Lasso-MPC – Predictive Control with ℓ-Regularised Least Squares

Introduction:

Lasso-MPC is an innovative predictive control technique that utilizes ℓ-regularised least squares for optimization. This approach combines the power of predictive control with the benefits of ℓ-regularisation, resulting in improved control performance and robustness.

Main Benefits of Lasso-MPC:

1. Enhanced Control Performance

Lasso-MPC leverages the predictive control framework to anticipate future system behavior and make optimal control decisions. By incorporating ℓ-regularisation, it effectively handles complex and high-dimensional systems, leading to enhanced control performance.

2. Robustness to Uncertainties

The ℓ-regularisation in Lasso-MPC provides a mechanism to handle uncertainties and disturbances in the system. It promotes sparsity in the control inputs, allowing the algorithm to adapt to changing conditions and maintain stability even in the presence of uncertainties.

How Lasso-MPC Works:

Lasso-MPC operates by formulating the control problem as an optimisation task. It aims to find the optimal control inputs that minimise a cost function while satisfying system constraints. The cost function incorporates both the predictive control objective and the ℓ-regularisation term.

Step 1: System Modelling

The first step in Lasso-MPC is to model the system dynamics and constraints. This involves identifying the relevant variables, their relationships, and any constraints on their values. The system model serves as the basis for predicting future system behavior.

Step 2: Cost Function Formulation

Next, a cost function is formulated that captures the control objectives and constraints. The cost function typically includes terms related to tracking performance, control effort, and system constraints. In Lasso-MPC, an additional term based on ℓ-regularisation is added to promote sparsity in the control inputs.

Step 3: Optimisation

The optimisation problem is solved iteratively to find the optimal control inputs. Lasso-MPC uses ℓ-regularised least squares as the optimisation technique, which balances the control objectives with the sparsity-promoting term. The solution provides the control inputs for the current time step.

Frequently Asked Questions:

Q: What is the advantage of using ℓ-regularisation in Lasso-MPC?

A: ℓ-regularisation promotes sparsity in the control inputs, allowing the algorithm to adapt to changing conditions and handle uncertainties effectively. It enhances control performance and robustness.

Q: Can Lasso-MPC handle high-dimensional systems?

A: Yes, Lasso-MPC is designed to handle complex and high-dimensional systems. The ℓ-regularisation term helps in effectively dealing with the curse of dimensionality and ensures efficient control optimization.

Conclusion:

Lasso-MPC is a powerful predictive control technique that incorporates ℓ-regularised least squares for optimization. It offers enhanced control performance and robustness to uncertainties. By leveraging the benefits of both predictive control and ℓ-regularisation, Lasso-MPC provides an innovative solution for control problems in various domains.