Constrained Control of Linear Discrete-Time Systems under Quartic Performance Criterion

In several applications, a performance criterion that is quartic in the state can be a desired alternative to the classic quadratic control. This letter proposes a receding horizon controller for linear time-invariant systems subject to linear state and input constraints, which makes use of a running cost that is quadratic in the input and quartic in the state. Stability and recursive feasibility of the proposed receding horizon scheme are proven. Numerical simulations are presented, considering the problem of controlling a single-link inverted pendulum on a cart.