Causal state-feedback parameterizations in robust model predictive control

In this paper, we investigate the problem of nonlinearity (and non-convexity) typically associated with linear state-feedback parameterizations in the Robust Model Predictive Control (RMPC) for uncertain systems. In particular, we propose two tractable approaches to compute an RMPC controller-consisting of both a causal, state-feedback gain and a control-perturbation component-for linear, discrete-time systems involving bounded disturbances and norm-bounded structured model-uncertainties along with hard constraints on the input and state. Both the state-feedback gain and the control-perturbation are explicitly considered as decision variables in the online optimization while avoiding nonlinearity and non-convexity in the formulation. The proposed RMPC controller-computed through LMI optimizations-is responsible for steering the uncertain system state to a terminal invariant set. Numerical examples from the literature demonstrate the advantages of the proposed scheme.