# On the design of regularized explicit predictive controllers from input-output data

@article{Breschi2021OnTD, title={On the design of regularized explicit predictive controllers from input-output data}, author={Valentina Breschi and Andrea Sassella and Simone Formentin}, journal={ArXiv}, year={2021}, volume={abs/2110.11808} }

On the wave of recent advances in data-driven predictive control, we present an explicit predictive controller that can be constructed from a batch of input/output data only. The proposed explicit law is build upon a regularized implicit data-driven predictive control problem, so as to guarantee the uniqueness of the explicit predictive controller. As a side benefit, the use of regularization is shown to improve the capability of the explicit law in coping with noise on the data. The…

## References

SHOWING 1-10 OF 48 REFERENCES

Learning explicit predictive controllers: theory and applications

- Computer Science, EngineeringArXiv
- 2021

This paper shows for the first time how explicit predictive laws can be learnt directly from data, without needing to identify the system to control, by resorts to the Willems’ fundamental lemma and derives the explicit formulas by suitably elaborating the constrained optimization problem under investigation.

On the design of terminal ingredients for data-driven MPC

- Computer Science, MathematicsIFAC-PapersOnLine
- 2021

We present a model predictive control (MPC) scheme to control unknown linear time-invariant systems using only measured input-output data and no model knowledge. The scheme includes a terminal cost…

Regularized and Distributionally Robust Data-Enabled Predictive Control

- Computer Science, Mathematics2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

It is proved that for certain objective functions, the worst-case optimization problem coincides with a regularized version of the DeePC algorithm, which supports the previously observed advantages of the regularized algorithm.

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

- Computer Science, EngineeringIEEE Transactions on Automatic Control
- 2021

The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme, including a slack variable with regularization in the cost.

Robust stability analysis of a simple data-driven model predictive control approach

- Mathematics, Computer ScienceArXiv
- 2021

A theoretical analysis of closed-loop properties of a simple data-driven model predictive control scheme that relies on an implicit description of linear time-invariant systems based on behavioral systems theory, which ensures exponential stability for the closed loop if the prediction horizon is sufficiently long.

Direct data-driven design of LPV controllers with soft performance specifications

- Computer ScienceJournal of the Franklin Institute
- 2021

A data-driven design scheme for linear parameter-varying (LPV) systems to account for soft performance specifications is proposed, where the reference model is treated as an additional hyper-parameter to be learned from data, while the user is asked to provide only indicative performance constraints.

Towards direct data-driven model-free design of optimal controllers

- Computer Science2018 European Control Conference (ECC)
- 2018

This paper proposes a novel approach to compute, directly from data, an “ optimal” reference model along with the corresponding controller, which is optimized through a suitable combination of particle swarm optimization and virtual reference feedback tuning.

Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness

- Computer ScienceIEEE Transactions on Automatic Control
- 2020

A parametrization of linear feedback systems is derived that paves the way to solve important control problems using data-dependent linear matrix inequalities only and is remarkable in that no explicit system's matrices identification is required.

On the Sample Complexity of Data-Driven Inference of the L2-Gain

- Computer ScienceIEEE Control Systems Letters
- 2020

It is shown that the number of samples needed to estimate the operator norm of a system is roughly the same as thenumber of samples required to approximate the system in the operators norm.

Direct Data-Driven Control of Constrained Systems

- Computer ScienceIEEE Transactions on Control Systems Technology
- 2018

A direct data-driven control method is proposed for designing controllers that can handle constraints without deriving a model of the plant and directly from data.