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In this paper, we propose an algorithm (SC+PAM) for solving large size linear programming problem with bounded variables where we combined two methods: the selection of constraint method (SC) and the pivot adaptive method (PAM). The step of (SC+PAM), consist in first, selecting the constraints of the starting problem, and a sequence of linear sub-problems of increasing size which will be obtained by adding to the previous a set of constraints unsatisfied by the optimal solution of the current problem, the constraints to be added at each iteration being the most orthogonal to the criterion of the strarting problem. The stop criterion of (SC+PAM) is when all the constraints are satisfied and thus the solution found is opitmal for the strating problem. Thus, this method takes less computing time than (PAM), which is confirmed by numerical examples. MSC code: 90C05, 90C06, 90C51.

International audience; A convergence analysis of the modified unscented Kalman filter (UKF), used as an observer for a class of nonlinear deterministic continuous time systems, is presented. Under certain conditions, the extended Kalman filter (EKF) is an exponential observer for non-linear systems, i.e., the dynamics of the estimation error is exponentially stable. It is shown that unlike the EKF, the UKF is not an exponentially converging observer. A modification of the UKF-the unscented Kalman observer-is proposed, which is a better candidate for an observer. This paper is a first step towards a proof of the global convergence of the high-gain version of the UKO.

In this paper, the Picard’s iteration method is proposed to obtain an approximate analytical solution for linear and nonlinear optimal control problems with quadratic objective functional. It consists in deriving the necessary optimality conditions using the minimum principle of Pontryagin, which result in a two-point-boundary-value-problem (TPBVP). By applying the Picard’s iteration method to the resulting TPBVP, the optimal control law and the optimal trajectory are obtained in the form of a truncated series. The efficiency of the proposed technique for handling optimal control problems is illustrated by four numerical examples, and comparison with other methods is made.

In this article, we studied a problem of minimizing an aircraft energy flow, the model used is obtained from the fundamental principle of dynamics. We solved this problem with the method of relaxation coupled with the method of shooting.

This paper presents a problem of minimizing an aircraft energy flow, the model is obtained from the fundamental principle of dynamics. The Pontryagin’s Maximum Principle (PMP) is applied to determine the optimal control, then the Shooting method coupled with the Relaxation method for the numerical resolution.

The extended Kalman filter is an exponentially converging observer as soon as it is written in a canonical form of observability and in its high-gain form. It is shown that unlike extended Kalman filter, unscented Kalman filter can not be an exponentially converging observer. We propose a slight modification of the unscented Kalman filter to build an exponentially converging observer called unscented Kalman observer. Performances of this new observer are illustrated on an example of geolocation problem.

An unmanned aerial vehicle (UAV) become increasingly present in military and commercial applications, the flight path efficiency and integration with current manned aircraft become important research topics to address in the coming years. In this paper, the optimal control problem for the quad-rotor to minimize energy is considered. For this, formulate this problem to an optimal control problem which minimizes energy of quad-rotor in free final time. The Solution for this, used a discretization method, and simulation results are given by Bocop software.

This paper presents an optimal control problem applied to the robot, the problem is to determine a command that allows to reach the final state from the initial state in record time. This problem will be solved by applying The Pontryagin’s Maximum Principle (PMP) combined with Picard’s successive approximation method and shooting method.

In this paper, we study a modelization of the evolution of cereal output production, controlled by adding fertilizers and in presence of locusts, then by adding insecticides. The aim is to maximize the cereal output and meanwhile minimize pollution caused by adding fertilizers and insecticides.The optimal control problem obtained is solved theoretically by using the Pontryagin Maximum Principle, and then numerically with shooting method.

In this paper, a new indirect method is proposed for the receding horizon control of dynamical systems. It consists in solving, over a control horizon, the optimality conditions using the variational iteration method. The optimality conditions are given by the Euler-Lagrange equations and their associated boundary conditions. This two-boundary values problem is solved iteratively using a correction functional that yields both the optimal state and the optimal control. Then by imposing, at each sampling time, the current boundary conditions, a system of algebraic equations is obtained and solved, which allows to define the piecewise optimal control to be applied at the current sampling time. The effectiveness of the proposed approach is illustrated by two application examples.

International audience; The main objective of an energy regulation of a building is to maintain internal thermal comfort, as well as minimize energy consumption, or reduce the peak of electrical consumption. The dynamic programming has been used to minimize a cost function, accounting for a high peak electricity tariff, under constraints related to comfort (minimal temperature, maximal temperature variation) and the maximum heating power. The proposed energy management consists in over-heating the building during the hours before the peak knowing in advance the weather, occupation and internal gains for the day. The method has been tested in a case study corresponding to a house of a four-person family with performance levels: high construction and poorly insulated old house.

