Boundary feedback control of nonlinear distributed parameter systems is considered. The goal is the development of systematic strategies of designing feedback laws which can shape or at least influence the response of nonlinear systems with distributed components. The authors extend the definition of zero dynamics to include nonlinear distributed parameter systems with an aim toward the design of stabilizing feedback laws. They also compute the zero dynamics for a controlled viscous Burgers equation. They precede this discussion with a simple but related illustration of a strategy for a controlled heat equation and, using a similar strategy for the Burgers equation, they conclude with a preliminary analysis and feedback design and present simulations of the trajectories of the corresponding closed-loop system.<>
{"title":"Boundary feedback design for nonlinear distributed parameter systems","authors":"C. Byrnes, D. Gilliam","doi":"10.1109/CDC.1991.261594","DOIUrl":"https://doi.org/10.1109/CDC.1991.261594","url":null,"abstract":"Boundary feedback control of nonlinear distributed parameter systems is considered. The goal is the development of systematic strategies of designing feedback laws which can shape or at least influence the response of nonlinear systems with distributed components. The authors extend the definition of zero dynamics to include nonlinear distributed parameter systems with an aim toward the design of stabilizing feedback laws. They also compute the zero dynamics for a controlled viscous Burgers equation. They precede this discussion with a simple but related illustration of a strategy for a controlled heat equation and, using a similar strategy for the Burgers equation, they conclude with a preliminary analysis and feedback design and present simulations of the trajectories of the corresponding closed-loop system.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"2016 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127398316","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}
An optimal stochastic control problem that minimizes the intensity for a signal to cross a level in the upward direction is solved. The optimal controller also approximately minimizes the probability that the signal is above the level. The latter problem has previously been solved approximately by minimum variance control, which is known to have a badly behaved control signal. To overcome this, weighting on the control signal-LQG-design-has been proposed, but there has been no good criterion on how to choose the weighting. The problem is rewritten as a one-parametric optimization problem over a set of LQG-problem solutions, and the solution can sometimes be thought of as finding optimal weightings in an LQG-problem.<>
{"title":"Control of extremes and level-crossings in stationary Gaussian random processes","authors":"A. Hansson","doi":"10.1109/CDC.1991.261727","DOIUrl":"https://doi.org/10.1109/CDC.1991.261727","url":null,"abstract":"An optimal stochastic control problem that minimizes the intensity for a signal to cross a level in the upward direction is solved. The optimal controller also approximately minimizes the probability that the signal is above the level. The latter problem has previously been solved approximately by minimum variance control, which is known to have a badly behaved control signal. To overcome this, weighting on the control signal-LQG-design-has been proposed, but there has been no good criterion on how to choose the weighting. The problem is rewritten as a one-parametric optimization problem over a set of LQG-problem solutions, and the solution can sometimes be thought of as finding optimal weightings in an LQG-problem.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129056887","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}
A singularly perturbed nonlinear system with a control input and a measured output is considered, under the supposition that a static nonlinear output feedback law is designed. It is shown that the operations 'compute the reduced-order system' and 'close the feedback loop'. It is then shown that, if the reduced-order system associated with the original system has uncertainties matched with the input, a condition frequently used in the design of robust control systems, then the closed-loop reduced-order system enjoys the same property.<>
{"title":"A further note on output feedback control for singularly perturbed systems","authors":"M. Corless, F. Garofalo, L. Glielmo","doi":"10.1109/CDC.1991.261517","DOIUrl":"https://doi.org/10.1109/CDC.1991.261517","url":null,"abstract":"A singularly perturbed nonlinear system with a control input and a measured output is considered, under the supposition that a static nonlinear output feedback law is designed. It is shown that the operations 'compute the reduced-order system' and 'close the feedback loop'. It is then shown that, if the reduced-order system associated with the original system has uncertainties matched with the input, a condition frequently used in the design of robust control systems, then the closed-loop reduced-order system enjoys the same property.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129067832","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 authors show that a simple modification of projecting the estimates continuously to stay in a compact convex set yields an adaptive controller which is robust to bounded disturbances and small unmodeled dynamics for continuous-time plants of arbitrary relative degree. It is demonstrated that eventually all the signals enter a compact set, the size of which is independent of initial conditions. Also, the upper-bounds on the size of allowable unmodeled dynamics are independent of initial conditions. An estimate of the performance as measured by the mean-square tracking error is obtained. The results show that the projection mechanism alone is sufficient to guarantee robust boundedness and robust performance with respect to bounded disturbances and small unmodeled dynamics. Some time-varying and nonlinear uncertainties are allowed. The nominal plant is however restricted to be minimum-phase.<>
