Feedback Linearization and LQ Based Constrained Predictive Control

Abstract

Feedback linearization is a powerful technique that allows to obtain linear model with exact dynamics (Isidori,1985), (Slotine & Li, 1991). Linear quadratic control is well known optimal control method and with its dynamic programming properties can be also easily calculated (Anderson & Moore, 1990). The combination of feedback linearization and LQ control has been used in many algorithms in Model Predictive Control applications for many years and it is used also in the current papers (He De-Feng et al.,2011), (Margellos & Lygeros, 2010). Another problem apart from finding the optimal solution on a given horizon (finite or infinite) is the constrained control. A method which uses the advantages of feedback linearization, LQ control and applying signals constraints was proposed in (Poulsen et al., 2001b). In every step it is based on interpolation between the LQ optimal control and a feasible solution – the solution that fulfils given constraints. A feasible solution is obtained by taking calculated from LQ method optimal gain for a perturbed reference signal. The compromise between the feasible and optimal solution is calculating by minimization of one variable – the number of degrees of freedom in prediction is reduced to one variable.