We examine a finite stage, finite state, and finite action dynamic program having a one transition value function and a terminal value function that are affine in an imprecisely known parameter. The special structural characteristics of the one transition value function and the terminal value function have been assumed in order to model parameter imprecision associated with the problem's reward or preference structure. We assume that the parameter of interest has no dynamics, no new information about its value is received once the decision process begins, and its imprecision is described by set inclusion. We seek the set of all parameter independent strategies that are optimal for some value of the imprecisely known parameter. We present a successive approximations procedure for solving this problem.
{"title":"Sequential decisionmaking with imprecise reward structure","authors":"C. White","doi":"10.1109/CDC.1984.272392","DOIUrl":"https://doi.org/10.1109/CDC.1984.272392","url":null,"abstract":"We examine a finite stage, finite state, and finite action dynamic program having a one transition value function and a terminal value function that are affine in an imprecisely known parameter. The special structural characteristics of the one transition value function and the terminal value function have been assumed in order to model parameter imprecision associated with the problem's reward or preference structure. We assume that the parameter of interest has no dynamics, no new information about its value is received once the decision process begins, and its imprecision is described by set inclusion. We seek the set of all parameter independent strategies that are optimal for some value of the imprecisely known parameter. We present a successive approximations procedure for solving this problem.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115957065","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}
In this paper we study a generalization of the almost disturbance decoupling problem by state feedback. Apart from approximate decoupling from the external disturbances to a first to-be-controlled output, we require a second output to be uniformly bounded with respect to the accuracy of decoupling. We also study the situation in which additionally we require the closed loop system to be internally stable. These problems are studied using the geometric approach to linear systems. We introduce some new almost controlled invariant subspaces and study their geometric structure. Necessary and sufficient conditions for the solvability of the above problems are then formulated in terms of these almost controlled invariant subspaces.
{"title":"Almost disturbance decoupling with bounded peaking","authors":"H. Trentelman","doi":"10.1109/CDC.1984.272074","DOIUrl":"https://doi.org/10.1109/CDC.1984.272074","url":null,"abstract":"In this paper we study a generalization of the almost disturbance decoupling problem by state feedback. Apart from approximate decoupling from the external disturbances to a first to-be-controlled output, we require a second output to be uniformly bounded with respect to the accuracy of decoupling. We also study the situation in which additionally we require the closed loop system to be internally stable. These problems are studied using the geometric approach to linear systems. We introduce some new almost controlled invariant subspaces and study their geometric structure. Necessary and sufficient conditions for the solvability of the above problems are then formulated in terms of these almost controlled invariant subspaces.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121711621","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}
Difficulties one faces in designing a satisfactory controller for systems involving stiff nonlinearities are well known. Stictions, Coulomb frictions and backlashes are but a few such examples. Unfortunately, there are few mechanical systems without such nonlinearities. The problem becomes even more complex if some of the state variables are not directly measurable, a situation which occurs not infrequently in practical systems. Unlike in linear systems where the missing state variables may be reconstructed [1], no corresponding methods are available for nonlinear systems. In fact, no general methods are currently available for analyzing and synthesizing controllers for nonlinear systems. At present, the describing function method is perhaps the best tool available for investigating stiff nonlinear systems [2]. A stable system is designed by adjusting the system gain or inserting a simple lead-lag compensation network. The parameter values are determined by graphically examining the Nyquist curve and the describing function. The process becomes very difficult, if not impossible, to apply when the order of the system is high and only the measurable variables are to be used in the feedback. When the reference input is a constant and only the output is available for feedback, the delayed feedback controller was given in [3]. In this paper, preliminary results are presented for the case when the reference input is a polynomial function and a multi-dimensional observable vector is available for feedback. It is based on augmenting the system by additional state variables and then feeding back delayed observable vectors as well as the augmented state variables.
