A State-Dependent Updating Period For Certified Real-Time Model Predictive Control
For control engineers, this work provides a certified real-time MPC framework, though it is incremental as it extends existing Fast Gradient methods with a state-dependent update scheme.
The paper proposes a state-dependent control updating period for real-time Model Predictive Control, ensuring certified practical stability and constraint satisfaction. The method is validated with a new certification bound for Fast Gradient iterations, demonstrated on a linear MPC example with four integrators.
In this paper, a state-dependent control updating period framework is proposed that leads to real-time implementable Model Predictive Control with certified practical stability results and constraints satisfaction. The scheme is illustrated and validated using new certification bound that is derived in the case where the Fast Gradient iteration is used through a penalty method to solve generally constrained convex optimization problems. Both the certification bound computation and its use in the state-dependent updating period framework are illustrated in the particular case of linear MPC. An illustrative example involving a chain of four integrators is used to show the explicit computation of the state-dependent control updating scheme.