The problem of estimating states in noisy nonsecond order distributed parameter systems, with non-linear observation, is considered for disturbances in the volume only. A least squares estimation criterion is assumed ...
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The problem of estimating states in noisy nonsecond order distributed parameter systems, with non-linear observation, is considered for disturbances in the volume only. A least squares estimation criterion is assumed and the resulting boundary value problem is embedded in a more general class of problems. The filtering problem is solved using running stage invariant embedding, and the fixed point and fixed lag smoothing using fixed stage invariant embedding. Fixed interval smoothing algorithm is developed using a backward sweep. It is found that the smoothing estimates are independent of their error covariances. Smoothing error covariances are computed approximately using a linearization procedure. The solutions so developed degenerate into the exact solution for distributedparameter estimation if linear models are considered.
This correspondence concerns the application of the state variable filters” technique for the hyperstable real-time identification system with adjustable model, synthetized by Landau via hyperstability of model refer...
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In this short version of a more detailled work of BEGIS-GLOWINSKI to appear, we shall consider briefly an optimization of domain problem, for a convenient class of feasible bidimensional domains in which occurs a stat...
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In this short version of a more detailled work of BEGIS-GLOWINSKI to appear, we shall consider briefly an optimization of domain problem, for a convenient class of feasible bidimensional domains in which occurs a stationary diffusion phenomenon. All results will be given without proof.
An approximate method is presented for the synthesis of an optimal control of distributed parameter systems, based on a combination of the ideas of Lyapunov's direct method and those of Bellman's successive ap...
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An approximate method is presented for the synthesis of an optimal control of distributed parameter systems, based on a combination of the ideas of Lyapunov's direct method and those of Bellman's successive approximations in policy space. The method is such that the approximate equation is improved after each iteration in the sense of the performance index being used.
We consider n-input n-output convolution feedback systems characterized by y = G * e and e = u - y, where the open-loop transfer function ĝ contains a finite number of unstable poles and the expansion ĝa(s) + ∑i=0 ĝ ...
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We consider n-input n-output convolution feedback systems characterized by y = G * e and e = u - y, where the open-loop transfer function ĝ contains a finite number of unstable poles and the expansion ĝa(s) + ∑i=0 ĝ Gi exp(-sti). The latter is such that, i) ĝa is the Laplace transform of L1 functions, ii) t0 = 0, iii) the delay-times ti, for i = 1, 2, ..., are positive and iv) the coefficient matrices Gi form an absolutely convergent series, i.e. ∑i=0 ĝ |Gi| < ∞. Thus the subsystem represented by G is an open-loop unstable distributedparameter system. One theorem is obtained. It gives necessary and sufficient conditions for stability. A basic device is the following: the sum of the principal parts of the Laurent expansions of ĝ at the unstable poles is factored as a ratio of two right coprime polynomial matrices. There are two necessary and sufficient conditions, the first is the usual infimum one, i.e. infRe s ĝ 0 |det[I+ ĝ(s)]| > 0, and the second is required to prevent the closed-loop transfer function from being unbounded in some small neighborhood of each open-loop unstable pole. The latter condition has a nice interpretation in terms of McMillan degree theory. The modification of the theorem for the discrete-time case is immediate. The same is true if, instead of unity feedback, constant nonunity feedback represented by a nonsingular matrix is used. This allows us, through the use of the small gain theorem or the contraction mapping theorem, to consider non-linear systems, derived from the original one by introducing a non-linear time-varying gain in the forward loop.
The control of dist,ributed parameter (DP) systems represents a real challenge, both from a theoretical and a practical point of view, to the systems engineer. *** parametersystems arise in various application areas,...
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The control of dist,ributed parameter (DP) systems represents a real challenge, both from a theoretical and a practical point of view, to the systems engineer. *** parametersystems arise in various application areas, such as chemical proms systems, aerospace systems, magneto-hydrodynamic systems, and communicat. ions systems, to *** just a few. Thus, there is sufficient motivation for research directed t,oward the analysis, ***, and design techniques for DP systems. On *** surface, it. may appear that *** available theory for distributed parameter systems is almost at the same level as that associated with lumped systems. However, there exists a much wider gap between the theory and its applications. In the remainder of this correspondence, we shall briefly discus the reasons for this gap and suggest, certain tentative approaches which may contribute to the development of a theory and computat,ional algorithms which take into account. some of the practical problems associated with the design of controllers for DP systems. In order to make these concepts clear it. becomes necessary to briefly review, in an informal manner, what a DP system is and in what sense it differs, from both a mat,*** and a practical point of view, from a conventional lumped system.
A major difficulty in the way of a successf ul systematic approach to the study of control processes by way of the theory of dynamic programming is the occurrence of processes having state vectors of high dimension. H...
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The transfer functions obtained by dynamic analysis of one shell pass and 2, 3, 4, 2n, 2n + 1 tube-pass heat exchangers as a distributedparameter system are presented in dimensionless forms. The heat-exchange process...
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The stability of any multivariable linear time-invariant control system can always be determined by existing methods. However, the designer needs to know how stability is affected by changes in loop gains and other pa...
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A technique is developed for the synthesis and design of a distributedparameter system guiding waves from one point in space to another. The parameter distributions are assumed to be nonrestricted except for the uppe...
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A technique is developed for the synthesis and design of a distributedparameter system guiding waves from one point in space to another. The parameter distributions are assumed to be nonrestricted except for the upper and lower bounds resulting from the imposition of physical realizability. The problem is similar to the "sensitivity" problem encountered in the optimal control of the systems. An improved version of the first-order gradient technique is used to obtain the optimal distributions of the parameters. The first-order gradient technique is sensitive to the form of the arbitrary distributions assumed at the start of the iterations. This technique has serious convergence problems associated with it. The problem is particularly severe and is encountered in "singular" optimal control problems. The algorithm devised here improves the first-order gradient technique so that it becomes less sensitive to the initial assumed distributions and virtually eliminates the convergence problems generated because of the bounds on the parameter distributions. A transmission line with distributed series r, l and shunt c is a particular case of the distributedparameter system. The optimal design of a notched filter employing a thin film circuit is a successful example of the application of the improved gradient technique. These distributions have been obtained by the use of a hybrid computer.
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