Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697290
Huan Zhang, P. Dower, W. McEneaney
This paper develops an efficient computational method for solving a class of discrete time linear regulator problems, in which the payoff functions are not necessarily quadratic. The proposed method exploits the convexity of the payoff functions and approximates the attendant value function via a max-plus sum of affine functions. As the number of affine functions represented in this approximation can grow exponentially with the number of iterations of the computational method, effective pruning algorithms to manage complexity are essential. Two such algorithms are developed in this work. The utility of these algorithms is demonstrated via an example.
{"title":"A pruning algorithm for managing complexity in the solution of a class of linear non-quadratic regulator problems","authors":"Huan Zhang, P. Dower, W. McEneaney","doi":"10.1109/AUCC.2013.6697290","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697290","url":null,"abstract":"This paper develops an efficient computational method for solving a class of discrete time linear regulator problems, in which the payoff functions are not necessarily quadratic. The proposed method exploits the convexity of the payoff functions and approximates the attendant value function via a max-plus sum of affine functions. As the number of affine functions represented in this approximation can grow exponentially with the number of iterations of the computational method, effective pruning algorithms to manage complexity are essential. Two such algorithms are developed in this work. The utility of these algorithms is demonstrated via an example.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127651213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697306
Zhang Zheng, Seunghwan Baek, D. Yu, K. Chong
A general order hold time discretization method for input-driven nonlinear continuous time-delay systems is proposed which can be applied for different order sampling hold assumptions. It is based on a combination of Taylor series expansion and the theory of sampling and hold where the mathematical structure for the new discretization scheme is introduced in detail in this paper. The performance of the proposed discretization procedure is compared by different types of systems through various sampling rates, time delays, input signals, order of sampling hold assumptions and truncation orders. Results show that the proposed scheme is applicable for use in control systems and several useful summarized rules for this method are presented in the conclusion.
{"title":"Comparison study of the Taylor series based discretization method for nonlinear input-delay systems","authors":"Zhang Zheng, Seunghwan Baek, D. Yu, K. Chong","doi":"10.1109/AUCC.2013.6697306","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697306","url":null,"abstract":"A general order hold time discretization method for input-driven nonlinear continuous time-delay systems is proposed which can be applied for different order sampling hold assumptions. It is based on a combination of Taylor series expansion and the theory of sampling and hold where the mathematical structure for the new discretization scheme is introduced in detail in this paper. The performance of the proposed discretization procedure is compared by different types of systems through various sampling rates, time delays, input signals, order of sampling hold assumptions and truncation orders. Results show that the proposed scheme is applicable for use in control systems and several useful summarized rules for this method are presented in the conclusion.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128664603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697241
D. Jiang
In this paper, a self-organizing map (SOM) based procedure is proposed for MRI image processing. Such images are usually corrupted by Rician noise generated during the image formation processing due to the nature of MRI technique. Rician noise is non-additive, signal dependent, and highly nonlinear, significantly different from those commonly discussed in images. These features make it very difficult to separate the signal from noise. A SOM algorithm is carefully applied to accurate MRI image processing by taking the decent Rician noise feature into consideration, resulting in a novel procedure for denosing and segmentation. The procedure is intuitively developed and justified, and demonstrated using simulation examples on a typical knee cartilage MRI image.
{"title":"A SOM algorithm based procedure for MRI image processing under significant Rician noise","authors":"D. Jiang","doi":"10.1109/AUCC.2013.6697241","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697241","url":null,"abstract":"In this paper, a self-organizing map (SOM) based procedure is proposed for MRI image processing. Such images are usually corrupted by Rician noise generated during the image formation processing due to the nature of MRI technique. Rician noise is non-additive, signal dependent, and highly nonlinear, significantly different from those commonly discussed in images. These features make it very difficult to separate the signal from noise. A SOM algorithm is carefully applied to accurate MRI image processing by taking the decent Rician noise feature into consideration, resulting in a novel procedure for denosing and segmentation. The procedure is intuitively developed and justified, and demonstrated using simulation examples on a typical knee cartilage MRI image.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128856284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697278
Daniel J. McInnes, B. Miller
We consider a time-inhomogeneous Markov chain with a compound Poisson process as an input as an important approximation to get the solution of real problems. Outflows are comprised of both controlled and uncontrolled counting processes. We demonstrate the utility of this model in the specific problem of demand control and flood prevention in a nearly full dam, where the dam is modeled as a continuous-time controllable Markov chain under control resource constraints. This work significantly extends previous results because the inflow of rain is potentially sudden and of large volume, so a compound Poisson process is preferred to simple counting processes. On the other hand the safe release of water is constrained and so is modelled as a simple counting process. A proof of the infinitesimal generator of the Markov chain with these characteristics is given and a numerical example demonstrates the effectiveness of the controls.
