Set Of Admissible Pairs Research Articles

Про одну задачу оптимального керування для нелiнiйного елiптичного рiвняння зi змiнним p(x)-лапласiаном

An optimal control problem for the Dirichlet boundary value problem for the nonlinear elliptic equation with p(x)-Laplacian is considered. It is shown that this problem has at least one solution with respect to certain set of admissible pairs. The corresponding theoretic framework regarding Sobolev-Orlicz spaces is given.

On admissible pairs and equivalent feedback—Youla parameterization in iterative learning control

This paper revisits a well-known synthesis problem in iterative learning control, where the objective is to optimize a performance criterion over a class of causal iterations. The approach taken here adopts an infinite-time setting and looks at limit behavior. The first part of the paper considers iterations without current-cycle-feedback (CCF) term. A notion of admissibility is introduced to distinguish between pairs of operators that define a robustly converging iteration and pairs that do not. The set of admissible pairs is partitioned into disjoint equivalence classes. Different members of an equivalence class are shown to correspond to different realizations of a (stabilizing) feedback controller. Conversely, every stabilizing controller is shown to allow for a (non-unique) factorization in terms of admissible pairs. Class representatives are introduced to remove redundancy. The smaller set of representative pairs is shown to have a trivial parameterization that coincides with the Youla parameterization of all stabilizing controllers (stable plant case). The second part of the paper considers the general family of CCF-iterations. Results derived in the non-CCF case carry over, with the exception that the set of equivalent controllers now forms but a subset of all stabilizing controllers. Necessary and sufficient conditions for full generalization are given.

Solving some optimal path planning problems using an approach based on measure theory

In this paper we solve a collection of optimal path planning problems using a method based on measure theory. First we consider the problem as an optimization problem and then we convert it to an optimal control problem by defining some artificial control functions. Then we perform a metamorphosis in the space of problem. In fact we define an injection between the set of admissible pairs, containing the control vector function and a collision-free path defined on free space and the space of positive Radon measures. By properties of this kind of measures we obtain a linear programming problem that its solution gives rise to constructing approximate optimal trajectory of the original problem. Some numerical examples are proposed.

Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems

We study the nonnegativity of quadratic functionals with separable endpoints which are related to the discrete symplectic system (S). In particular, we characterize the nonnegativity of these functionals in terms of (i) the focal points of the natural conjoined basis of (S) and (ii) the solvability of an implicit Riccati equation associated with (S). This result is closely related to the kernel condition for the natural conjoined basis of (S). We treat the situation when this kernel condition is possibly violated at a certain index. To accomplish this goal, we derive a new characterization of the set of admissible pairs (sequences) that does not require the validity of the above mentioned kernel condition. Finally, we generalize our results to the variable stepsize case.

Existence theory for nonlinear distributed parameter optimal control problems

In this paper we develop the existence theory for a class of nonlinear, infinite demensional optimal control problems, with a priori feedback. This is achieved with the help of property (Q) of Cesari. First we provide verifiable conditions on the data, which guarantee the validity of property (Q). Then we prove two results on the nonemptiness of the set of admissible pairs. This is done by solving an appropriate evolution inclusion of the subdifferential type. Subsequently, we use the reduction technique to prove the existence of optimal pairs. Finally we work in detail four examples illustrating the applicability of our work. These examples include systems governed by both ordinary and partial differential equations.

On secrecy systems with side information about the message available to a cryptanalyst (Corresp.)

The performance of a class of encipherers is examined in the situation where a cryptanalyst has available side information about the message. A set of admissible pairs of distortion and key rate are determined for which good encipherers exist. The concepts of random ciphering and exponential bounding are used.