Estimação de estados com restrições intervalares utilizando abordagens estocástica e zonotópica

Abstract

Since 1960, with the proposition of the Kalman lter (KF), the problem of state estimation has owned relevance in the literature. KF and its derivations are well known solutions to estimate states for both linear and nonlinear systems. The essence of the KF is to treat the variables of the system as random variables (VA) with Gaussian probability density function (PDF), characterizing this methodology as stochastic. Given that nonlinear transformations do not preserve the Gaussian PDF of VAs, the solution generated by KFs are approximated. Therefore, variations of the KF have been proposed to estimate states satisfying constraints, both equality and inequality, improving, then, the estimates. Other way to estimate states, which has owned relevance on the last decades, is given by the set member ship approach due to two factors: (i) estimating states guaranteed and (ii) considering the system noise terms as unknown, but limited. Thus, given that the assumptions realized in the beginning of the project are satised, it is possible to obtain state estimates that contain the exact states of a given system independently the noise statistical distribution. The essence of the set membership approach is to represent states by compact sets. Among set membership approaches, zonotopes have highlighted for the trade-o between accuracy and computational burden. On the one hand, the stochastic approach is already consolidated in the literature for linear and nonlinear cases. On the other hand, the set membership approach is not consolidated for nonlinear cases and the related concepts are not clear in the literature. This work investigates the use of these approaches to estimate states of discrete-time linear and nonlinear dynamic systems. The presented content was directed to the following objectives: (i) to study algorithms with stochastic and zonotopic approaches, (ii) to present algorithms with unied notation and (iii) to apply these in case studies, to compare the performance of algorithms.