Pub Date : 1900-01-01DOI: 10.1137/1.9781611974072.45
H. Kazemi, A. Yazdizadeh, A. Aliabadi
This paper presents an inversion-based fault reconstruction approach for a wide class of nonlinear systems subject to an actuator or plant fault. If the nonlinear system has finite relative order with respect to the fault signal, the inverse system as an observer-based filter, reproduces the fault at its output. A simulation for a continuous-stirred tank reactor (CSTR) model include flow rate fault is used to illustrate the effectiveness of the proposed method.
{"title":"An Inversion-Based Fault Reconstruction Approach in Nonlinear Systems","authors":"H. Kazemi, A. Yazdizadeh, A. Aliabadi","doi":"10.1137/1.9781611974072.45","DOIUrl":"https://doi.org/10.1137/1.9781611974072.45","url":null,"abstract":"This paper presents an inversion-based fault reconstruction approach for a wide class of nonlinear systems subject to an actuator or plant fault. If the nonlinear system has finite relative order with respect to the fault signal, the inverse system as an observer-based filter, reproduces the fault at its output. A simulation for a continuous-stirred tank reactor (CSTR) model include flow rate fault is used to illustrate the effectiveness of the proposed method.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116908989","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 : 1900-01-01DOI: 10.1137/1.9781611974072.63
A. Ruszczynski, Jianing Yao
In this paper, we study the risk-averse control problem for diffusion processes. We make use of a forward–backward system of stochastic differential equations to evaluate a fixed policy and to formulate the optimal control problem. Weak formulation is established to facilitate the derivation of the risk-averse dynamic programming equation. We prove that the value function of the risk-averse control problem is a viscosity solution of a risk-averse analog of the Hamilton– Jacobi–Bellman equation. On the other hand, a verification theorem is provedwhen the classical solution of the equation exists.
{"title":"A Risk-Averse Analog of the Hamilton-Jacobi-Bellman Equation","authors":"A. Ruszczynski, Jianing Yao","doi":"10.1137/1.9781611974072.63","DOIUrl":"https://doi.org/10.1137/1.9781611974072.63","url":null,"abstract":"In this paper, we study the risk-averse control problem for diffusion processes. We make use of a forward–backward system of stochastic differential equations to evaluate a fixed policy and to formulate the optimal control problem. Weak formulation is established to facilitate the derivation of the risk-averse dynamic programming equation. We prove that the value function of the risk-averse control problem is a viscosity solution of a risk-averse analog of the Hamilton– Jacobi–Bellman equation. On the other hand, a verification theorem is provedwhen the classical solution of the equation exists.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"4 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122597829","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 : 1900-01-01DOI: 10.1137/1.9781611974072.52
W. McEneaney, P. Dower
The use of stationary-action formulations for dynamical systems allows one to generate fundamental solutions for classes of two-point boundary-value problems (TPBVPs). One solves for stationary points of the payoff as a function of inputs, a task which is significantly different from that in optimal control problems. Both a dynamic programming principle (DPP) and a Hamilton-Jacobi partial differential equation (HJ PDE) are obtained for a class of problems subsuming the stationary-action formulation. Although convexity (or concavity) of the payoff may be lost as one propagates forward, stationary points continue to exist, and one must be able to use the DPP and/or HJ PDE to solve forward to such time horizons. In linear/quadratic models, this leads to a requirement for propagation of solutions of differential Riccati equations past finite escape times. Such propagation is also required in (nonlinear) n-body problem formulations where the potential is represented via semiconvex duality.
