The max-plus finite element method for optimal control problems: further approximation results

We develop the max-plus finite element method to solve finite horizon deterministic optimal control problems. This method, that we introduced in a previous work, relies on a max-plus variational formulation, and exploits the properties of projectors on max-plus semimodules. We prove here a convergence result, in arbitrary dimension, showing that for a subclass of problems, the error estimate is of order $\delta+\Delta x(\delta)^{-1}$, where $\delta$ and $\Delta x$ are the time and space steps respectively. We also show how the max-plus analogues of the mass and stiffness matrices can be computed by convex optimization, even when the global problem is non convex. We illustrate the method by numerical examples in dimension 2.Comment: 13 pages, 2 figure

A max-plus finite element method for solving finite horizon deterministic optimal control problems

We introduce a max-plus analogue of the Petrov-Galerkin finite element method, to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation, and exploits the properties of projectors on max-plus semimodules. We obtain a nonlinear discretized semigroup, corresponding to a zero-sum two players game. We give an error estimate of order $(\Delta t)^{1/2}+\Delta x(\Delta t)^{-1}$, for a subclass of problems in dimension 1. We compare our method with a max-plus based discretization method previously introduced by Fleming and McEneaney.Comment: 13 pages, 5 figure

Using fuzzy logic for automatic control: Case study of a problem of cereals samples classification

The aim of this paper is to present the use of fuzzy logic for automatic control of industrial systems particularly the way to approach a problem of classification. We present a case study of a grading system of cereals that allows us to determine the price of transactions of cereals in Tunisia. Our contribution in this work consists in proposing not only an application of the fuzzy logic on the grading system of cereals but also a methodology enabling the proposing of a new grading system based on the concept of 'Grade' while using the fuzzy logic techniques.

The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis

We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation. We show that the error in the sup norm can be bounded from the difference between the value function and its projections on max-plus and min-plus semimodules, when the max-plus analogue of the stiffness matrix is exactly known. In general, the stiffness matrix must be approximated: this requires approximating the operation of the Lax-Oleinik semigroup on finite elements. We consider two approximations relying on the Hamiltonian. We derive a convergence result, in arbitrary dimension, showing that for a class of problems, the error estimate is of order $\delta+\Delta x(\delta)^{-1}$ or $\sqrt{\delta}+\Delta x(\delta)^{-1}$, depending on the choice of the approximation, where $\delta$ and $\Delta x$ are respectively the time and space discretization steps. We compare our method with another max-plus based discretization method previously introduced by Fleming and McEneaney. We give numerical examples in dimension 1 and 2.Comment: 31 pages, 11 figure

Cyclosporine A and steroid therapy in childhood steroid-resistant nephrotic syndrome

Gargah Tahar, Lakhoua M RachidDepartment of Pediatric Nephrology, Charles Nicolle Hospital, Tunis, TunisiaBackground: In children, idiopathic nephrotic syndrome (INS) is primarily treated using corticosteroids. When remission is not achieved, the coadministration of potent immunosuppressant therapy becomes imperative. Cyclosporine A (CsA) is reportedly associated with a higher incidence of remission in comparison with other immunosuppressive agents.Methods: The present study investigated the response of combination therapy using CsA and prednisolone in 30 Tunisian children with idiopathic steroid-resistant nephrotic syndrome (ISRNS). Renal histopathology was compatible with focal segmental glomerular sclerosis (FSGS) in 15 children, minimal change disease (MCD) in nine children, and diffuses mesangiale proliferation (DMP) in six children.Results: The therapy protocol produced a complete remission of proteinuria in 15 patients (50%) and a partial remission in nine patients (30%). Six patients (20%) showed no response to therapy. Progression to end stage renal disease occurred in five CsA-resistant children and in four CsA-responsive patients. CsA-related nephrotoxicity was detected by renal biopsy in one patient.Conclusions: CsA remains the primary cytotoxic treatment for childhood steroid-resistant nephrotic syndrome. Its use in combination with corticosteroids provides optimum efficiency without high risk of nephrotoxicity.Keywords: children, corticosteroids, cyclosporine A, nephrotic syndrom

Dependability Evaluation and Supervision in Thermal Power Plants

In order to improve the productivity and the consistency of its maintenance strategies, the industrial world is based on different techniques and tools developed to ensure safe operation and the supervision of production systems. In fact, dependability evaluation is crucial to controlling the risks associated with system failure, and for this reason, it is one of the fundamental steps in automated system design. In this paper, we present firstly the basic concepts for the study of dependability as well as functional systems analysis. Thus, we present the method SADT (Structured Analysis Design technique). Given the ineffectiveness of methods that are currently exploited are not appropriate because the level of complexity of such industrial systems, we propose in the first the Safe-SADT method which allows the explicit formalization of functional interaction, the identification of the characteristic values affecting complex system dependability, the quantification of RAMS parameters (Reliability, Availability, Maintainability, and Safety) for the system’s operational architecture. Secondly, a methodology for designing supervisory production systems has been presented and has been applied on an example of a SCADA (supervisory control and data acquisition) system of a thermal power plant. Finally, a model of operating safety and supervision of a production system is proposed

Modeling and simulation of building energy consumption

Building energy consumption represents much of the total energy consumed in advanced countries. For this reason, the aim of this paper is to study the energy consumption profile by day for each domestic appliance: controllable appliances (heating, ventilation and air conditioning, electric water heater, dishwasher, washing machine) and non-controllable appliances (oven, TV, PC, iron, refrigerator and freezer) where the modeling and the simulation based on MATLAB/Simulink software are presented