An optimization problem of initial-boundary conditions for first-order multi-dimensional semiiincar hyperbolic systems is considered in this paper. The special feature of the general optimization problem for boundary ...
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An optimization problem of initial-boundary conditions for first-order multi-dimensional semiiincar hyperbolic systems is considered in this paper. The special feature of the general optimization problem for boundary conditions is non-validity uf the classic optimality condition of Pontryagin's type. The idea of special 'inner' variations of admissible smooth controls is used For deriving a new optimality condition. The numerical algorithm based on the optimality condition is given. Some possible applications are discussed
作者：
Fattorini, HOProfessor
Department of Mathematics University of California Los Angeles California
We consider optimal control problems for distributed-parameter systems described by semilinear equations, with constraints on the control and on the state, and an exact pointwise target condition. As an application of...
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We consider optimal control problems for distributed-parameter systems described by semilinear equations, with constraints on the control and on the state, and an exact pointwise target condition. As an application of a general theory of nonlinear programming problems in Banach spaces, a version of the Pontryagin maximum principle is obtained.
Methods for the study of weakly nonlinear continuous (distributed-parameter) systems are discussed. Approximate solution procedures based on reduced-order models via the Galerkin method are contrasted with direct appl...
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Methods for the study of weakly nonlinear continuous (distributed-parameter) systems are discussed. Approximate solution procedures based on reduced-order models via the Galerkin method are contrasted with direct application of the method of multiple scales to the governing partial-differential equations and boundary conditions. By means of several examples and an experiment, Nayfeh and co-worker had shown that reduced-order models of nonlinear continuous systems obtained via the Galerkin procedure can lead to erroneous results. A method is developed for producing reduced-order models that overcomes the shortcomings of the Galerkin procedure. Treatment of these models yields results in agreement with those obtained experimentally and those obtained by directly attacking the continuous system.
This article proposes an infinite-dimensitional state-space representation and a finite-dimensional approximation for fractional linear filters with transfer function C d ( s ) := C 0 ((1 + s / w b ) / (1 + s / w h ))...
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This article proposes an infinite-dimensitional state-space representation and a finite-dimensional approximation for fractional linear filters with transfer function C d ( s ) := C 0 ((1 + s / w b ) / (1 + s / w h )) d where 0 < w b < w h and d is a real number. This representation is derived from the Taylor expansion in zero of the function (1 - z ) d , and is made up of an infinite number of first-order ordinary differential equations. Finite-dimensional approximations obtained by truncating this representation are shown to converge towards C d in H ∞ . The use of C d in a standard linear feedback loop (CRONE control) is discussed, and closed-loop exponential and input-output stabilities are shown to be equivalent. The example of CRONE car suspension is presented, for which robustness of closed-loop resonance and step response overshoot vis-a-vis a variation in the vehicule mass is achieved. Cet article propose une représentation d'état de dimension infinie et une approximation de dimension finie des filtres linéaires fractionnaires de fonction de transfert C d ( s ) := C 0 ((1 + s / w b ) / (1 + s / w h )) d , où 0 < w b < w h et d est un nombre réel. Cette représentation est dérivée du développement de Taylor en zéro de la fonction (1 - z ) d , et est composée d'une infinité d'équations différentielles ordinaires du premier ordre. Les approximations de dimension finie obtenues par troncature de cette représentation convergent vers C d dans H ∞ . L'utilisation de C d dans une boucle linéaire de rétroaction standard (commande CRONE) est discutée, et on montre que la stabilité de la boucle fermée et la stabilité entrées-sorties sont équivalentes. L'exemple de la suspension automobile CRCNE est présenté, pour lequel on obtient la robustesse à des variations de la masse du véhicule de la résonance en boucle fermée et du dépassement de la réponse à l'échelon.
This paper deals with large-angle rapid slew maneuvers of a flexible spacecraft, which consists of a rigid central body and a flexible beam attached to it. Dynamic model for the spacecraft described by a coupled nonli...
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This paper deals with large-angle rapid slew maneuvers of a flexible spacecraft, which consists of a rigid central body and a flexible beam attached to it. Dynamic model for the spacecraft described by a coupled nonlinear hybrid system is derived. With the control torque applied to the rigid central body only, a PD control law is presented using the measurements of the attitude angle of the rigid body and its velocity. Based upon the Lyapunov method in infinite dimensional space, it is shown that implementation of the control algorithm results in the slew maneuvering with the simultaneous vibration suppression.
A self-organizing, fuzzy controller is proposed for the adaptive control of a tubular reactor. Its design is based on a heuristic approach and it involves two functions: creating and modifying the control rules for a ...
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A self-organizing, fuzzy controller is proposed for the adaptive control of a tubular reactor. Its design is based on a heuristic approach and it involves two functions: creating and modifying the control rules for a fuzzy logic controller and adjusting the universe of discourse based on system performance observed. The proposed controller is compared against a conventional PID controller which is tuned by two methods: either by the process reaction tuning method or by minimising the IAE time integral performance criterion. The proposed self-organizing controller, exhibits a superior performance in comparison with the PID tuned through the process and an equivalent, if not better performance than the PID controller whose parameters are adjusted optimally for minimising the IAE dynamic criterion.
The grey-box modelling technique is employed here for the identification of a model of a continuous digester. A physically based model is complemented with empirical data to produce a model with quantitative predictio...
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The grey-box modelling technique is employed here for the identification of a model of a continuous digester. A physically based model is complemented with empirical data to produce a model with quantitative prediction capabilities. The method of orthogonal collocation is utilized to reduce this infinite-dimensional system into a finite-dimensional state-space approximation. A grey-box identification session, including different sources for process disturbances, shows that new insight into the process behavior can be gained by this approach. Copyright (C) 1997 Elsevier Science Ltd.
It is shown that the weight determines the stability of the H-infinity-optimal controller for weighted sensitivity minimization problems for a large class of scalar plants and weights. Necessary and sufficient interpo...
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It is shown that the weight determines the stability of the H-infinity-optimal controller for weighted sensitivity minimization problems for a large class of scalar plants and weights. Necessary and sufficient interpolation conditions on the weight are given in order for the optimal controller to be stable. An easily evaluated formula for the optimal controller is provided when the interpolation conditions are met. It is also shown that for many scalar plants it is possible to choose the weights for weighted mixed sensitivity minimization so that the optimal controller is stable and minimum-phase. (C) 1997 Elsevier Science Ltd.
A linear distributed-parameter system, described by diffusion equation in R with uncertainty in the right-hand side is considered. It is assumed that all accessible information on the solution of the system is given b...
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A linear distributed-parameter system, described by diffusion equation in R with uncertainty in the right-hand side is considered. It is assumed that all accessible information on the solution of the system is given by the measurements perfomed by the sensors at the finite number of points. The considered model of uncertainty and measurements errors is non-stochastic with set-membership description of unknowns. The problem of allocation of the sensors inside given domain in order to ensure the best possible estimate of the linear functional of solution is considered. The ”duality” results, which states that considered problem is equivalent to some impulsive control problem are given. Assuming that unknown data do not depend on time the theorem on sufficient number of sensors is proved and the reduction of measurements allocation problem to the nonlinear programming problem is described.
The concept of uniform power stability is studied in detail. A characterization of the class of linear time-varying infinite-dimensional discrete-time systems for which uniform power stability implies uniform power eq...
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The concept of uniform power stability is studied in detail. A characterization of the class of linear time-varying infinite-dimensional discrete-time systems for which uniform power stability implies uniform power equistability is given.
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