# A Semismooth Predictor Corrector Method for Suboptimal Model Predictive Control

## TL;DR

This paper introduces a semismooth predictor-corrector method for suboptimal model predictive control, reducing computational costs while maintaining stability and constraint satisfaction through a dynamic interconnection approach.

## Contribution

It develops a novel semismooth predictor-corrector approach for suboptimal MPC and analyzes its stability and constraint enforcement using input-to-state stability and small gain conditions.

## Key findings

- The method achieves reduced computational complexity.
- Closed-loop stability is guaranteed under certain conditions.
- Numerical simulations confirm the effectiveness of the approach.

## Abstract

Suboptimal model predictive control is a technique that can reduce the computational cost of model predictive control (MPC) by exploiting its robustness to incomplete optimization. Instead of solving the optimal control problem exactly, this method maintains an estimate of the optimal solution and updates it at each sampling instance. The resulting controller can be viewed as a dynamic compensator which runs in parallel with the plant. This paper explores the use of the semismooth predictor-corrector method to implement suboptimal MPC. The dynamic interconnection of the combined plant-optimizer system is studied using the input-to-state stability framework and sufficient conditions for closed-loop asymptotic stability and constraint enforcement are derived using small gain arguments. Numerical simulations demonstrate the efficacy of the scheme.