2 research outputs found
Online Optimization of Dynamical Systems with Deep Learning Perception
This paper considers the problem of controlling a dynamical system when the
state cannot be directly measured and the control performance metrics are
unknown or partially known. In particular, we focus on the design of
data-driven controllers to regulate a dynamical system to the solution of a
constrained convex optimization problem where: i) the state must be estimated
from nonlinear and possibly high-dimensional data; and, ii) the cost of the
optimization problem -- which models control objectives associated with inputs
and states of the system -- is not available and must be learned from data. We
propose a data-driven feedback controller that is based on adaptations of a
projected gradient-flow method; the controller includes neural networks as
integral components for the estimation of the unknown functions. Leveraging
stability theory for perturbed systems, we derive sufficient conditions to
guarantee exponential input-to-state stability (ISS) of the control loop. In
particular, we show that the interconnected system is ISS with respect to the
approximation errors of the neural network and unknown disturbances affecting
the system. The transient bounds combine the universal approximation property
of deep neural networks with the ISS characterization. Illustrative numerical
results are presented in the context of control of robotics and epidemics.Comment: This is an extended version of the paper submitted to the IEEE Open
Journal of Control Systems - Special Section on Machine Learning with
Control, containing proof
Perception-Based Sampled-Data Optimization of Dynamical Systems
Motivated by perception-based control problems in autonomous systems, this
paper addresses the problem of developing feedback controllers to regulate the
inputs and the states of a dynamical system to optimal solutions of an
optimization problem when one has no access to exact measurements of the system
states. In particular, we consider the case where the states need to be
estimated from high-dimensional sensory data received only at discrete time
intervals. We develop a sampled-data feedback controller that is based on
adaptations of a projected gradient descent method, and that includes neural
networks as integral components to estimate the state of the system from
perceptual information. We derive sufficient conditions to guarantee (local)
input-to-state stability of the control loop. Moreover, we show that the
interconnected system tracks the solution trajectory of the underlying
optimization problem up to an error that depends on the approximation errors of
the neural network and on the time-variability of the optimization problem; the
latter originates from time-varying safety and performance objectives, input
constraints, and unknown disturbances. As a representative application, we
illustrate our results with numerical simulations for vision-based autonomous
driving.Comment: This is an extended version of the paper accepted to IFAC World
Congress 2023 for publication, containing proof