  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.