{"title":"Delayed feedback tracking controller for single-input single-output nonlinear systems","authors":"S. Won, D. Chyung","doi":"10.1109/CDC.1984.272134","DOIUrl":"https://doi.org/10.1109/CDC.1984.272134","url":null,"abstract":"Difficulties one faces in designing a satisfactory controller for systems involving stiff nonlinearities are well known. Stictions, Coulomb frictions and backlashes are but a few such examples. Unfortunately, there are few mechanical systems without such nonlinearities. The problem becomes even more complex if some of the state variables are not directly measurable, a situation which occurs not infrequently in practical systems. Unlike in linear systems where the missing state variables may be reconstructed [1], no corresponding methods are available for nonlinear systems. In fact, no general methods are currently available for analyzing and synthesizing controllers for nonlinear systems. At present, the describing function method is perhaps the best tool available for investigating stiff nonlinear systems [2]. A stable system is designed by adjusting the system gain or inserting a simple lead-lag compensation network. The parameter values are determined by graphically examining the Nyquist curve and the describing function. The process becomes very difficult, if not impossible, to apply when the order of the system is high and only the measurable variables are to be used in the feedback. When the reference input is a constant and only the output is available for feedback, the delayed feedback controller was given in [3]. In this paper, preliminary results are presented for the case when the reference input is a polynomial function and a multi-dimensional observable vector is available for feedback. It is based on augmenting the system by additional state variables and then feeding back delayed observable vectors as well as the augmented state variables.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116782463","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}
{"title":"Computer-aided design of complex computing systems","authors":"B. Mercer, A. Ross, J. Trimble","doi":"10.1109/CDC.1984.272072","DOIUrl":"https://doi.org/10.1109/CDC.1984.272072","url":null,"abstract":"","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122398525","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}
This paper uses the fundamental matrix of a regular discrete descriptor system to derive expressions for descriptor reachability and observability matrices. Reachable and unobservable subspaces and a subspace of admissible boundary conditions are defined. It is shown that the natural space for analyzing descriptor system properties seems to be R2n (where n is the dimension of the system), not Rn as is the case for state-space systems. Solutions are provided for the descriptor open-loop control and estimation problems.
{"title":"Descriptor systems: Fundamental matrix, reachability and observability matrices, subspaces","authors":"Frank L. Lewis","doi":"10.1109/CDC.1984.272360","DOIUrl":"https://doi.org/10.1109/CDC.1984.272360","url":null,"abstract":"This paper uses the fundamental matrix of a regular discrete descriptor system to derive expressions for descriptor reachability and observability matrices. Reachable and unobservable subspaces and a subspace of admissible boundary conditions are defined. It is shown that the natural space for analyzing descriptor system properties seems to be R2n (where n is the dimension of the system), not Rn as is the case for state-space systems. Solutions are provided for the descriptor open-loop control and estimation problems.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"263 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122895796","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}
Formulas for the pseudoinverse of a compact operator are applied to linear system identification and scattering function estimation from a finite set of noisy measurements. The result is a nonparametric estimator possessing several desirable features. The approach encompasses the Modified Discrete Fourier Transform and is applied herein to the important problem of closely spaced object resolsution in radar/optical signal processing.
{"title":"Nonparametric identification of continuous linear systems with discrete measurements","authors":"C. Chang, R. Holmes","doi":"10.1109/CDC.1984.272155","DOIUrl":"https://doi.org/10.1109/CDC.1984.272155","url":null,"abstract":"Formulas for the pseudoinverse of a compact operator are applied to linear system identification and scattering function estimation from a finite set of noisy measurements. The result is a nonparametric estimator possessing several desirable features. The approach encompasses the Modified Discrete Fourier Transform and is applied herein to the important problem of closely spaced object resolsution in radar/optical signal processing.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121875091","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 topic of the paper is stable, or robust, detection of deterministic signals in noise, or the estimation of their amplitudes. The space of observations is an L2-space and the detectors or estimators are linear. For the case of one nominally known signal in nominally Gaussian noise, it is allowed that the actual underlying probability measure lies anywhere within distance ¿ of the nominal measure in the Prokhorov metric. An optimization problem is formulated and solved; its solution is a most stable detector according to a reasonable criterion for optimality for the class of perturbations mentioned. For the case of several nominally known signals in nominally known noise, the problem is recast as estimation of signal amplitudes. An optimization problem, similar to that for the one-signal case, is formulated and solved. The solution is a most stable estimator, by a criterion justified now only in an L2-context, without reference to probability measures.
