# zbMATH — the first resource for mathematics

Time-distributed optimization for real-time model predictive control: stability, robustness, and constraint satisfaction. (English) Zbl 1447.93090
First, it is presented a general system theoretic framework for analyzing a broad class of time-distributed optimization algorithms. This framework applies to any model predictive control feedback law that is locally input-to-state stable combined with any optimization algorithm whose convergence rate that is at least locally $$q$$-linear. Moreover, the existence of a joint region of attraction for the state and solution estimate is established. Next, the proposed theoretical framework is applied to a real-time iteration scheme which uses a Gauss-Newton hessian approximation and solves a single quadratic program per sampling instant. The robustness of this scheme is established. Also, the effect of the number of the sequential quadratic programming iterations performed at each sampling instant is analyzed and sufficient conditions for robust constraint satisfaction are obtained. At last, simulation results concerning a bicycle model of a sedan illustrate the proposed approach.

##### MSC:
 93B45 Model predictive control 93D25 Input-output approaches in control theory 90C31 Sensitivity, stability, parametric optimization
##### Keywords:
model predictive control; real-time optimization