Striped Parameterized Tube Model Predictive Control

Optimal robust MPC for constrained linear systems that are subject to additive uncertainty requires a closed loop optimization with computation that rises exponentially with the prediction horizon, N . This was overcome by parameterized tube MPC (PTMPC) that used a triangular separable prediction strategy in which predictions are decomposed into a nominal and N − 1 partial prediction sequences, each concerned with the compensation of a particular future disturbance. Beyond the first N steps, the PTMPC control law can be taken to be a static state feedback. Use of N − 1 partial prediction sequences causes the number of free variables and constraints to rise quadratically with N . To reduce this to linear, this paper proposes a modification of PTMPC that uses a single partial prediction sequence that is used in connection with all particular future disturbances but allows the compensatory effect of the partial prediction sequences to extend beyond the first N predictions. The prediction structure is of a triangular striped nature and extends over an infinite horizon. As illustrated by a simulation example, the resulting scheme can outperform PTMPC in terms of the size of the domain of attraction and affords a reduction in computation which allows for the use of longer horizon (for the same computational demand).