Control with finite stabilization time

• Grant number: 20/07574-6
• Support type: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): August 01, 2020
• Effective date (End): July 31, 2021
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal researcher: José Claudio Geromel
• Grantee: Carlos Eduardo Celeste Junior
• Home Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Optimal Control has as one of its practical applications the optimization of trajectories, in which the referred trajectory is projected, optimizing a selected variable within a set of pre-established restrictions. Thus, it is desired, for example, to obtain a trajectory where a car travels between point A and point B previously determined in finite time (the shortest possible). This problem can be developed considering the model of a car, of length L, where it is known its center of gravity, the angle between the axis of the car and a stipulated axis and the control variable is the steering angle, in relation to the car axle, which is subject to maximum value restriction. One of the strategies that can be adopted to control this model is the control with variable structure, aiming mainly to satisfy the criterion of convergence in finite time. Therefore, applying this method, the objective of the project is to determine a control law, such that, within a given region X, the trajectory of the car converges asymptotically to the desired position and angle, and outside that region it evolves until it reaches the X contour in finite time. To achieve the mentioned objective, a kinematic model for the car will be developed, which will have its limitations studied, in addition to the control method development for this model, which will be implemented in numerical simulations to study cases. As further developments, it is expected to generalize the results obtained, in addition to the elaboration of the car dynamic model, with the study of its limitations, the control method development for this model and the numerical implementation comparing with the results obtained in the kinematic model.