{"title":"Stability in detection of signals in noise","authors":"P. Kelly, W. Root","doi":"10.1109/CDC.1984.272273","DOIUrl":"https://doi.org/10.1109/CDC.1984.272273","url":null,"abstract":"The topic of the paper is stable, or robust, detection of deterministic signals in noise, or the estimation of their amplitudes. The space of observations is an L2-space and the detectors or estimators are linear. For the case of one nominally known signal in nominally Gaussian noise, it is allowed that the actual underlying probability measure lies anywhere within distance ¿ of the nominal measure in the Prokhorov metric. An optimization problem is formulated and solved; its solution is a most stable detector according to a reasonable criterion for optimality for the class of perturbations mentioned. For the case of several nominally known signals in nominally known noise, the problem is recast as estimation of signal amplitudes. An optimization problem, similar to that for the one-signal case, is formulated and solved. The solution is a most stable estimator, by a criterion justified now only in an L2-context, without reference to probability measures.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132589737","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}
Solutions to certain 2-D polynomial coprime conditions are obtained in this work. Given the 2-D polynomials f(x,y) and g(x,y), the problems are: (1) If f and g have no common zeros, to find u(x,y) and v(x,y) such that uf + vg = 1. (2) If f and g have no common zeros in ¿¿C2, to find u(x,y) and v(x,y) such that uf + vg has no zeros in ¿. The proofs of the existence of u and v are constructive and algebraic. Problem (2) has applications to 2-D feedback system design.
{"title":"A constructive algorithm for the solution of a 2-D coprime condition","authors":"V. Raman, Ruey-Wen Liu","doi":"10.1109/CDC.1984.272397","DOIUrl":"https://doi.org/10.1109/CDC.1984.272397","url":null,"abstract":"Solutions to certain 2-D polynomial coprime conditions are obtained in this work. Given the 2-D polynomials f(x,y) and g(x,y), the problems are: (1) If f and g have no common zeros, to find u(x,y) and v(x,y) such that uf + vg = 1. (2) If f and g have no common zeros in ¿¿C2, to find u(x,y) and v(x,y) such that uf + vg has no zeros in ¿. The proofs of the existence of u and v are constructive and algebraic. Problem (2) has applications to 2-D feedback system design.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133904247","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}
Many systems exhibiting self-excited oscillations of determinate amplitude may be modelled by a system of differential equations which includes the scalar nonlinear equation (cf. discussion in [1]) y + h(�, y, y)y + k(�, y) = u(t) + g*x(t) (I) where h, k are smooth functions involving a bifurcation parameter �. We will assume that, uniformly in �, yk(�, y) > 0, ?k/?y(�, 0) > 0 and that ?0 ? k(�, y)dy = ?. Further, we assume that the function h may be expressed in the form h(�, y, y) = -h1(�, y)y + h2(�, y)(y)3... with h1 (�, y) > 0 uniformly throughout the y interval of interest. Also, we assume that there is a value of �, call it �0, such that (�-�0)h2 (�, y) > 0, in the same region. Under these assumotions one can show that for � > �0 there is a unique periodic solution yp(t, �) near y = y = 0 with weriod T(�), a smooth function of � with-T(�0) equal to the common period of all solutions of the linear oscillator equation y + ?k/?y(�0, 0)y, having average amplitude A(�) =1/T(�) ?0 T(�)((yp(t, �))2+(yp(t, �))2)dt The question which we address initially is: suppose u(t) = 0, g = 0 in (I) and we have a single measurement (t) = ay(t) + by(t) available from the system (I). Assuming fixed for the present, ?p(t, �) = ayp(t, �) + byp(t, �) will be the data obtained from the periodic solution yp(t, �). How may we obtain an estimate of the system state vector (yp(t, �), yp(t, �)) from present and recorded bast values of ?p(t, �)? With T = T(�) assumed fixed, let us consider the system with delay w(t) = v(t) v(t) = v(t-T). (II) The oeriodic function ?p (t, �) is a particular output corresponding to a particular solution of this system. For w(t) = yp (t, �), w(t) = v(t) = yp(t, �) will satisfy (II) if yp (t, �) is periodic with period T. Then ?