{"title":"Staticization and Associated Hamilton-Jacobi and Riccati Equations","authors":"W. McEneaney, P. Dower","doi":"10.1137/1.9781611974072.52","DOIUrl":"https://doi.org/10.1137/1.9781611974072.52","url":null,"abstract":"The use of stationary-action formulations for dynamical systems allows one to generate fundamental solutions for classes of two-point boundary-value problems (TPBVPs). One solves for stationary points of the payoff as a function of inputs, a task which is significantly different from that in optimal control problems. Both a dynamic programming principle (DPP) and a Hamilton-Jacobi partial differential equation (HJ PDE) are obtained for a class of problems subsuming the stationary-action formulation. Although convexity (or concavity) of the payoff may be lost as one propagates forward, stationary points continue to exist, and one must be able to use the DPP and/or HJ PDE to solve forward to such time horizons. In linear/quadratic models, this leads to a requirement for propagation of solutions of differential Riccati equations past finite escape times. Such propagation is also required in (nonlinear) n-body problem formulations where the potential is represented via semiconvex duality.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116614391","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 : 1900-01-01DOI: 10.1137/1.9781611973273.27
W. McEneaney, P. Dower
Two-point boundary problems for conservative systems are studied in the context of the least action principle. The emphasis is on the N -body problem under gravitation. There, the least action principle optimal control problem is converted to a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. For problems where the time-duration is below a specified bound, fundamental solutions are obtained as indexed sets of solutions of Riccati equations.
{"title":"The Principle of Least Action and Solution of Two-Point Boundary Value Problems on a Limited Time Horizon","authors":"W. McEneaney, P. Dower","doi":"10.1137/1.9781611973273.27","DOIUrl":"https://doi.org/10.1137/1.9781611973273.27","url":null,"abstract":"Two-point boundary problems for conservative systems are studied in the context of the least action principle. The emphasis is on the N -body problem under gravitation. There, the least action principle optimal control problem is converted to a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. For problems where the time-duration is below a specified bound, fundamental solutions are obtained as indexed sets of solutions of Riccati equations.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"48 9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117294244","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 : 1900-01-01DOI: 10.1137/1.9781611974072.11
A. Mansouri
We consider the problem of local asymptotic feedback stabilization – via a continuously differentiable feedback law – of a control system ẋ = f(x,u) defined in Euclidean space R n (with f being continuously differentiable) to a compact, connected, oriented p−dimensional submanifold P of R, subject to the constraint that the scalar entries of the system function f and of the feedback law u depend only on selected subsets of the state variables. Such constraints arise naturally in the context of distributed control systems, typically consisting of multiple agents with only local communication between the various agents. We obtain topological necessary conditions for the existence of such a stabilizing feedback control law when the submanifold to be stabilized to is even-dimensional; these topological conditions are expressed in terms of the generators of the homology groups of certain topological spaces naturally associated with the control problem, as well as the topology of the submanifold to which stabilization is to be performed.
{"title":"Topological obstructions to distributed feedback stabilization to a submanifold","authors":"A. Mansouri","doi":"10.1137/1.9781611974072.11","DOIUrl":"https://doi.org/10.1137/1.9781611974072.11","url":null,"abstract":"We consider the problem of local asymptotic feedback stabilization – via a continuously differentiable feedback law – of a control system ẋ = f(x,u) defined in Euclidean space R n (with f being continuously differentiable) to a compact, connected, oriented p−dimensional submanifold P of R, subject to the constraint that the scalar entries of the system function f and of the feedback law u depend only on selected subsets of the state variables. Such constraints arise naturally in the context of distributed control systems, typically consisting of multiple agents with only local communication between the various agents. We obtain topological necessary conditions for the existence of such a stabilizing feedback control law when the submanifold to be stabilized to is even-dimensional; these topological conditions are expressed in terms of the generators of the homology groups of certain topological spaces naturally associated with the control problem, as well as the topology of the submanifold to which stabilization is to be performed.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"22 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120894308","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 : 1900-01-01DOI: 10.1137/1.9781611973273.12
H. Banks, D. Rubio, N. Saintier, M. I. Troparevsky
Parameter estimation problems consist in approximating parameter values of a given mathematical model based on measured data. They are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. The problem of collecting data in the “best way” in order to assure a statistically efficient estimate of the parameter is known as Optimal Design. In this work we consider the problem of finding optimal locations for source identification in the 3D unit sphere from data on its boundary. We apply three different optimal design criteria to this 3D problem: the Incremental Generalized Sensitivity Function (IGSF), the classical D-optimal criterion and the SE-criterion recently introduced in [3]. The estimation of the parameters is then obtained by means of the Ordinary Least Square procedure. In order to analyze the performance of each strategy, the data are numerically simulated and the estimated values are compared with the values used for simulation.