{"title":"Optimal control of time-inhomogeneous Markov chains with application to dam management","authors":"Daniel J. McInnes, B. Miller","doi":"10.1109/AUCC.2013.6697278","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697278","url":null,"abstract":"We consider a time-inhomogeneous Markov chain with a compound Poisson process as an input as an important approximation to get the solution of real problems. Outflows are comprised of both controlled and uncontrolled counting processes. We demonstrate the utility of this model in the specific problem of demand control and flood prevention in a nearly full dam, where the dam is modeled as a continuous-time controllable Markov chain under control resource constraints. This work significantly extends previous results because the inflow of rain is potentially sudden and of large volume, so a compound Poisson process is preferred to simple counting processes. On the other hand the safe release of water is constrained and so is modelled as a simple counting process. A proof of the infinitesimal generator of the Markov chain with these characteristics is given and a numerical example demonstrates the effectiveness of the controls.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121171150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697279
A. Miller, B. Miller
The article considers the optimal stochastic control approach to the analysis of TCP. Generally the analysis of TCP schemes is based on so-called fluid models which provide the asymptotic behavior of the queuing system where the number of jobs is huge. At this level of consideration only the asymptotic results could be obtained and the real performance of existing protocols is still unclear particularly if there are the seasonal changes and congestions. Meanwhile, the models of controllable Markov chains (CMC) are more appropriate to the analysis of control of flows in the Internet that has been observed by many authors long ago. The principal difficulty of the CMC application is the high dimension particularly for connected controllable Markov chains (CCMC). But nowadays this problem is less important due to the development of multiprocessor supercomputers that make the numerical solution of the optimal control problems for CMC more achievable. Models of CCMC arise in queuing systems with many service lines where some idle lines may be used to avoid the congestion if the principal lines have been subjected the huge workload. Here we suggest the tensor form of such CMC description and give the dynamic programming equation in corresponding tensor form. As examples we consider the results of CMC approach to control the system with one service line, system with two service lines, namely the main and reserve ones, having different service rates and the cost of service, and to the system with incomplete information about the router state.
{"title":"Application of stochastic control to analysis and optimization of TCP","authors":"A. Miller, B. Miller","doi":"10.1109/AUCC.2013.6697279","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697279","url":null,"abstract":"The article considers the optimal stochastic control approach to the analysis of TCP. Generally the analysis of TCP schemes is based on so-called fluid models which provide the asymptotic behavior of the queuing system where the number of jobs is huge. At this level of consideration only the asymptotic results could be obtained and the real performance of existing protocols is still unclear particularly if there are the seasonal changes and congestions. Meanwhile, the models of controllable Markov chains (CMC) are more appropriate to the analysis of control of flows in the Internet that has been observed by many authors long ago. The principal difficulty of the CMC application is the high dimension particularly for connected controllable Markov chains (CCMC). But nowadays this problem is less important due to the development of multiprocessor supercomputers that make the numerical solution of the optimal control problems for CMC more achievable. Models of CCMC arise in queuing systems with many service lines where some idle lines may be used to avoid the congestion if the principal lines have been subjected the huge workload. Here we suggest the tensor form of such CMC description and give the dynamic programming equation in corresponding tensor form. As examples we consider the results of CMC approach to control the system with one service line, system with two service lines, namely the main and reserve ones, having different service rates and the cost of service, and to the system with incomplete information about the router state.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114118327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697242
Changjun Yu, K. Teo, T. Tay
In this paper, we consider a class of optimal control problems where the variation of the control variable is appended as a penalty term into the cost function to reduce the fluctuation of the control. A new computational approach is developed for solving this type of problems, based on control parametrization technique used in conjunction with the time scaling transform, the constraint transcription method and a smoothing technique. This computational method is supported by rigorous convergence analysis.
{"title":"Optimal control with a cost of changing control","authors":"Changjun Yu, K. Teo, T. Tay","doi":"10.1109/AUCC.2013.6697242","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697242","url":null,"abstract":"In this paper, we consider a class of optimal control problems where the variation of the control variable is appended as a penalty term into the cost function to reduce the fluctuation of the control. A new computational approach is developed for solving this type of problems, based on control parametrization technique used in conjunction with the time scaling transform, the constraint transcription method and a smoothing technique. This computational method is supported by rigorous convergence analysis.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123471401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697247
J. Doná, J. Lévine
In this paper, the problem of state and input constrained control is addressed. We obtain a local description of the boundary of the admissible subset of the state space where the state and input constraints can be satisfied for all times. This boundary is made of two disjoint parts: the subset of the state constraint boundary on which there are trajectories pointing towards the interior of the admissible set or tangentially to it; and a barrier, namely a semipermeable surface which is constructed via a minimum-like principle.
