# Instant MPC for linear systems and dissipativity-based stability analysis

## TL;DR

This paper introduces instant model predictive control (iMPC) for linear systems, which computes control actions directly from a dynamic optimization process, reducing computational load while maintaining stability and performance.

## Contribution

The paper proposes a novel iMPC approach using a continuous-time primal-dual gradient algorithm, enabling real-time control without explicit optimization solutions.

## Key findings

- iMPC emulates traditional MPC in control performance
- iMPC reduces computational burden compared to MPC
- Stability of iMPC is established via dissipativity analysis

## Abstract

This letter is devoted to the concept of ``instant'' model predictive control (iMPC) for linear systems. An optimization problem is formulated to express the finite-time constrained optimal regulation control, like conventional MPC. Then, iMPC determines the control action based on the optimization process rather than the optimizer, unlike MPC. The iMPC concept is realized by a continuous-time dynamic algorithm of solving the optimization; the primal-dual gradient algorithm is directly implemented as a dynamic controller. On the basis of the dissipativity evaluation of the algorithm, the stability of the control system is analyzed. Finally, a numerical experiment is performed in order to demonstrate that iMPC emulates MPC and to show its less computational burden.