{"title":"Robust continuous time adaptive control by parameter projection","authors":"Sanjeev M. Naik, P. R. Kumar, B. Ydstie","doi":"10.1109/CDC.1991.261410","DOIUrl":"https://doi.org/10.1109/CDC.1991.261410","url":null,"abstract":"The authors show that a simple modification of projecting the estimates continuously to stay in a compact convex set yields an adaptive controller which is robust to bounded disturbances and small unmodeled dynamics for continuous-time plants of arbitrary relative degree. It is demonstrated that eventually all the signals enter a compact set, the size of which is independent of initial conditions. Also, the upper-bounds on the size of allowable unmodeled dynamics are independent of initial conditions. An estimate of the performance as measured by the mean-square tracking error is obtained. The results show that the projection mechanism alone is sufficient to guarantee robust boundedness and robust performance with respect to bounded disturbances and small unmodeled dynamics. Some time-varying and nonlinear uncertainties are allowed. The nominal plant is however restricted to be minimum-phase.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122374011","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}
G. Dumont, M. Davies, K. Natarajan, C. Lindeborg, F. T. Ordubadi, Y. Fu, K. Kristinsson, I. Jonsson
An improved estimation algorithm for use in processing data generated online by a scanning sensor is described. The algorithm is to be used as part of a paper machine control system to maintain the moisture content of the sheet at a target value. The algorithm rapidly estimates, in the presence of noise, cross and machine direction moisture profiles. The basic algorithm consists of a modified least-squares parameter identifier for estimating cross direction profile deviations and a Kalman filter for estimating machine direction disturbances. Simulation results showing the effectiveness of the algorithm in estimating known profiles are given. Results of the offline application of the algorithm to industrial data are also given. Online tests have been performed to demonstrate the improvements in accuracy and speed of detection of process upsets.<>
{"title":"An improved algorithm for estimating paper machine moisture profiles using scanned data","authors":"G. Dumont, M. Davies, K. Natarajan, C. Lindeborg, F. T. Ordubadi, Y. Fu, K. Kristinsson, I. Jonsson","doi":"10.1109/CDC.1991.261734","DOIUrl":"https://doi.org/10.1109/CDC.1991.261734","url":null,"abstract":"An improved estimation algorithm for use in processing data generated online by a scanning sensor is described. The algorithm is to be used as part of a paper machine control system to maintain the moisture content of the sheet at a target value. The algorithm rapidly estimates, in the presence of noise, cross and machine direction moisture profiles. The basic algorithm consists of a modified least-squares parameter identifier for estimating cross direction profile deviations and a Kalman filter for estimating machine direction disturbances. Simulation results showing the effectiveness of the algorithm in estimating known profiles are given. Results of the offline application of the algorithm to industrial data are also given. Online tests have been performed to demonstrate the improvements in accuracy and speed of detection of process upsets.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130776992","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 authors deal with the class of noisy observations of a controlled finite-state Markov process which modulates the rate of point processes. The control problems for a finite-state Markov process under partial observations are reformulated as ones for piecewise deterministic processes. In a weak sense, the value function is shown to be a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equations.<>
{"title":"Optimal control of finite state Markov processes under counting observations","authors":"D. Shin, Erik I. Verriest","doi":"10.1109/CDC.1991.261351","DOIUrl":"https://doi.org/10.1109/CDC.1991.261351","url":null,"abstract":"The authors deal with the class of noisy observations of a controlled finite-state Markov process which modulates the rate of point processes. The control problems for a finite-state Markov process under partial observations are reformulated as ones for piecewise deterministic processes. In a weak sense, the value function is shown to be a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equations.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133000332","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 authors present different approaches for stabilizing mechanical systems with parametric uncertainties. They focus on incompletely controlled manipulators having less actuators than degrees of freedom, and use two stabilization techniques, the linearization technique and the Lyapunov approach. Adaptive versions of these methods are introduced to deal with the problem of parametric uncertainties. The results are applied to the control of an overhead crane. On this example the robustness of the nonadaptive control laws is compared and simulation results of the two adaptive schemes are analyzed.<>