International audience; A new variant of the Adaptive Method (AM) of Gabasov is presented, to minimize the computation time. Unlike the original method and its some variants, we need not to compute the inverse of the basic matrix at each iteration, or to solve the linear systems with the basic matrix. In fact, to compute the new support feasible solution, the simplex pivoting rule is used by introducing a matrix that we will define. This variant is called “the Pivot Adaptive Method” (PAM); it allows presenting the resolution of a given problem under the shape of successive tables as we will see in example. The proofs that are not given by Gabasov will also be presented here, namely the proofs for the theorem of the optimality criterion and for the theorem of existence of an optimal support, and at the end, a brief comparison between our method and the Simplex Method will be given.

International audience; Our aim is to solve a problem of optimal control with free final time using the Pontryagin's maximum principle. As an illustration, we consider a navigation problem which is solved analytically and numerically by the shooting method in the case without constraint. The two approaches are compared. In the second case, we solve numerically the same problem with constraint on the state. At the end, we prove the convergence of the method for the second case.

International audience; The studied problem concerns the optimal regulation with a fixed horizon of two vertical ovens having respectively three or twelve heating areas. The model of the thermal process is described thanks to a linear state equation with a quadratic criterion to minimize. Furthermore, the terminal state is fixed and the state is subjected to some constraints. We propose and analyze the relaxation method coupled with the shooting method to solve this problem. The convergence of the numerical procedure is presented. Numerical experiments are done and validate our approach.

We are studying an optimal control problem with free initial condition. The initial state of the optimized system is not known exactly, information on initial state is exhausted by inclusions x0 2 X0. Accessible controls for optimization of continuous dynamic system are discrete controls defined on quantized axes. The method presented is based on the concepts and operations of the adaptive method (9) of linear programming. The results are illustrated by a fourth order problem, efficiency estimates of proposed methods are given.

Algeria is rich country, it uses fertilizers to improve its cereal production as it is usually known. However, Algerian farmers use fertilizers in a bad manner and in a quite random way. This causes both ground, water pollution, and a loss of output. In the present paper we study a modelization of the evolution of the cereal output production controlled by means of adding fertilizers. We set an optimal control problem where we aim at maximizing the cereal output and meanwhile minimizing pollution effects. We solve theoretically this optimal control problem with the Pontryagin Maximum Principle and then provide different numerical methods to implement it: indirect methods based on the shooting method and direct methods based on a combination of AMPL with IPOPT.

This paper presents a novel method for power quality analysis based on S-Transform. The objective is the detection of certain disturbances that pollute the electrical network such as interruptions, sags and swells. S-Transform provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. The proposed approach consists in the application of Shannon Energy computed on each local spectrum obtained with the S-Transform. Using simulated and real data, the proposed method has been evaluated according to the accuracy of detecting the start and the end of each considered disturbance.

International audience

In this work the Adomian's Decomposition Method (ADM) is used to solve optimal control problems. The Lagrange multiplier method is adopted to derive the necessary conditions of optimality as a set of first-order differential equations. Then, by doing some algebraic manipulations, these equations are converted to a one ordinary differential equation, which can be easily solved, iteratively, using Adomian's Decomposition Method to deduce the optimal control law. The proposed design approach is illustrated by several examples.

In this work, we have solved two practices problems in agriculture by modeling in problems of optimal control. An emphasis is placed on nonlinear control optimal problems, since the output of the resulting models are nonlinear. It provided a way to choose defaults for the weight between minimizing pollution caused by an improper addition of fertilizers and insecticides and maximize cereal production. The first problem is to maximize cereal production taking into account the detrimental effects of pollution generated by adding abusive fertilizers. Subsequently, the second problem, we refined the first problem by introducing the constraint of the presence of locusts. For digital applications, were used actual data from the Algerian Ministry of Agriculture and Data from the National Institute of Plant Protection (INPV).; Dans ce travail, nous avons résolu deux problèmes pratiques en agriculture en les modélisant en des problèmes de contrôle optimal. Un accent est mis sur les problèmes de contrôle optimal non linéaires, puisque les entrées résultantes de la modélisation sont non linéaires. On a fourni un moyen de choisir des valeurs adaptées pour le poids entre minimiser la pollution engendrée par un ajout abusif d’engrais et d’insecticides et maximiser le rendement des céréales. Le premier problème consiste à maximiser une production céréalière en tenant compte des effets néfastes de la pollution dégagée par un ajout abusif des engrais. Par la suite, dans le second problème, on a raffiné le premier problème en introduisant la contrainte de la présence des criquets. Pour les applications numériques, on a utilisé des données réelles du ministère de l’agriculture Algérien et des données de l’Institut National de la Protection des Végétaux (INPV).