This work aims at presenting an algorithm for solving a minmax problem with essential and direct constraints bounded above and below, by the adaptive method. The advantage of this algorithm is to solve the problem such as it was posed at the beginning, to thus keep the specificity of the minmax. The optimaltiy and suboptimality criteria are given and validate the results by numerical example.

A direct multiple shooting method is considered to solve optimal control problems. The direct multiple shooting method is a numerical method for the solution of boundary value problems. The method divides the interval over which a solution is sought into several smaller intervals, solves an initial value problem in each of the smaller intervals, and imposes additional matching conditions to form a solution on the whole interval. This method transforms an optimal control problem into a non-linear programming problem. To solve this last problem, the zeros of the Jacobian of Lagrangian are computed by using the Newton's method. Then, this method is illustrated by a numerical example and finally, applied to control a quadrotor to minimize energy.

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 aim of this paper is to find the path planning of an Unmanned Ground Vehicle (UGV) using shortest path algorithm that is a path of a string sequence of n vertices. Before that, the estimated point which has chosen is thought near real points with two experiences. These estimated points are chosen as the points which its minimum distance equal between 0.4m and 0.5m respectively. The goal is to calculate a path between the vertices of a graph that minimizes the robot path of estimated points. It can explain by finding the shortest path between two points. The main contribution of this work is seeking the shortest path of these points and minimizes the computational time and the energy that the robot will be provided along this path in minimal distance.

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.

An unmanned aerial vehicle (UAV) has grown rapidly the last years. They are being engaged in many types of missions, ranging from military to agriculture passing from entertainment and rescue or even delivery. This work consist to ensure the convergence of positions and yaw angle, to their desired trajectories while maintaining stability of roll and pitch angle. For this, formulate this problem to an optimal control problem which minimizes the distance between state and desired state in free final time. Our contribution is to use the Bocop software to solve this problem. And to implement Shooting method with Matlab software.

This paper aims to present a Decentralised Cooperative Simultaneous Localization and Mapping (DCSLAM) solution based on 2D laser data using an Adaptive Covariance Intersection (ACI). The ACI-DCSLAM algorithm will be validated on a swarm of Unmanned Ground Vehicles (UGVs) receiving features to estimate the position and covariance of shared features before adding them to the global map. With the proposed solution, a group of (UGVs) will be able to construct a large reliable map and localise themselves within this map without any user intervention. The most popular solutions to this problem are the EKF-SLAM, Nonlinear H-infinity SLAM and the FAST-SLAM. The former suffers from two important problems which are the poor consistency caused by the linearization problem and the calculation of Jacobian. The second solution is the which is a very promising filter because it doesn’t make any assumption about noise characteristics, while the latter is not suitable for real time implementation. Therefore, a new alternative solution based on the smooth variable structure filter (SVSF) is adopted. Cooperative adaptive SVSF-SLAM algorithm is proposed in this paper to solve the UGVs SLAM problem. Our main contribution consists in adapting the SVSF filter to solve the Decentralised Cooperative SLAM problem for multiple UGVs. The algorithms developed in this paper were implemented using two mobile robots Pioneer , equiped with 2D laser telemetry sensors. Good results are obtained by the Cooperative adaptive SVSF-SLAM algorithm compared to the Cooperative EKF/-SLAM algorithms, especially when the noise is colored or affected by a variable bias. Simulation results confirm and show the efficiency of the proposed algorithm which is more robust, stable and adapted to real time applications.