-line optimization based on a single sample path","authors":"M. He, Xi-Ren Cao","doi":"10.1109/CDC.2001.981188","DOIUrl":"https://doi.org/10.1109/CDC.2001.981188","url":null,"abstract":"Link layer error control is one of the important technologies in mobile systems. In this paper, adaptive error control investigated using a modified Markov decision process (MDP) model is discussed. An adaptive error control strategy, where the MAC frame length adapts to the varying channel condition, was developed. The proposed algorithm implemented online, achieves better average link layer throughput in a dynamic data channel. The simulation example provided shows that the algorithm can improve the throughput of the wireless data channel by 23%.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133608432","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}
The tracking control problem is addressed for a class of nonlinear delay systems with unknown parameters. Such a problem is solved in the case that the nonlinear delay system has some geometrical properties, that is full delay relative degree and no unstable internal dynamics when the output and its derivatives are taken bounded by the control law. It is supposed moreover that the unknown parameters do not affect the output and its derivatives until n-1, where n is the dimension of the state Euclidean vector. As usual, the control law here found depends on the state variables in present and past times, and on the control law itself in past times too. Standard Lyapunov methodology is here used to-find out the adaptive control law and the dynamics of estimated parameters. It is proved that when the found out control law is applied to the system, the tracking error asymptotically goes to zero. The case of unknown delay is considered too. An upper bound for the error in delay knowledge is found which can be tolerated when controlling the system by recent methodologies based on standard nonlinear analysis. Simulation results are here shown for a prey-predator Lotka Volterra system.
{"title":"Some results on adaptive tracking for a class of nonlinear time-delay systems","authors":"P. Pepe","doi":"10.1109/CDC.2001.980240","DOIUrl":"https://doi.org/10.1109/CDC.2001.980240","url":null,"abstract":"The tracking control problem is addressed for a class of nonlinear delay systems with unknown parameters. Such a problem is solved in the case that the nonlinear delay system has some geometrical properties, that is full delay relative degree and no unstable internal dynamics when the output and its derivatives are taken bounded by the control law. It is supposed moreover that the unknown parameters do not affect the output and its derivatives until n-1, where n is the dimension of the state Euclidean vector. As usual, the control law here found depends on the state variables in present and past times, and on the control law itself in past times too. Standard Lyapunov methodology is here used to-find out the adaptive control law and the dynamics of estimated parameters. It is proved that when the found out control law is applied to the system, the tracking error asymptotically goes to zero. The case of unknown delay is considered too. An upper bound for the error in delay knowledge is found which can be tolerated when controlling the system by recent methodologies based on standard nonlinear analysis. Simulation results are here shown for a prey-predator Lotka Volterra system.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"254 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133288551","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}
Singularly-perturbed relay control systems with 2nd-order sliding modes (SP2SM) are considered for modeling sliding-mode control systems with inertial sensors. It is shown that the asymptotically stable slow-motions integral manifold (ASSMIM) of a smooth singularly-perturbed system, describing the motion of the original SP2SM in the 2nd-order sliding domain, is the ASSMIM of the original SP2SM. For sliding-mode control systems with inertial sensors, sufficient conditions for the exponentially decreasing amplitude of chattering and the unlimited growth of frequency are found. A formula for the asymptotic representation of "ideal" switching surface oscillations is suggested for sliding-mode systems with inertial sensors.
{"title":"Chattering analysis in sliding mode systems with inertial sensors","authors":"L. Fridman","doi":"10.1109/CDC.2001.981167","DOIUrl":"https://doi.org/10.1109/CDC.2001.981167","url":null,"abstract":"Singularly-perturbed relay control systems with 2nd-order sliding modes (SP2SM) are considered for modeling sliding-mode control systems with inertial sensors. It is shown that the asymptotically stable slow-motions integral manifold (ASSMIM) of a smooth singularly-perturbed system, describing the motion of the original SP2SM in the 2nd-order sliding domain, is the ASSMIM of the original SP2SM. For sliding-mode control systems with inertial sensors, sufficient conditions for the exponentially decreasing amplitude of chattering and the unlimited growth of frequency are found. A formula for the asymptotic representation of \"ideal\" switching surface oscillations is suggested for sliding-mode systems with inertial sensors.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133645673","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}
The paper addresses multiple local-linear model structures for control. Improvements in gain scheduling through local linear modelling without offset terms (LPV), and a subsequent controller design based on linear matrix inequalities (LMIs) over a popular ad hoc approach are shown using an example published in recent journals.
{"title":"Counter-example to ad-hoc off-equilibrium linearisation methods in gain-scheduling","authors":"P. Korba, H. Werner","doi":"10.1109/CDC.2001.981076","DOIUrl":"https://doi.org/10.1109/CDC.2001.981076","url":null,"abstract":"The paper addresses multiple local-linear model structures for control. Improvements in gain scheduling through local linear modelling without offset terms (LPV), and a subsequent controller design based on linear matrix inequalities (LMIs) over a popular ad hoc approach are shown using an example published in recent journals.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133668885","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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