3 research outputs found
Iterative, Small-Signal L2 Stability Analysis of Nonlinear Constrained Systems
This paper provides a method to analyze the small-signal L2 gain of
control-affine nonlinear systems on compact sets via iterative semi-definite
programs (SDPs). First, a continuous piecewise affine (CPA) storage function
and the corresponding upper bound on the L2 gain are found on a bounded,
compact set's triangulation. Then, to ensure that the state does not escape
this set, a (CPA) barrier function is found that is robust to small-signal
inputs. Small-signal L2 stability then holds inside each sublevel set of the
barrier function inside the set where the storage function was found. The bound
on the inputs is also found while searching for a barrier function. The
method's effectiveness is shown in a numerical example
Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Sets
Imitation learning enables the synthesis of controllers for complex
objectives and highly uncertain plant models. However, methods to provide
stability guarantees to imitation learned controllers often rely on large
amounts of data and/or known plant models. In this paper, we explore an
input-output (IO) stability approach to dissipative imitation learning, which
achieves stability with sparse data sets and with little known about the plant
model. A closed-loop stable dynamic output feedback controller is learned using
expert data, a coarse IO plant model, and a new constraint to enforce
dissipativity on the learned controller. While the learning objective is
nonconvex, iterative convex overbounding (ICO) and projected gradient descent
(PGD) are explored as methods to successfully learn the controller. This new
imitation learning method is applied to two unknown plants and compared to
traditionally learned dynamic output feedback controller and neural network
controller. With little knowledge of the plant model and a small data set, the
dissipativity constrained learned controller achieves closed loop stability and
successfully mimics the behavior of the expert controller, while other methods
often fail to maintain stability and achieve good performance