Linear systems with fuzzy parameters and crisp variables defined by the Zadehs extension principle are called possibilistic linear systems. The purpose of this paper is to outline some properties of these systems.

Introduction In the theory of dynamic programming (Bellman, 1957; Bellman and Dreyfus, 1962), the Bellman principle of optimality was not called into question until Rudd and Blum found a wrong solution for a chemical reaction system (Jackson, 1963; Rudd and Blum, 1962). Although the Bellman principle of optimality is true for almost all practical problems, there are still some problems, both th...

in most of the real-life applications we deal with the problem of transporting some special fruits, as banana, which has particular production and distribution processes. in this paper we restrict our attention to formulating and solving a new bi-criterion problem on a network in which in addition to minimizing the traversing costs, admissibility of the quality level of fruits is a main objecti...

This paper interrelates the performance criteria involving path independent curvilinear integrals, the multitime maximum principle, the multitime Hamilton-Jacobi-Bellman PDEs and the multitime dynamic programming, to study the linear-quadratic regulator problems and to characterize the optimal control by means of multitime variant of the Riccati PDE that may be viewed as a feedback law. Section...

The original version of this article unfortunately contained a mistake: The spelling of the Ebrahim Gafar-Zadehs' name was incorrect. The corrected name is given above.

The original version of this article unfortunately contained a mistake: the spelling of the Ebrahim Gafar-Zadehs' name was incorrect. The corrected name is given above.

A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...

Topics considered here include: examples of optimal control problems; dynamic programming and the Hamilton-Jacobi-Bellman equation; verification theorems; the Pontryagin Maximum Principle Principle. The examples include many with an economic flavor, but others too (including the Hopf-Lax solution formula for ut + H(Du) = 0 with H convex). There’s much more here than we’ll have time to do in lec...

This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.