Pub Date : 2010-09-27DOI: 10.1109/MMAR.2010.5587247
Christian Clason, B. Kaltenbacher, I. Lasiecka, S. Veljović
Motivated by a medical application from lithotripsy, we study an optimal boundary control problem given by Westervelt equation − 1/c2D2t u + Δu + b/c2Δ(Dt u) = − βa/ρc4D2t u2 in (0, T) × Ω (1) modeling the nonlinear evolution of the acoustic pressure u in a smooth, bounded domain Ω ⊂ Rd, d ∊ {1, 2, 3}. Here c > 0 is the speed of sound, b > 0 the diffusivity of sound, ρ > 0 the mass density and βa > 1 the parameter of nonlinearity. We study the optimization problem for existence of an optimal control and derive the first-order necessary optimality conditions. In addition, all results are extended for the more general Kuznetsov equation D2tψ − c2Δψ = Dt(bΔψ + 1/c2 B/2A (Dtψ)2 + |∇ψ|2) (2) given in terms of the acoustic velocity potential ψ.
受岩石力学医学应用的激励，我们研究了由Westervelt方程−1/c2D2t u + Δu + b/c2Δ(Dt u) =−βa/ρc4D2t u2 in (0, T) × Ω(1)给出的最优边界控制问题，该方程模拟了声压u在光滑有界域中的非线性演化Ω∧Rd, d{1,2,3}。其中c >为声速，b >为声音扩散系数，ρ >为质量密度，βa bbb_1为非线性参数。研究了一类最优控制存在的优化问题，导出了一阶必要最优性条件。此外，将所有结果推广到更一般的库兹涅佐夫方程D2tψ−c2Δψ = Dt(bΔψ + 1/c2 B/2A (Dtψ)2 + |∇ψ|2)(2)，以声速势ψ的形式给出。
{"title":"Optimal boundary control for equations of nonlinear acoustics","authors":"Christian Clason, B. Kaltenbacher, I. Lasiecka, S. Veljović","doi":"10.1109/MMAR.2010.5587247","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587247","url":null,"abstract":"Motivated by a medical application from lithotripsy, we study an optimal boundary control problem given by Westervelt equation − <sup>1</sup>/c<sup>2</sup>D<sup>2</sup><inf>t</inf> u + Δu + b/c<sup>2</sup>Δ(D<inf>t</inf> u) = − β<inf>a</inf>/ρc<sup>4</sup>D<sup>2</sup><inf>t</inf> u<sup>2</sup> in (0, T) × Ω (1) modeling the nonlinear evolution of the acoustic pressure u in a smooth, bounded domain Ω ⊂ R<sup>d</sup>, d ∊ {1, 2, 3}. Here c > 0 is the speed of sound, b > 0 the diffusivity of sound, ρ > 0 the mass density and β<inf>a</inf> > 1 the parameter of nonlinearity. We study the optimization problem for existence of an optimal control and derive the first-order necessary optimality conditions. In addition, all results are extended for the more general Kuznetsov equation D<sup>2</sup><inf>t</inf>ψ − c<sup>2</sup>Δψ = D<inf>t</inf>(bΔψ + 1/c<sup>2</sup> B/2A (D<inf>t</inf>ψ)<sup>2</sup> + |∇ψ|<sup>2</sup>) (2) given in terms of the acoustic velocity potential ψ.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128155889","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 : 2010-09-27DOI: 10.1109/MMAR.2010.5587199
B. Fajdek, Alicja Golnik
The paper presents a new numerical package for modelling and simulation of human circulatory system. The package provides many functions that are required in cardiovascular biomechanics. It is very useful tool for studing behavior of individual components of the human circulatory system, such as: left/right ventricular, systemic venous/arterial circulation, pulmonary arterial/venous circulation etc. It can also be a useful tool for education purposes. Moreover, it can be used for developing and testing of new mechanical circulatory devices, or ventricular assist devices (VAD). A short presentation of blocks that are the part of the package, is included. Also a example of application is presented.
