Unified Theory for Sampled-Data Control of Hybrid Dynamic Systems

• Grant number: 16/06343-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2016
• End date: July 11, 2018
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: José Claudio Geromel
• Grantee: Gabriela Werner Gabriel
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The purpose of this research plan is to develop a unified formulation to the sampled-data optimal control applied to non-linear continuous-time systems. This research plan is a sequence of other previous projects, among which is the doctorate project, FAPESP process 2012/23634-2, in conclusion by the applicant. First, a general hybrid formulation will be done for the non-linear sampled-data control system. This new system will be analyzed using a Two Point Boundary Value Problem (TPBVP) based on the Bellman's Principle of Optimality expressed by the Hamilton-Jacobi-Bellman Equation (HJBE). With this result, necessary and sufficient conditions will be proposed to analyse the stability of the system assuring the exact value of the H2 and Hoo norms. Finally, these conditions will be adapted in order to synthesize an optimal sampled-data control. In the literature, these optimal results can be found in particular derivations of linear systems, including deterministic or Markov Jump Linear Systems (MJLS). However, there is no analytic results to general non-linear systems that will be considered. The theoretical results will be validated by comparing this theory to the particular cited cases, already studied and so available in the present literature.

Scientific publications

(6)

(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)

GABRIEL, GABRIELA W.; GEROMEL, JOSE C.. Performance evaluation of sampled-data control of Markov jump linear systems. AUTOMATICA, v. 86, p. 212-215, DEC 2017. (16/06343-5)

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)

CUNHA, RAFAEL F.; GABRIEL, GABRIELA W.; GEROMEL, JOSE C.. Partial Sampled-Data State Feedback Control of Markov Jump Linear Systems. IFAC PAPERSONLINE, v. 51, n. 25, p. 6-pg., 2018-01-01. (16/06343-5)

GABRIEL, GABRIELA W.; GEROMEL, JOSE C.. Unified Approach to the Analysis and Performance Evaluation of Sampled-Data Control Applied to Nonlinear Systems. IFAC PAPERSONLINE, v. 51, n. 25, p. 6-pg., 2018-01-01. (16/06343-5)

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)