Indefinite linear MPC and approximated economic MPC for nonlinear systems

The stability proof for economic model predictive control (MPC) relies on strict dissipativity, which is in general hard to check. In this contribution, we will first analyze the linear quadratic case with possibly indefinite cost. The conditions for stability will be recalled and it will be shown that every stabilizing LQR/MPC has an equivalent positive definite LQR/MPC which yields the same open loop and closed loop behavior. This analysis will then be used to formulate an approximated nonlinear economic MPC scheme, which has stability guarantees. An example will be used to illustrate the proposed technique and show its potential in terms of performance.