Stochastic adaptive receding horizon controllers

Abstract

In this thesis, the deterministic, stochastic and stochastic adaptive coritrolpossibilities based on the method of receding horizon is examiried. The receding horizon method assumes a fixed horizon length for feedback law calculation at each step. Therefore, the feedback law is optimal in one-step-ahead manner and the feedback gain is constant. The other advantages are of not having to choose the state penalization matrix and of replacing the solution of Riccati equation by a linear one. We alleviated some problems associated with the practical use of this method, such as calculation time and singular state transition matrices by some fast algorithms and non-zero set points by modification of the basic equations. Modelling the system in state space innovations representation or transforming it to this form if it is not modelled in innovations form originally, solves the problem of state reconstruction under noise effects. The overall design enjoys the separation property, that is, of having a separate design for control and estimation parts. In the case of some unknozn parameters in the system equations, our controller works using the state estimates, found by utilizing the parameter estimates, in the control law, and parameter estimates, found by using the state estimates, in the feedback gain calculation. This controller with this enforced certainty equivalence property enjoys many favorable characteristics such as refraining from the use of Riccati equation in control, matrix update equations for state and parameter estimation uncertainties, external perturbation signals to secure stability, and trial and error procedures in the choice of state penalization matrices. Moreover, the method is general enough to control with any prescribed control strength, multi-input, multi-output systems under noise effects, modelled in difference equation from with multi-parameter uncertainty.