{"title":"On constrained continuous-time nonlinear control systems","authors":"J. Doná, J. Lévine","doi":"10.1109/AUCC.2013.6697247","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697247","url":null,"abstract":"In this paper, the problem of state and input constrained control is addressed. We obtain a local description of the boundary of the admissible subset of the state space where the state and input constraints can be satisfied for all times. This boundary is made of two disjoint parts: the subset of the state constraint boundary on which there are trajectories pointing towards the interior of the admissible set or tangentially to it; and a barrier, namely a semipermeable surface which is constructed via a minimum-like principle.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124985945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697255
Ying Zhang, Rui Zhang, A. Wu
This study considers the design of l2 - l∞ filters for Markov jump systems under asynchronous switching. The asynchronous behavior described by a stochastic variable is considered to be random mismatch between system modes and candidate filters. The jumping process of the filtering error system is modeled as a two component Markov chain. Using a stochastic parameter-dependent approach, sufficient conditions for the addressed filtering problem are obtained. By solving the proposed conditions, a desired l2 - l∞ filter can be constructed for any admissible random mismatch. Moreover, a key relationship of l2 - l∞ performance between the presented results and the classical mode-dependent, mode-independent filtering is demonstrated. A numerical example is provided to illustrate the validity and potential of the developed method.
{"title":"Asynchronous l2 − l∞ filtering for Markov jump systems","authors":"Ying Zhang, Rui Zhang, A. Wu","doi":"10.1109/AUCC.2013.6697255","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697255","url":null,"abstract":"This study considers the design of l2 - l∞ filters for Markov jump systems under asynchronous switching. The asynchronous behavior described by a stochastic variable is considered to be random mismatch between system modes and candidate filters. The jumping process of the filtering error system is modeled as a two component Markov chain. Using a stochastic parameter-dependent approach, sufficient conditions for the addressed filtering problem are obtained. By solving the proposed conditions, a desired l2 - l∞ filter can be constructed for any admissible random mismatch. Moreover, a key relationship of l2 - l∞ performance between the presented results and the classical mode-dependent, mode-independent filtering is demonstrated. A numerical example is provided to illustrate the validity and potential of the developed method.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123780727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697317
K. Karvinen, S. Moheimani
We review the modulated-demodulated control technique, emphasize its linear time invariant nature and develop state space controller models. We have previously outlined the implementation of a modulated-demodulated positive position feedback controller and extend upon this result with the implementation of a resonant controller. Negative imaginary systems theory has important implications in the control of many practical systems and use of the derived state space model simplifies the design of negative imaginary controllers. To conclude, we demonstrate the closed loop control of the quality factor of a Bruker DMASP microcantilever and highlight improvements in atomic force microscopy (AFM). The modulated-demodulated control technique is well suited to the control of systems with high-frequency resonant dynamics.
{"title":"Analysis and application of modulated-demodulated control","authors":"K. Karvinen, S. Moheimani","doi":"10.1109/AUCC.2013.6697317","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697317","url":null,"abstract":"We review the modulated-demodulated control technique, emphasize its linear time invariant nature and develop state space controller models. We have previously outlined the implementation of a modulated-demodulated positive position feedback controller and extend upon this result with the implementation of a resonant controller. Negative imaginary systems theory has important implications in the control of many practical systems and use of the derived state space model simplifies the design of negative imaginary controllers. To conclude, we demonstrate the closed loop control of the quality factor of a Bruker DMASP microcantilever and highlight improvements in atomic force microscopy (AFM). The modulated-demodulated control technique is well suited to the control of systems with high-frequency resonant dynamics.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116470997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-11-01DOI: 10.1109/AUCC.2013.6697316
Robert Schmid, L. Ntogramatzidis, T. Nguyen, Amit P. Pandey
We consider the classic problem of pole placement by state feedback. Recently [1] offered an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing gain matrix to deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. In this paper we employ this parametric formula to introduce an unconstrained nonlinear optimisation algorithm to obtain a gain matrix that delivers any desired pole placement with optimal robustness.
{"title":"Robust repeated pole placement","authors":"Robert Schmid, L. Ntogramatzidis, T. Nguyen, Amit P. Pandey","doi":"10.1109/AUCC.2013.6697316","DOIUrl":"https://doi.org/10.1109/AUCC.2013.6697316","url":null,"abstract":"We consider the classic problem of pole placement by state feedback. Recently [1] offered an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing gain matrix to deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. In this paper we employ this parametric formula to introduce an unconstrained nonlinear optimisation algorithm to obtain a gain matrix that delivers any desired pole placement with optimal robustness.","PeriodicalId":177490,"journal":{"name":"2013 Australian Control Conference","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124428228","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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