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[en] A control problem of a class of input-delayed linear systems is considered in this paper. Due to the delay τ in the input, any designed feedback controller can only be engaged after t ≥ τ. Then, this can become the cause of slow regulation since any feedback information cannot be available during the delay. So, the initial function defined for -τ ≤ t ≤ 0 is engaged as an ‘initial non-feedback input’ for 0 ≤ t ≤ τ, which governs the system behavior during this initial time period. There have been numerous research results on the control of input-delayed linear systems by far. Yet, there have been no results on the examination and design of this initial function. Utilizing a time optimal control in the existing results, we show that if some pre-feedback as the initial function is engaged, the system response of the input-delayed linear system can be much improved, and a bang-bang input function is a good candidate as a pre-feedback which can provide better starting state values for the state feedback controller in order to perform the fast regulation. Two examples are given for the illustration of our results.
[en] We investigate the control of singular distributed systems with a nonlinearity of exponential or more rapid growth. We show that for a natural cost function a similar singular optimality system may be obtained as in the case of polynomial growth
[fr]On etudie le controle des systemes distribues singuliers avec une non-linearite exponentielle ou de croissance plus rapide. On montre que pour une fonction cout naturelle on peut obtenir un systeme d'optimalite singulier comme dans cas de croissance polynomiale
[en] The study of infinite-horizon nonstationary dynamic programs using the operator approach is continued. The point of view here differs slightly from that taken by others, in that Denardo's local income function is not used as a starting point. Infinite-horizon values are defined as limits of finite-horizon values, as the horizons get long. Two important conditions of an earlier paper are weakened, yet the optimality equations, the optimality criterion, and the existence of optimal ''structured'' strategies are still obtained
[en] In this paper we give conditions for (the existence and) several characterizations of overtaking optimal policies for a general class of controlled diffusion processes. Our characterization results are of a lexicographical type; namely, first we identify the class of so-called canonical policies, and then within this class we search for policies with some special feature-for instance, canonical policies that in addition maximize the bias
[en] The problem of optimal control of solutions of an elliptic equation in a domain with a small cavity is discussed. Uniform asymptotic formulae for the solutions are obtained up to an arbitrary degree of the small parameter by the method of matching asymptotic expansions. Other aspects of the same problem have been considered by Kapustyan
[en] The optimal path of the consecutive chemical reactions xA→yB→zC (x, y and z are the orders of chemical reactions) is analyzed numerically by taking temperature as a control variable, using the optimal-control theory based on Bak et al's work (2002 J. Phys. Chem. A 106 10961-4). Starting with pure A and maximizing the yield of B at the end of the given process duration, the optimal path starts with a branch at infinite temperature. A curve in which switching from this temperature to a lower temperature is possible is derived. For given parameters, there is a unique 'maximal useful time' that results in the highest possible yield of B. If a duration longer than this is specified, all reactions should be shut off during that excess amount of time in the optimal path. A numerical example for the optimal path is provided by the Taylor method. Finally, the results obtained are compared with the results of A→B→C (the orders of chemical reactions are all equal to 1) (Bak et al 2002 J. Phys. Chem. A 106 10961-4). When the orders of chemical reactions are taken into account, the optimal time sequences of the concentrations change markedly, the maximum obtainable yield is smaller, the initial values of co-state variables are bigger and the optimal phase trajectory changes.
[en] Task of optimal control of thermal reactors is considered. Solution of optimal reactor control task including process equation solvability, optimal control existence and derivation of necessary conditions of maximum principle is given. Nonlinear integral functional is selected as an optimum criterion
[en] We consider a method for constructing dodecagonal quasi-lattices, which involves the recurrent multiplication of the initial group of sites that are vertices of a regular dodecagon. The algorithm of modeling of reciprocal lattices of dodecagonal quasicrystals has been analyzed. The proposed modeling method is compared with the traditional projection method. We have performed indexing of the diffraction pattern from dodecagonal quasicrystals, which is analogous to indexing proposed by Cahn for icosahedral quasicrystals. The ambiguity of the choice of the basis vectors of the quasicrystal reciprocal lattice has been considered.
[en] This report presents a review of the basic techniques developed over the recent years for the optimum supervision and detection/location of failures in dynamic technological systems such as nuclear reactors, aircrafts, etc. Regarding the optimum supervision problem the following policies are considered: optimum selection of supervision frequency, optimum supervision policies, optimum selection of sequential tests, and finally the effect of supervision capability upon the system availability. Regarding the optimum detection/location/identification of failures the following techniques are briefly presented: majority technique, failure sensitive filter technique, generalized maximum likelihood technique, output estimation error technique, dynamic redundancy technique with Luenberger observer, and finally jump processes technique. Some examples and comments on open problems for further research are also presented. (author)