{"title":"Adaptive control of a class of mechanical systems using linearization and Lyapunov methods: a comparative study on the overhead crane example","authors":"B. d'Andréa-Novel, F. Boustany","doi":"10.1109/CDC.1991.261268","DOIUrl":"https://doi.org/10.1109/CDC.1991.261268","url":null,"abstract":"The authors present different approaches for stabilizing mechanical systems with parametric uncertainties. They focus on incompletely controlled manipulators having less actuators than degrees of freedom, and use two stabilization techniques, the linearization technique and the Lyapunov approach. Adaptive versions of these methods are introduced to deal with the problem of parametric uncertainties. The results are applied to the control of an overhead crane. On this example the robustness of the nonadaptive control laws is compared and simulation results of the two adaptive schemes are analyzed.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132098980","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}
Some results on strict positive realness of families of discrete polynomials are given. The main motivation is the need in the area of identification and adaptive control for design criteria of filters ensuring convergence of algorithms in the presence of uncertainty in the plant model. Two main results are given. The first result provides analytical conditions under which a family of polynomials with zeros in a prescribed region of the complex plane is strict positive real or can be made strict positive real over an assigned region of the complex plane through the use of a suitable filter. The second contribution is a design result providing a parameterization of a family of filters maximizing the region of the complex plane on which strict positive realness is achievable and enjoying other optimality properties, such as order minimality.<>
{"title":"Analysis and filter design for strict positive realness of families of polynomials","authors":"A. Tesi, G. Zappa, A. Vicino","doi":"10.1109/CDC.1991.261245","DOIUrl":"https://doi.org/10.1109/CDC.1991.261245","url":null,"abstract":"Some results on strict positive realness of families of discrete polynomials are given. The main motivation is the need in the area of identification and adaptive control for design criteria of filters ensuring convergence of algorithms in the presence of uncertainty in the plant model. Two main results are given. The first result provides analytical conditions under which a family of polynomials with zeros in a prescribed region of the complex plane is strict positive real or can be made strict positive real over an assigned region of the complex plane through the use of a suitable filter. The second contribution is a design result providing a parameterization of a family of filters maximizing the region of the complex plane on which strict positive realness is achievable and enjoying other optimality properties, such as order minimality.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132210010","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 authors address the problems in using a fiber-optic proximity sensor to detect robot end-effector positioning errors in performing a contact task when uncertainties about target position exist. An extended Kalman filter approach is employed to solve the nonlinear filtering problem. Some experimental results are given.<>
{"title":"Extended Kalman filtering for robotic proximity sensing","authors":"Y.F. Li, R. W. Daniel, P. Sharkey","doi":"10.1109/CDC.1991.261481","DOIUrl":"https://doi.org/10.1109/CDC.1991.261481","url":null,"abstract":"The authors address the problems in using a fiber-optic proximity sensor to detect robot end-effector positioning errors in performing a contact task when uncertainties about target position exist. An extended Kalman filter approach is employed to solve the nonlinear filtering problem. Some experimental results are given.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132256040","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 author shows a controller design in which a fuzzy proportional plus derivative (PD) controller augments an adaptive disturbance accommodating controller (DAC) applied to a bank of heat exchangers. The fuzzy PD uses simple rules to enhance the adaptive DAC to improve setpoint regulation. To illustrate the concept, this method is applied to a simulation of the internal thermal control system of Space Station Freedom.<>
{"title":"Fuzzy adaptive proportional-derivative (PD) disturbance accommodation control (DAC) of a bank of heat exchangers","authors":"S. Rogers","doi":"10.1109/CDC.1991.261737","DOIUrl":"https://doi.org/10.1109/CDC.1991.261737","url":null,"abstract":"The author shows a controller design in which a fuzzy proportional plus derivative (PD) controller augments an adaptive disturbance accommodating controller (DAC) applied to a bank of heat exchangers. The fuzzy PD uses simple rules to enhance the adaptive DAC to improve setpoint regulation. To illustrate the concept, this method is applied to a simulation of the internal thermal control system of Space Station Freedom.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130899365","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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