# Robust Model Predictive Control for Linear Systems with State and Input Dependent Uncertainties

## TL;DR

This paper develops a computationally efficient robust model predictive control method for linear systems with uncertainties depending on state and input, enabling real-time implementation with guarantees on feasibility and optimality.

## Contribution

It introduces a novel MPC formulation that exactly captures input-dependent uncertainties and approximately handles state-dependent uncertainties within a second order cone programming framework.

## Key findings

- Linear complexity in planning horizon
- Guarantees on recursive feasibility and global optimality
- Effective robust control demonstrated on satellite positioning

## Abstract

This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being non-convex, we are able to capture it exactly for input dependency and approximately for state dependency in at most a second order cone programming problem. The formulation has linear complexity in the planning horizon length. The approach is thus amenable to efficient real-time implementation with a guarantee on recursive feasibility and global optimality. Robust position control of a satellite is considered as an illustrative example.