{"title":"Optimal Design Techniques for Distributed Parameter Systems","authors":"H. Banks, D. Rubio, N. Saintier, M. I. Troparevsky","doi":"10.1137/1.9781611973273.12","DOIUrl":"https://doi.org/10.1137/1.9781611973273.12","url":null,"abstract":"Parameter estimation problems consist in approximating parameter values of a given mathematical model based on measured data. They are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. The problem of collecting data in the “best way” in order to assure a statistically efficient estimate of the parameter is known as Optimal Design. In this work we consider the problem of finding optimal locations for source identification in the 3D unit sphere from data on its boundary. We apply three different optimal design criteria to this 3D problem: the Incremental Generalized Sensitivity Function (IGSF), the classical D-optimal criterion and the SE-criterion recently introduced in [3]. The estimation of the parameters is then obtained by means of the Ordinary Least Square procedure. In order to analyze the performance of each strategy, the data are numerically simulated and the estimated values are compared with the values used for simulation.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127170543","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 : 1900-01-01DOI: 10.1137/1.9781611973273.5
M. Benosman, Gökhan M. Atinç
We study here the problem of robust ‘soft-landing’ control for electromagnetic actuators. The soft landing requires accurate control of the actuators moving element between two desired positions. We present here two nonlinear adaptive controllers to solve the problem of robust trajectory tracking for the moving element. The first controller is based on classical nonlinear adaptive technique. We show that this controller ensures bounded tracking errors of the reference trajectories and bounded estimation error of the uncertain parameters. Second, we present a controller based on the so-called Input-to-State Stability (ISS), merged with gradient descent estimation filters to estimate the uncertain parameters. We show that it ensures bounded tracking errors for bounded estimation errors, furthermore, due to the ISS results we conclude that the tracking errors bounds decrease as function of the estimation errors. We demonstrate the effectiveness of these controllers on a simulation example.
{"title":"Nonlinear Adaptive Control for Electromagnetic Actuators","authors":"M. Benosman, Gökhan M. Atinç","doi":"10.1137/1.9781611973273.5","DOIUrl":"https://doi.org/10.1137/1.9781611973273.5","url":null,"abstract":"We study here the problem of robust ‘soft-landing’ control for electromagnetic actuators. The soft landing requires accurate control of the actuators moving element between two desired positions. We present here two nonlinear adaptive controllers to solve the problem of robust trajectory tracking for the moving element. The first controller is based on classical nonlinear adaptive technique. We show that this controller ensures bounded tracking errors of the reference trajectories and bounded estimation error of the uncertain parameters. Second, we present a controller based on the so-called Input-to-State Stability (ISS), merged with gradient descent estimation filters to estimate the uncertain parameters. We show that it ensures bounded tracking errors for bounded estimation errors, furthermore, due to the ISS results we conclude that the tracking errors bounds decrease as function of the estimation errors. We demonstrate the effectiveness of these controllers on a simulation example.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126709196","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 : 1900-01-01DOI: 10.1137/1.9781611973273.28
N. Bayramov, Tigran Nagapetyan, R. Pinnau
We present optimization problem for Asymmetric Flow Field Flow Fractionation, which is a widely used technique for segregation of two or more particles of submicron scale, according to their hydrodynamic radius. We give a short description of AF4 and present one way coupled model. For an optimization problem we use the sensitivities due to the special structure of the objective functional for this specific application and memory constraints.
