Time-Varying Model Predictive Control Based on Dynamics Decomposition and Exponential Data Weighting Approach

This paper deals with the nonlinear control of under-actuated systems and describes a Time Varying Model Predictive Control (TV-MPC) approach for a class of nonlinear systems in the context of nonlinear control synthesis. The approach comprises the formulation of the TV-MPC which is based on the model structure derived using a novel dynamics decomposition approach. Furthermore, deploying this model structure, the future control trajectory for the response prediction is modelled using a set of orthonormal basis functions- the Laguerre functions. The mathematical details of the proposed TV-MPC algorithm is supported by a simulation example and the results are presented for two different cases; firstly, using the exponential data weighting technique and then without using the exponential data weighting in the cost function for the time-varying reference tracking problem. The time-varying reference trajectory thus considered is a differentially flat cubic polynomial type trajectory reference. The results shows that with the addition of prescribed degree of stability through exponential data weighting, an asymptotically stable behaviour of the nonlinear system is guaranteed.