Linear differential inequalities: numerical solution and applications

• Grant number: 16/08043-9
• Support Opportunities: Scholarships in Brazil - Master
• Start date: August 01, 2016
• End date: July 31, 2018
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: José Claudio Geromel
• Grantee: Tiago Rocha Gonçalves
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The analysis of dynamic linear or non-linear control systems, in many cases, leads to problems based on finite horizon differential inequalities, whose analytical solutions most of time are not trivial. In such a way, the goal of this research project is to study and to analyze a new technique for the solution of these inequalities in linear or non-linear control problems as well as to apply it to known dynamical systems. The technique to be studied will be analyzed according to three different approaches: the first one corresponds to use the Euler method to solve differential equations; the second, to adopt the hypothesis that the solution can be written in the form of a power series; and the third one, to adopt the solution as a combination of linear functions. The main idea will be to solve the resulting inequalities through numerical methods based on LMIs. Finally, these outcomes will be validated by applying this theory on dynamic systems available in the current literature. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GONCALVES, TIAGO R.; GABRIEL, GABRIELA W.; GEROMEL, JOSE C.. Differential Linear Matrix Inequalities Optimization. IEEE CONTROL SYSTEMS LETTERS, v. 3, n. 2, p. 6-pg., 2019-04-01. (16/06343-5, 16/08043-9)

GABRIEL, GABRIELA W.; GONCALVES, TIAGO R.; GEROMEL, JOSE C.. Optimal and Robust Sampled-Data Control of Markov Jump Linear Systems: A Differential LMI Approach. IEEE Transactions on Automatic Control, v. 63, n. 9, p. 3054-3060, SEP 2018. (16/06343-5, 16/08043-9)

GABRIEL, GABRIELA W.; GEROMEL, JOSE C.; GONCALVES, TIAGO R.; IEEE. Optimal Sampled-Data Control of Markov Jump Linear Systems through Differential LMIs. 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), v. N/A, p. 6-pg., 2017-01-01. (16/06343-5, 16/08043-9)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

GONÇALVES, Tiago Rocha. Differential linear matrix inequalities: numerical solution and applications. 2018. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação Campinas, SP.