A Maxmin Distance Problem

1972 ◽  
Vol 94 (2) ◽  
pp. 155-158 ◽  
Author(s):  
R. Aggarwal ◽  
G. Leitmann
Keyword(s):  
Minimum Distance ◽  
Terminal State ◽  
Initial State ◽  
Closed Set ◽  
Distance Problem

The problem of maximizing the minimum distance of a dynamical system’s state from a given closed set, while transferring the system from a given initial state to a given terminal state, is considered. Two different methods of solution of this problem are given.

Control synthesis of a class of DEDS

Kybernetes ◽  
2002 ◽  
Vol 31 (9/10) ◽  
pp. 1274-1281 ◽  
Author(s):  
František Čapkovič
Keyword(s):  
Discrete Event ◽  
Synthesis Method ◽  
Terminal State ◽  
The State ◽  
Synthesis Process ◽  
Control Synthesis ◽  
Discrete Event Dynamic Systems ◽  
Initial State ◽  
Output Place ◽  
Reachability Tree

A new control synthesis method suitable for a special kind of discrete event dynamic systems (DEDS) is presented in this paper. The systems to be controlled are modelled by a special class of Petri nets (PN) named state machine (SM). The class is distinctive by the fact that each PN transition has only one input place and only one output place. Bipartite directed graphs (BDG) are utilized in the control synthesis process. Namely, PN in general are (from the structure point of view) the BDG. Both the state reachability tree and the corresponding control one are developed in the straight‐line procedure starting from the given initial state and directed to the desirable terminal one as well as in the backtracking procedure starting from the terminal state and directed to the initial one. After a suitable intersection of both the straight‐lined state reachability tree and the backtracking one the state trajectories of the system are obtained. After the intersection of both the straight‐lined control reachability tree and the backtracking one the control interferences corresponding to the state trajectories are obtained.

The Hydrogen Molecular Ion With Time-Dependent Magnetic Field Strength as Control

2014 ◽  
Author(s):  
Katherine A. Kime
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Terminal State ◽  
Time Dependent ◽  
Initial State ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion ◽  
Prolate Spheroidal Coordinates ◽  
Spheroidal Coordinates

We consider the hydrogen molecular ion with time-dependent magnetic field strength. We discretize the corresponding Schroedinger equation with the Hamiltonian written in prolate spheroidal coordinates. We formulate a control problem and give an example of steering a restricted initial state to a restricted terminal state.

Symmetric Control Systems

2021 ◽  
pp. 37-51
Author(s):  
A.I. Diveev ◽  
E.A. Sofronova
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Systems ◽  
Control Object ◽  
Terminal State ◽  
Initial State ◽  
Phase Constraints ◽  
The Mathematical Model

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

On the Calculation of Pair Creation by Fast Charged Particles and the Effect of Screening

1935 ◽  
Vol 31 (3) ◽  
pp. 394-406 ◽  
Author(s):  
H. J. Bhabha
Keyword(s):  
Impact Parameter ◽  
Momentum Space ◽  
Minimum Distance ◽  
Rest Mass ◽  
Charged Particles ◽  
The Other ◽  
Initial State ◽  
Special Cases ◽  
The Creation ◽  
The Impact

In a recent paper I developed a method for calculating the probability of the creation of an electron pair in the collision of two charged particles moving with a relative velocity very near that of light. I showed there that under certain conditions it is legitimate to treat one of the colliding particles, say the heavier one of charge Z2 and rest mass M2, which we shall call the particle 2, as fixed at the origin of coordinates, and the other, of charge Z1 and rest mass M1, which we shall call the particle 1, as moving classically along a straight line with uniform velocity V in the direction of the z-axis, passing the other particle 2 at a minimum distance of approach (impact parameter) b. I developed expressions (given by (18) to (22) of A) giving the probability of the transition of an electron from an initial state of negative energy E0 and momentum p0 lying in an element of momentum space dp0 to a final state of energy E and momentum p lying in an element of momentum space dp, under the combined perturbing influence of the two colliding particles when they pass at a minimum distance b. The initial state of the electron, left vacant after the transition, appears as a positron of momentum p+ = − p0. To get the differential effective cross-section for the creation of the above pair, we must integrate this probability over all values of the impact parameter b, and this integration can be performed easily as shown in A. The final result can be written as a sum of a finite number of doubly infinite integrals (A, (24)). The purpose of this paper is to carry through the evaluation of these integrals for certain special cases, and to consider the effects of screening. The results have already been communicated in A.

scholarly journals Medial and lateral orbitofrontal cortices represent unique components of cognitive maps of task space

2019 ◽  
Author(s):  
Laura Bradfield ◽  
Genevra Hart
Keyword(s):  
Orbitofrontal Cortex ◽  
Mental Model ◽  
Cognitive Maps ◽  
Initial Position ◽  
Terminal State ◽  
Cognitive Map ◽  
Task Space ◽  
Functional Heterogeneity ◽  
Initial State ◽  
Broad Array

The orbitofrontal cortex (OFC) has recently been proposed to function as a cognitive map oftask space: a mental model of the various steps involved in a task. This idea has proven popularbecause it provides a cohesive explanation for a number of disparate findings regarding the OFC’srole in a broad array of tasks. Concurrently, mounting evidence has begun to reveal the functional heterogeneity of OFC subregions, particularly the medial and lateral OFC. How these subregions might uniquely contribute to the OFC’s role as a cognitive map of task space, however, has not been explored. Here we propose that the lateral OFC represents the agent’s initial position within that task map (i.e. initial state), determining which actions are available as a consequence of that position, whereas the medial OFC represents the agent’s desired future position within the task map(i.e. terminal state), influencing which actions are selected to achieve that position. We argue thatthese processes are achieved somewhat independently and somewhat interdependently, and are achieved through similar but non-identical circuitry.

Using Genetic Algorithms With Niche Formation to Solve the Minimum Distance Problem Among Concave Objects

2002 ◽  
Author(s):  
J. A. Carretero ◽  
M. A. Nahon ◽  
O. Ma
Keyword(s):  
Minimum Distance ◽  
Optimization Technique ◽  
Combinatorial Problem ◽  
The Body ◽  
Optimization Approach ◽  
Multiple Minima ◽  
Niche Formation ◽  
Distance Problem ◽  
Set Of Points ◽  
Global Optimization Technique

In this paper an optimization approach is used to solve the problem of finding the minimum distance between concave objects, without the need for partitioning the objects into convex sub-objects. Since the optimization problem is not unimodal (i.e., has more than one local minimum point), a global optimization technique, namely a Genetic Algorithm, is used to solve the concave problem. In order to reduce the computational expense of evaluating the constraints at runtime, the objects’ geometry is replaced by a set of points on the surface of the body. This reduces the problem to a combinatorial problem where the combination of points (one on each body) that minimizes the distance will be the solution. Additionally, niche formation is used to allow the minimum distance algorithm to track multiple minima rather than exclusively looking for the global minimum.

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