Controllable Neural Architectures for Multi-Task Control

TL;DR

This paper introduces a neural control architecture with a fixed connectivity matrix and adaptable bias vectors, enabling multi-task regulation of linear systems by approximating various controllers through gradient-based training.

Contribution

It proposes a novel multi-task neural control framework with fixed connectivity and adaptable biases, allowing flexible control across multiple linear systems.

Findings

Neural controllers can replicate any linear controller dynamics.

Gradient-based algorithms effectively train the neural control parameters.

Numerical examples validate the control strategy's effectiveness.

Abstract

This paper studies a multi-task control problem where multiple linear systems are to be regulated by a single non-linear controller. In particular, motivated by recent advances in multi-task learning and the design of brain-inspired architectures, we consider a neural controller with (smooth) ReLU activation function. The parameters of the controller are a connectivity matrix and a bias vector: although both parameters can be designed, the connectivity matrix is constant while the bias vector can be varied and is used to adapt the controller across different control tasks. The bias vector determines the equilibrium of the neural controller and, consequently, of its linearized dynamics. Our multi-task control strategy consists of designing the connectivity matrix and a set of bias vectors in a way that the linearized dynamics of the neural controller for the different bias vectors provide a good approximation of a set of desired controllers. We show that, by properly choosing the bias vector, the linearized dynamics of the neural controller can replicate the dynamics of any single, linear controller. Further, we design gradient-based algorithms to train the parameters of the neural controller, and we provide upper and lower bounds for the performance of our neural controller. Finally, we validate our results using different numerical examples.