[en] We give in this work some qualitative results for problems of control with prescribed rearrangement

[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

[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] Spin chains are promising candidates for quantum communication and computation. Using quantum optimal control (OC) theory based on the Krotov method, we present a protocol to perform quantum state transfer with fast and high fidelity by only manipulating the boundary spins in a quantum spin-1/2 chain. The achieved speed is about one order of magnitude faster than that is possible in the Lyapunov control case for comparable fidelities. Additionally, it has a fundamental limit for OC beyond which optimization is not possible. The controls are exerted only on the couplings between the boundary spins and their neighbors, so that the scheme has good scalability. We also demonstrate that the resulting OC scheme is robust against disorder in the chain.

[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] Optimal control experiments can readily identify effective shaped laser pulses, or “photonic reagents,” that achieve a wide variety of objectives. An important additional practical desire is for photonic reagent prescriptions to produce good, if not optimal, objective yields when transferred to a different system or laboratory. Building on general experience in chemistry, the hope is that transferred photonic reagent prescriptions may remain functional even though all features of a shaped pulse profile at the sample typically cannot be reproduced exactly. As a specific example, we assess the potential for transferring optimal photonic reagents for the objective of optimizing a ratio of photoproduct ions from a family of halomethanes through three related experiments. First, applying the same set of photonic reagents with systematically varying second- and third-order chirp on both laser systems generated similar shapes of the associated control landscape (i.e., relation between the objective yield and the variables describing the photonic reagents). Second, optimal photonic reagents obtained from the first laser system were found to still produce near optimal yields on the second laser system. Third, transferring a collection of photonic reagents optimized on the first laser system to the second laser system reproduced systematic trends in photoproduct yields upon interaction with the homologous chemical family. These three transfers of photonic reagents are demonstrated to be successful upon paying reasonable attention to overall laser system characteristics. The ability to transfer photonic reagents from one laser system to another is analogous to well-established utilitarian operating procedures with traditional chemical reagents. The practical implications of the present results for experimental quantum control are discussed

[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] We study the problem of finding approximations to the optimal control with respect to a quadratic-type quality criterion in the form of feedback (synthesis) for a linear-quadratic problem in the from of a hyperbolic equation with rapidly oscillating coefficients and distributed control on the right-hand side. On the basis of the exact formula of synthesis, its approximate version (based on the replacement of the rapidly oscillating variables by averaged quantities) is substantiated.