(t) = ?p (t, ) = aw(t) + bv(t). (III) The question now becomes one of constructing an observer (cf. [2]) for the system (II) based on the observation (III), so that the estimated state will tend, asymototically, to the state (yp(t, �), yp(t, �)) in an appropriate sense. Our paper will concern the construction of the estimator and the nature of the convergence of the estimate. We will also discuss feedback synthesis of the control u(t) from this estimate. We will also deal with the case wherein a controlled elastic system x = Ax + cy(t) + dy(t) + fu(t) (IV) is coupled to the nonlinear oscillator (I).
{"title":"A distributed compensator for a nonlinear control problem","authors":"D. Russell","doi":"10.1109/CDC.1984.272202","DOIUrl":"https://doi.org/10.1109/CDC.1984.272202","url":null,"abstract":"Many systems exhibiting self-excited oscillations of determinate amplitude may be modelled by a system of differential equations which includes the scalar nonlinear equation (cf. discussion in [1]) y + h(�, y, y)y + k(�, y) = u(t) + g*x(t) (I) where h, k are smooth functions involving a bifurcation parameter �. We will assume that, uniformly in �, yk(�, y) > 0, ?k/?y(�, 0) > 0 and that ?0 ? k(�, y)dy = ?. Further, we assume that the function h may be expressed in the form h(�, y, y) = -h1(�, y)y + h2(�, y)(y)3... with h1 (�, y) > 0 uniformly throughout the y interval of interest. Also, we assume that there is a value of �, call it �0, such that (�-�0)h2 (�, y) > 0, in the same region. Under these assumotions one can show that for � > �0 there is a unique periodic solution yp(t, �) near y = y = 0 with weriod T(�), a smooth function of � with-T(�0) equal to the common period of all solutions of the linear oscillator equation y + ?k/?y(�0, 0)y, having average amplitude A(�) =1/T(�) ?0 T(�)((yp(t, �))2+(yp(t, �))2)dt The question which we address initially is: suppose u(t) = 0, g = 0 in (I) and we have a single measurement (t) = ay(t) + by(t) available from the system (I). Assuming fixed for the present, ?p(t, �) = ayp(t, �) + byp(t, �) will be the data obtained from the periodic solution yp(t, �). How may we obtain an estimate of the system state vector (yp(t, �), yp(t, �)) from present and recorded bast values of ?p(t, �)? With T = T(�) assumed fixed, let us consider the system with delay w(t) = v(t) v(t) = v(t-T). (II) The oeriodic function ?p (t, �) is a particular output corresponding to a particular solution of this system. For w(t) = yp (t, �), w(t) = v(t) = yp(t, �) will satisfy (II) if yp (t, �) is periodic with period T. Then ?(t) = ?p (t, ) = aw(t) + bv(t). (III) The question now becomes one of constructing an observer (cf. [2]) for the system (II) based on the observation (III), so that the estimated state will tend, asymototically, to the state (yp(t, �), yp(t, �)) in an appropriate sense. Our paper will concern the construction of the estimator and the nature of the convergence of the estimate. We will also discuss feedback synthesis of the control u(t) from this estimate. We will also deal with the case wherein a controlled elastic system x = Ax + cy(t) + dy(t) + fu(t) (IV) is coupled to the nonlinear oscillator (I).","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132233411","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：