Min-max model predictive control with robust zonotope-based observer

This paper considers the problem of robust estimation and constrained model predictive control (MPC). The paper deals with a discrete linear time-invariant system affected by additive bounded disturbances, whose states are measurable, but not directly accessible. In order to improve the control performance, a state estimator is desirable. The design problem of an observer based on zonotopes to estimate the system states of the uncertain system is addressed. Then, the min-max MPC optimisation problem formulation based on the designed robust observer as a quadratic program (QP) is described. An efficient implementation of the proposed robust observer-based control algorithm that can be solved by a standard QP is validated by simulation through the regulator problem of a cart pendulum system.