OPTIMAL CONTROL theory is a branch of mathematics. It is developed to find OPTIMAL ways to CONTROL a dynamic system. In 1957, R.Bellman applied dynamic programming to solve OPTIMAL CONTROL of discrete-time systems. His procedure resulted in closed-loop,  generally nonlinear, AND feedback schemes. OPTIMAL CONTROL PROBLEMs which will be tackled involve the minimization of a cost function subject to constraints on the state vector AND the CONTROL. Lagrange multipliers provide a method of converting a constrained minimization PROBLEM into an unconstrained minimization PROBLEM of higher order. The necessary condition for OPTIMALity can be obtained as the solution of the unconstrained optimization PROBLEM of the Lagrange function AND the bordered Hessian matrix is used for the second-derivative test. A spectral method for solving OPTIMAL CONTROL PROBLEMs is presented. The method is based on Bernoulli polynomials approximation. By using the Bernoulli operational matrix of integration AND the Lagrangian function, STOCHASTIC OPTIMAL CONTROL is transformed into an optimisation PROBLEM, where the unknown Bernoulli coefficients are determined by using Newton's iterative method. The convergence analysis of the proposed method is given. The simulation results based on the Monte-Carlo technique prove the performance of the proposed method. Some error estimations are provided AND illustrative examples are also included to demonstrate the efficiency AND applicability of the proposed method.

Non-cooperative intelligent CONTROL agents (ICAs) with dedicated cost functions, can lead the system to poor performance AND in some cases, closed-loop instability. A robust solution to this challenge is to place the ICAs at the feedback Nash equilibrium point (FNEP) of the differential game between them. This paper introduces the designation of a robust decentralized infinite horizon LQR CONTROL system based on the FNEP for a linear time-invariant system. For this purpose, two CONTROL strategies are defined. The first one is a centralized infinite horizon LQR (CIHLQR) PROBLEM (i.e. a supervisory PROBLEM), AND the second one is a decentralized CONTROL PROBLEM (i.e. an infinite horizon linear-quadratic differential game). Then, while examining the OPTIMAL solution of each of the above strategies on the performance of the other, the necessary AND sufficient conditions for the equivalence of the two PROBLEMs are presented. In the absence of the conditions, by using the least-squares error criterion, an approximated CIHLQR CONTROLler is presented. It is shown that the theorems could be extended from a two-agent CONTROL system to a multi-agent system. Finally, the results are evaluated using the simulation results of a Two-Area non-reheat power system.

In Kant AND the PROBLEM of Metaphysics (KPM), Heidegger shows how the initial image-making power of the imagination is pictorial in the pure image of time. He further clarifies the recognized link between the syntheses AND the time-visualizing power of images which is pictorial formative power, which can visualize time. The three syntheses of imagination are replaced with the modes of existence of Dasein. Three kinds of photographs resemble the images produced when the transcendental imagination functions as Dasein. We can address the ways to visualize time by considering Dasein with a photographic preoccupation through 1. A possible look in the form of presentation (a photograph shows an immediate look of a house or person as intuitable this-here); 2. An immediate look of the thing, house, or deceased person, as well as a copy or its reproduction as a death mask; AND, 3. The manner of contemplation of a likeness is an immediate look of a being present in the form of representation.

This paper deals with the numerical solution of nonlinear fractional STOCHASTIC integro-differential equations with the n-dimensional WIENER PROCESS. A new computational method is employed to approximate the solution of the considered PROBLEM. This technique is based on the modi, ed hat functions, the Caputo derivative, AND a suitable numerical integration rule. Error estimate of the method is investigated in detail. In the end, illustrative examples are included to demonstrate the validity AND effectiveness of the presented approach.

The present study was conducted by examining the views of relevant experts AND their exposure to child labor in Shiraz. Data were obtained through in-depth interviews AND analyzed based on grounded theory. Ten axial categories AND one core category were extracted from the coding PROCESS. The core category was developed under the title of "institutional passivity AND sectoralism". The results of the research showed that the causal conditions such as incompatibility AND institutional AND managerial confusion, diversity of perspectives to the phenomenon of child labor AND non-governmental organizations AND indifference towards child labor has caused the emergence of this phenomenon. Intervening conditions include: negative representation AND conflicting media activities, Inhibition of some domestic AND international rules AND laws AND child labor of nationals AND the PROBLEM of identification AND identity. This central phenomenon is located in special conditions AND contexts due to family pressure AND starting the work PROCESS in childhood, child labor as an income generating industry, child labor as a source of financial support for the family AND the unique opportunity for working children, AND Shiraz's oppurtunities for immigrants. The type of encounter with working children in Shiraz has caused numerous consequences that can be seen Unreasonable increase of child labor of nationals, Failure to contain AND CONTROL the PROBLEM of working children, lack of proper organization AND social support of working children, Anonymity of working children AND persuasion AND encouragement of nationals to immigrate to Shiraz.

The boundary CONTROL of nonlinear parabolic equation with an integral performance criterion AND a fixed final state is considered. By means of a well-known PROCESS of embedding (used by Rubio AND others) for finite-dimensional system, this PROBLEM is replaced by one in which a linear form is minimized over a set of pairs of positive radon measures satisfying linear constraints. The OPTIMAL pair measures are then approximated by a finite combination of atomic measures AND the PROBLEM converted to a finite-dimensional linear programming PROBLEM. The solution of this PROBLEM is used to construct a piecewise constant OPTIMAL CONTROL.The Advantages of this formulation are:(i) There is automatic existence theory.(ii) There exists the possibility of using linear functional analysis to developed the theory.(iii) The minimization is global.A numerical example is considered to illustrate the procedure.