# State and Input Constrained Model Reference Adaptive Control with Robustness and Feasibility Analysis

## TL;DR

This paper introduces an optimization-free, adaptive control method for uncertain LTI systems that guarantees state and input constraints are maintained despite disturbances, with proven feasibility conditions and simulation validation.

## Contribution

It presents the first adaptive control approach that ensures both state and input constraints for uncertain systems with disturbances, with explicit feasibility conditions.

## Key findings

- Effective constraint satisfaction demonstrated in simulations
- Comparison shows improved robustness over traditional MRAC
- Feasibility conditions enable practical implementation

## Abstract

We propose a model reference adaptive controller (MRAC) for uncertain linear time-invariant (LTI) plants with user-defined state and input constraints in the presence of unmatched bounded disturbances. Unlike popular optimization-based approaches for constrained control, such as model predictive control (MPC) and control barrier function (CBF) that solve a constrained optimization problem at each step using the system model, our approach is optimization-free and adaptive; it combines a saturated adaptive controller with a barrier Lyapunov function (BLF)-based design to ensure that the plant state and input always stay within pre-specified bounds despite the presence of unmatched disturbances. To the best of our knowledge, this is the first result that considers both state and input constraints for control of uncertain systems with disturbances and provides sufficient feasibility conditions to check for the existence of an admissible control policy. Simulation results, including a comparison with a robust MRAC, demonstrate the effectiveness of the proposed algorithm.