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.
News published in Agência FAPESP Newsletter about the scholarship: