Indefinite linear MPC and approximated economic MPC for nonlinear systems

• Every stabilizing possibly indefinite LQR can be reformulated as a positive definite one.
• Every stabilizing possibly indefinite MPC scheme can be reformulated as a positive definite one which delivers the same open and closed loop trajectory.
• The proposed theoretical framework allows to formulate a positive definite tracking nonlinear MPC scheme that mimics a given economic MPC formulation.

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.