{"title":"Fast Optimal Control of Asymmetric Flow Field Flow Fractionation Processes","authors":"N. Bayramov, Tigran Nagapetyan, R. Pinnau","doi":"10.1137/1.9781611973273.28","DOIUrl":"https://doi.org/10.1137/1.9781611973273.28","url":null,"abstract":"We present optimization problem for Asymmetric Flow Field Flow Fractionation, which is a widely used technique for segregation of two or more particles of submicron scale, according to their hydrodynamic radius. We give a short description of AF4 and present one way coupled model. For an optimization problem we use the sensitivities due to the special structure of the objective functional for this specific application and memory constraints.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126768119","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 : 1900-01-01DOI: 10.1137/1.9781611974072.21
Robert Schmid, Qingbin Gao, N. Olgaç
We consider the problem of pole assignment for a linear time invariant plant with state feedback subject to multiple time delays in the control input. For systems with a known time delay, we offer a parametric formula for the feedback gain matrix that will assign a desired set of closedloop eigenvalues to the time-delay system. We consider some well-established pole placement methods for systems without delay that utilise pole placement via state feedback in order to achieve their desired performance objective. We explore the extent to which their desired control performance objective may be successfully achieved for a time-delay system by placing the primary poles of the delayed system at the same locations as for the system without delay. The role of the secondary poles of the time-delay system will also be investigated since they are known to affect both the stability and performance.
{"title":"Eigenvalue assignment for systems with multiple time-delays","authors":"Robert Schmid, Qingbin Gao, N. Olgaç","doi":"10.1137/1.9781611974072.21","DOIUrl":"https://doi.org/10.1137/1.9781611974072.21","url":null,"abstract":"We consider the problem of pole assignment for a linear time invariant plant with state feedback subject to multiple time delays in the control input. For systems with a known time delay, we offer a parametric formula for the feedback gain matrix that will assign a desired set of closedloop eigenvalues to the time-delay system. We consider some well-established pole placement methods for systems without delay that utilise pole placement via state feedback in order to achieve their desired performance objective. We explore the extent to which their desired control performance objective may be successfully achieved for a time-delay system by placing the primary poles of the delayed system at the same locations as for the system without delay. The role of the secondary poles of the time-delay system will also be investigated since they are known to affect both the stability and performance.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129824168","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 : 1900-01-01DOI: 10.1137/1.9781611974072.13
V. D. S. Martins, M. Rodrigues
This paper considers the control design of a nonlinear distributed parameter system in infinite dimension, described by the hyperbolic Partial Differential Equations (PDEs) of de Saint-Venant. The nonlinear system dynamic is formulated by a Multi-Models approach over a wide operating range, where each local model is defined around a set of operating regimes. A Proportional Integral (PI) feedback was designed and performed through Bilinear Operator Inequality (BOI) and Linear Operator Inequality (LOI) techniques for infinite dimensional systems. The authors propose in this paper to improve the numerical part by introducing weight μi not only equal to {0,1}, but μi ∈ [0, 1].
{"title":"Some numerical extension for the LOI/BOI approach for the control of de Saint-Venant equations in infinite dimension","authors":"V. D. S. Martins, M. Rodrigues","doi":"10.1137/1.9781611974072.13","DOIUrl":"https://doi.org/10.1137/1.9781611974072.13","url":null,"abstract":"This paper considers the control design of a nonlinear distributed parameter system in infinite dimension, described by the hyperbolic Partial Differential Equations (PDEs) of de Saint-Venant. The nonlinear system dynamic is formulated by a Multi-Models approach over a wide operating range, where each local model is defined around a set of operating regimes. A Proportional Integral (PI) feedback was designed and performed through Bilinear Operator Inequality (BOI) and Linear Operator Inequality (LOI) techniques for infinite dimensional systems. The authors propose in this paper to improve the numerical part by introducing weight μi not only equal to {0,1}, but μi ∈ [0, 1].","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121582315","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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