{"title":"Modelling and simulation of human circulatory system","authors":"B. Fajdek, Alicja Golnik","doi":"10.1109/MMAR.2010.5587199","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587199","url":null,"abstract":"The paper presents a new numerical package for modelling and simulation of human circulatory system. The package provides many functions that are required in cardiovascular biomechanics. It is very useful tool for studing behavior of individual components of the human circulatory system, such as: left/right ventricular, systemic venous/arterial circulation, pulmonary arterial/venous circulation etc. It can also be a useful tool for education purposes. Moreover, it can be used for developing and testing of new mechanical circulatory devices, or ventricular assist devices (VAD). A short presentation of blocks that are the part of the package, is included. Also a example of application is presented.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122172538","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 : 2010-09-27DOI: 10.1109/MMAR.2010.5587223
R. Różycki
We consider a problem of optimal allocation of a continuous doubly-constrained resource to jobs performed on a single machine. The processing speed of a job depends on an amount of the continuous resource allotted to this job at a moment. This relation is expressed by a processing speed function characterizing each job. We propose a method of resource allocating for jobs which have to be performed sequentially (for example on a single machine) to minimize the schedule length. The problem for jobs with unique concave processing speed functions has not been considered so far.
{"title":"Resource allocation to minimize the makespan for jobs performed on a single machine","authors":"R. Różycki","doi":"10.1109/MMAR.2010.5587223","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587223","url":null,"abstract":"We consider a problem of optimal allocation of a continuous doubly-constrained resource to jobs performed on a single machine. The processing speed of a job depends on an amount of the continuous resource allotted to this job at a moment. This relation is expressed by a processing speed function characterizing each job. We propose a method of resource allocating for jobs which have to be performed sequentially (for example on a single machine) to minimize the schedule length. The problem for jobs with unique concave processing speed functions has not been considered so far.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132768772","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 : 2010-09-27DOI: 10.1109/MMAR.2010.5587271
A. Rauh, H. Aschemann
The computation of tracking controllers is one of the most important tasks in control engineering. For differentially flat systems, this task can be solved analytically if the initial conditions of all system states are consistent with the desired output trajectories. However, exact analytical solutions are not possible if the initial conditions are contradictory with desired output profiles or if non-flat outputs are specified for systems with complex nonlinearities in the state equations and the systems' input characteristics. For that reason, strategies based on the computation of differential sensitivities are investigated in this contribution to find approximate solutions for the tracking control problem. In contrast to classical output feedback structures, the proposed algorithm is capable of both providing dynamic feedforward and feedback control strategies. Selected application scenarios are presented to highlight the applicability of the suggested procedure which is based on the computation of the required partial derivatives online with the help of operator overloading techniques provided by algorithmic differentiation.
{"title":"Sensitivity-based feedforward and feedback control using algorithmic differentiation","authors":"A. Rauh, H. Aschemann","doi":"10.1109/MMAR.2010.5587271","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587271","url":null,"abstract":"The computation of tracking controllers is one of the most important tasks in control engineering. For differentially flat systems, this task can be solved analytically if the initial conditions of all system states are consistent with the desired output trajectories. However, exact analytical solutions are not possible if the initial conditions are contradictory with desired output profiles or if non-flat outputs are specified for systems with complex nonlinearities in the state equations and the systems' input characteristics. For that reason, strategies based on the computation of differential sensitivities are investigated in this contribution to find approximate solutions for the tracking control problem. In contrast to classical output feedback structures, the proposed algorithm is capable of both providing dynamic feedforward and feedback control strategies. Selected application scenarios are presented to highlight the applicability of the suggested procedure which is based on the computation of the required partial derivatives online with the help of operator overloading techniques provided by algorithmic differentiation.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133359728","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 : 2010-09-27DOI: 10.1109/MMAR.2010.5587225
M. Mika, Grzegorz Waligóra, J. Weglarz
In this paper we present a review of the new concepts of resource categories, motivated by practical situations, which have appeared in the project scheduling theory over the last decade. A basic resource classification from the point of view of resource constraints, divisibility, and preemptibility is presented. A new category of multi-site resources is introduced, and a multi-more resource-constrained project scheduling problem with multi-site resources and transportation network is defined.
