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The problem of maximizing expected utility of final wealth in an incomplete market is investigated. The incomplete market is modelled by a bond and a finite number of stocks, the latter being driven by a d-dimensional Brownian motion. The coefficients of the bond and stock price processes are adapted to this Brownian motion, and the number of stocks is less than or equal to the dimension of the driving...
Many theorical studies have been conducted about decoupling and linearization of nonlinear systems. This approach is a means to synthesize the control laws of single-input single-output systems. It is used here for the piloting of nonrolling missiles, of which transverse acceleration is to be controlled. In this paper, it is proved that for this kind of problem, it is possible to associate such a...
In spite of obvious industrial needs in crystallization little has been done till now to improve and optimize the control of the equipments. The field of crystallization process technology is very complex and the knowledge based industrial applications still remain remarkable. Moreover, it is generally difficult to propose some simplified approaches leading to effective improvements. We present here...
This paper describes a search for the time-optimal “bang bang” control strategy for the three dimensional broom balancing (inverted pendulum) problem by genetically breeding populations of control strategies using a recently developed new “genetic computing” paradigm. The new paradigm produces results in the form of a control strategy consisting of a composition of functions, including arithmetic...
Some of the most difficult problems associated with process control are due to process nonlinearity, manipulated variable constraints, uncertain parameters and unmeasured variables. In this paper a nonlinear programming approach is developed to estimate process parameters, unmeasured state variables and process disturbances. A constrained optimization-based procedure is also used to maintain a desired...
A frequency-domain realization theory is developed for the class of autonomous, but not necessarily stationary, boundary-value linear systems. It is shown that this realization problem, which consists of coastructing autonomous boundary-value linear systems from prescribed input-output functions (weighting patterns), reduces to the factorization of several rational matrices in two variables having...
Successful application of modern control methods to industrial processes assumes some expertise with the algorithms. This is necessary in order to gain some feeling for tuning the design parameters. Computer-based instruction, learning and training of the user is of great value. An interactive personal computer training and design software system is presented. It was mainly developed for ‘in-house’...
In this paper we study existence conditions and closed form solutions of Cauchy problems and boundary value problems related to the regular equation A2X"+A1X'+A0X=F(t), in terms of a solution of the algebraic matrix equation A2X2+A1X+A0=0 and without increasing the dimension of the problem.
In this paper we prove an estimate of the rate of convergence of the approximation scheme for the nonlinear minimum time problem presented in [2]. The estimate holds provided the system have time-optimal controls with bounded variation. This estimate is of order v with respect to the discretization step in time, if the minimal time function is Hölder continuous of exponent v. The proof combines the...
In this paper, the resolution of Hamilton-Jacobi-Bellman equations by multigrid methods is studied. The Howard-multigrid algorithm FMGH is presented and, under some regularity assumptions, a convergence result is established. In addition, it is shown that the complexity of this algorithm is in the order of the number of discretisation points. Some numerical examples are reported.
A dynamic programming based Gas Pipeline Optimizer (GPO) has been developed at Scientific Software-Intercomp for the HBJ gas transmission pipeline system in India. Used as an operating and planning tool, the GPO will determine the discharge pressures at the compressor stations and the number of compressor trains to operate at each compressor station so that fuel consumption and start-up/shut-down...
This paper presents and compares two systematic and effective approaches for the hydroelectric generation scheduling problem (HSP). The objective of the HSP is to determine the best substitution of hydro energy for thermal energy in electric generation so that the fuel cost is minimized while meeting the system load and constraints. In the first approach, HSP is formulated as an optimal control problem,...
A free-boundary problem arising from the manipulation of microscopic particles immersed in a liquid film by means of a gas jet is considered. The objective is to determine the total force acting on the particle due to the flow inside the liquid induced by the gas jet. An iterative algorithm for the numerical solution of this problem is presented. The basic approach is to solve the flows in the liquid...
By the penalty method, Ekeland’s Variational Principle and lower-semicontinuity of some set-valued mappings, necessary conditions of optimal control for some abstract elliptic variational inequalities are obtained in the cases where the convex sets satisfy some smoothness conditions. The idea is to find optimality conditions first for some penalized problems by Ekeland’s Variational Principle then...
An optimal shape design problem of an elastic body described by system of two nolinear elliptic equations of the fourth order is considered. The problem is to find the boundary of the domain occupied by the body in such a way that the cost functional approximating the stiffness of the system in the equilibrium state is minimized. It is assumed that the volume of the body is constant. Moreover the...
Various optimization problems associated with the optimal control of distributed-parameter systems with time delays appearing in the boundary conditions have been studied recently in Refs. [1]÷[7] and [11], [12]. In this paper, we consider an optimal boundary control problem for a linear parabolic system in which constant time delays appear in the equation and in the boundary condition simultaneously...
We study the filtering problem of a homogeneous Markov chain in a singular case, according to the time the scale of the observed process. Under assumptions, we obtain a new asymptotic expansion of the unnormalized conditional distribution of the Zakai equation, by introducing the time scale and boundary layer terms. The terms of this expansion are calculated easier by decentralization and aggregation...
We study the asymptotic behaviour of a nonlinear one-dimensional filtering discrete time problem, as some parameter ε tends to 0. We treate the case of a nonlinear discrete time problem coming from a continuous time one with small observation noise. Finite dimensional aproximate filters are proposed and results concerning estimations of their performance are stated and proved. For the result concerning...
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