MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.
MCRF is edited by a group of international leading experts in mathematical control theory and related fields. A key feature of MCRF is the journal's rapid publication, with a special emphasis on the highest scientific standard. The journal is essential reading for scientists and researchers who wish to keep abreast of the latest developments in the field.
- AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
- Publishes 4 issues a year in March, June, September and December.
- Publishes online only.
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- Archived in Portico and CLOCKSS.
- MCRF is a publication of the American Institute of Mathematical Sciences. All rights reserved.
Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.
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We study an optimal control problem with a nonlinear Volterra-type integral equation considered on a nonfixed time interval, subject to endpoint constraints of equality and inequality type, mixed state-control constraints of inequality and equality type, and pure state constraints of inequality type. The main assumption is the linear–positive independence of the gradients of active mixed constraints with respect to the control. We obtain first-order necessary optimality conditions for an extended weak minimum, the notion of which is a natural generalization of the notion of weak minimum with account of variations of the time. The conditions obtained generalize the corresponding ones for problems with ordinary differential equations.
In this paper, we investigate controllability of fractional dynamical systems involving monotone nonlinearities of both Lipchitzian and non-Lipchitzian types. We invoke tools of nonlinear analysis like fixed point theorem and monotone operator theory to obtain controllability results for the nonlinear system. Examples are provided to illustrate the results. Controllability results of fractional dynamical systems with monotone nonlinearity is new.
In this paper, we investigate an optimal stopping problem (mixed with stochastic controls) for a manager whose utility is nonsmooth and nonconcave over a finite time horizon. The paper aims to develop a new methodology, which is significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, so as to figure out the manager's best strategies. The problem is first reformulated into a free boundary problem with a fully nonlinear operator. Then, by means of a dual transformation, it is further converted into a free boundary problem with a linear operator, which can be consequently tackled by the classical method. Finally, using the inverse transformation, we obtain the properties of the optimal trading strategy and the optimal stopping time for the original problem.
In this paper, a time-inconsistent optimal control problem is studied for diffusion processes modulated by a continuous-time Markov chain. In the performance functional, the running cost and terminal cost depend on not only the initial time, but also the initial state of the Markov chain. By modifying the method of multi-person game, we obtain an equilibrium Hamilton-Jacobi-Bellman equation under proper conditions. The well-posedness of this equilibrium HJB Equation is studied in the case where the diffusion term is independent of the control variable. Furthermore, a time-inconsistent linear-quadratic control problem is considered as a special case.
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