{"title":"New resource concepts in project scheduling including multi-site resources with transportation network","authors":"M. Mika, Grzegorz Waligóra, J. Weglarz","doi":"10.1109/MMAR.2010.5587225","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587225","url":null,"abstract":"In this paper we present a review of the new concepts of resource categories, motivated by practical situations, which have appeared in the project scheduling theory over the last decade. A basic resource classification from the point of view of resource constraints, divisibility, and preemptibility is presented. A new category of multi-site resources is introduced, and a multi-more resource-constrained project scheduling problem with multi-site resources and transportation network is defined.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117296831","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 : 2010-09-27DOI: 10.1109/MMAR.2010.5587222
O. Pantz, K. Trabelsi
In most shape optimization problems, the optimal solution does not belong to the set of genuine shapes but is a composite structure. The homogenization method consists in relaxing the original problem thereby extending the set of admissible structures to composite shapes. From the numerical viewpoint, an important asset of the homogenization method with respect to traditional geometrical optimization is that the computed optimal shape is quite independent from the initial guess (at least for the compliance minimization problem). Nevertheless, the optimal shape being a composite, a post-treatement is needed in order to produce an almost optimal non-composite (i.e. workable) shape. The classical approach consists in penalizing the intermediate densities of material, but the obtained result deeply depends on the underlying mesh used and the level of details is not controllable. In a previous work, we proposed a new post-treatement method for the compliance minimization problem of an elastic structure. The main idea is to approximate the optimal composite shape with a locally periodic composite and to build a sequence of genuine shapes converging toward this composite structure. This method allows us to balance the level of details of the final shape and its optimality. Nevertheless, it was restricted to particular optimal shapes, depending on the topological structure of the lattice describing the arrangement of the holes of the composite. In this article, we lift this restriction in order to extend our method to any optimal composite structure for the compliance minimization problem.
{"title":"Construction of minimization sequences for shape optimization","authors":"O. Pantz, K. Trabelsi","doi":"10.1109/MMAR.2010.5587222","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587222","url":null,"abstract":"In most shape optimization problems, the optimal solution does not belong to the set of genuine shapes but is a composite structure. The homogenization method consists in relaxing the original problem thereby extending the set of admissible structures to composite shapes. From the numerical viewpoint, an important asset of the homogenization method with respect to traditional geometrical optimization is that the computed optimal shape is quite independent from the initial guess (at least for the compliance minimization problem). Nevertheless, the optimal shape being a composite, a post-treatement is needed in order to produce an almost optimal non-composite (i.e. workable) shape. The classical approach consists in penalizing the intermediate densities of material, but the obtained result deeply depends on the underlying mesh used and the level of details is not controllable. In a previous work, we proposed a new post-treatement method for the compliance minimization problem of an elastic structure. The main idea is to approximate the optimal composite shape with a locally periodic composite and to build a sequence of genuine shapes converging toward this composite structure. This method allows us to balance the level of details of the final shape and its optimality. Nevertheless, it was restricted to particular optimal shapes, depending on the topological structure of the lattice describing the arrangement of the holes of the composite. In this article, we lift this restriction in order to extend our method to any optimal composite structure for the compliance minimization problem.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116926592","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 : 2010-09-27DOI: 10.1109/MMAR.2010.5587202
L. Zuniga, C. Gonzalez, J. Pedraza, E. Gorrostieta, M. Aceves, J. M. Ramos
This paper presents a novel modeling and simulation methodology applied in the study case of dynamic behavior analysis of a manipulator robot of three degree freedom, so to consider the full mathematical model of the manipulator it is possible to provide support for planning, design and evaluation of the robot, later, an evaluation of the control strategies is performed by adding a PD control with gravity torque compensation. The simulations are executed and it shows the compensation of the gravity effects during the point-to-point trajectory tracking, and therefore the validation of the methodology is done.
{"title":"Modeling and simulation methodology applied in the study case of the analysis of an anthropomorphic manipulator robot","authors":"L. Zuniga, C. Gonzalez, J. Pedraza, E. Gorrostieta, M. Aceves, J. M. Ramos","doi":"10.1109/MMAR.2010.5587202","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587202","url":null,"abstract":"This paper presents a novel modeling and simulation methodology applied in the study case of dynamic behavior analysis of a manipulator robot of three degree freedom, so to consider the full mathematical model of the manipulator it is possible to provide support for planning, design and evaluation of the robot, later, an evaluation of the control strategies is performed by adding a PD control with gravity torque compensation. The simulations are executed and it shows the compensation of the gravity effects during the point-to-point trajectory tracking, and therefore the validation of the methodology is done.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123981196","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 : 2010-09-27DOI: 10.1109/MMAR.2010.5587268
D. Necsulescu, Elisha Pruner, J. Sasiadek, Bumsoo Kim
This paper analyzes several control schemes for nonholonomic vehicles (mobile robots with differential rear wheels) in stabilization and leader — follower manoeuvres. Extensive simulation studies have been conducted to evaluate the performance of existing control schemes and to test new control schemes suggested in this paper. The results for nonholomic vehicles show that polar coordinates control is effective for a variety of initial conditions of the follower, both in stabilization and in tracking.
