Receding Horizon Optimization in Haar Domain for Unconstrained Linear Time-invariant Systems

Abstract

The focus of this study is on developing Haar wavelet based Model Predictive Controller (MPC) for linear unconstrained systems. The problem of computation load in MPC has been addressed. By utilizing the structure of the Haar transformation, the coefficients that construct the first control input in the prediction horizon of the MPC are isolated. Considering only these coefficients, Haar based optimization procedure has been modified. The performance and computational load are compared with those of a Dynamic Matrix Controller (DMC) for a velocity regulation problem of a DC motor. Using the proposed modified Haar based MPC, position and orientation control of a two link planar robot and a wheeled mobile robot are provided as examples toreinforce the discussions.Modifications in the Haar based MPC reduced the amount of computation necessary to construct the first control action in the prediction horizon. Despite the modification and reduction in computation, the controller could handle sudden changes in setpoint, which was depicted in a velocity regulationof a DC motor. For increase in the size of prediction horizon beyond 26 time steps, Haar based MPC requires less computation than DMC. Large prediction horizons provide more stability, less aggressive control action and smoother response for the Haar based MPC.