{"title":"Control of nonholonomic autonomous vehicles and their formations","authors":"D. Necsulescu, Elisha Pruner, J. Sasiadek, Bumsoo Kim","doi":"10.1109/MMAR.2010.5587268","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587268","url":null,"abstract":"This paper analyzes several control schemes for nonholonomic vehicles (mobile robots with differential rear wheels) in stabilization and leader — follower manoeuvres. Extensive simulation studies have been conducted to evaluate the performance of existing control schemes and to test new control schemes suggested in this paper. The results for nonholomic vehicles show that polar coordinates control is effective for a variety of initial conditions of the follower, both in stabilization and in tracking.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125243744","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 : 2010-09-27DOI: 10.1109/MMAR.2010.5587254
Z. Zwierzewicz
The paper is concerned with a problem of adaptive tracking system control synthesis. It is assumed that a nonlinear object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that a nonlinear state feedback plus parameter adaptation are able to ensure its asymptotic stability. The proposed controller design is based on modified adaptive backstepping method. In this approach, as opposite to the standard backstepping, the design process has been reduced to a single iteration, which enables avoiding complicated recursive procedure. An extra task here is to find a control synthesis of linear-like, chained system. The solution of the last problem in general framework is also presented. The obtained thereby controller has several attractive features of both the feedback linearization and backstepping schemes.
{"title":"Adaptive tracking-control synthesis for functionally uncertain systems via modified backstepping","authors":"Z. Zwierzewicz","doi":"10.1109/MMAR.2010.5587254","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587254","url":null,"abstract":"The paper is concerned with a problem of adaptive tracking system control synthesis. It is assumed that a nonlinear object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that a nonlinear state feedback plus parameter adaptation are able to ensure its asymptotic stability. The proposed controller design is based on modified adaptive backstepping method. In this approach, as opposite to the standard backstepping, the design process has been reduced to a single iteration, which enables avoiding complicated recursive procedure. An extra task here is to find a control synthesis of linear-like, chained system. The solution of the last problem in general framework is also presented. The obtained thereby controller has several attractive features of both the feedback linearization and backstepping schemes.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131084522","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 : 2010-09-27DOI: 10.1109/MMAR.2010.5587206
A. Janczak, D. Kujawa
A new approach to the identification of linear repetitive processes based on subspace algorithms is presented. The order of a linear repetitive process, the unknown process matrices, and the noise covariance matrices are determined based on sequences of the actual pass input and the previous pass output, and the actual pass output. The identification procedure can be restarted consecutively starting from the first pass data and boundary conditions. Therefore, the proposed approach can be very useful not only for time invariant linear repetitive processes but also for processes with dynamics that changes rapidly from pass to pass. Simulation example is provided to demonstrate the asymptotic convergence of parameter estimates and the effectiveness of the proposed approach.
{"title":"Identification of linear repetitive processes using subspace algorithms","authors":"A. Janczak, D. Kujawa","doi":"10.1109/MMAR.2010.5587206","DOIUrl":"https://doi.org/10.1109/MMAR.2010.5587206","url":null,"abstract":"A new approach to the identification of linear repetitive processes based on subspace algorithms is presented. The order of a linear repetitive process, the unknown process matrices, and the noise covariance matrices are determined based on sequences of the actual pass input and the previous pass output, and the actual pass output. The identification procedure can be restarted consecutively starting from the first pass data and boundary conditions. Therefore, the proposed approach can be very useful not only for time invariant linear repetitive processes but also for processes with dynamics that changes rapidly from pass to pass. Simulation example is provided to demonstrate the asymptotic convergence of parameter estimates and the effectiveness of the proposed approach.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129532311","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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