22 research outputs found
Dissipative Deep Neural Dynamical Systems
In this paper, we provide sufficient conditions for dissipativity and local
asymptotic stability of discrete-time dynamical systems parametrized by deep
neural networks. We leverage the representation of neural networks as pointwise
affine maps, thus exposing their local linear operators and making them
accessible to classical system analytic and design methods. This allows us to
"crack open the black box" of the neural dynamical system's behavior by
evaluating their dissipativity, and estimating their stationary points and
state-space partitioning. We relate the norms of these local linear operators
to the energy stored in the dissipative system with supply rates represented by
their aggregate bias terms. Empirically, we analyze the variance in dynamical
behavior and eigenvalue spectra of these local linear operators with varying
weight factorizations, activation functions, bias terms, and depths.Comment: Under review at IEEE Open Journal of Control System
Power Grid Behavioral Patterns and Risks of Generalization in Applied Machine Learning
Recent years have seen a rich literature of data-driven approaches designed
for power grid applications. However, insufficient consideration of domain
knowledge can impose a high risk to the practicality of the methods.
Specifically, ignoring the grid-specific spatiotemporal patterns (in load,
generation, and topology, etc.) can lead to outputting infeasible,
unrealizable, or completely meaningless predictions on new inputs. To address
this concern, this paper investigates real-world operational data to provide
insights into power grid behavioral patterns, including the time-varying
topology, load, and generation, as well as the spatial differences (in peak
hours, diverse styles) between individual loads and generations. Then based on
these observations, we evaluate the generalization risks in some existing ML
works causedby ignoring these grid-specific patterns in model design and
training
Robust Differentiable Predictive Control with Safety Guarantees: A Predictive Safety Filter Approach
In this paper, we propose a novel predictive safety filter that is robust to
bounded perturbations and is combined with a learning-based control called
differentiable predictive control (DPC). The proposed method provides rigorous
guarantees of safety in the presence of bounded perturbations and implements
DPC so long as the DPC control satisfies the system constraints. The approach
also incorporates two forms of event-triggering to reduce online computation.
The approach is comprised of a robust predictive safety filter that extends
upon existing work to reject disturbances for discrete-time, time-varying
nonlinear systems with time-varying constraints. The safety filter is based on
novel concepts of robust, discrete-time barrier functions and can be used to
filter any control law. Here we use the safety filter in conjunction with DPC
as a promising policy optimization method. The approach is demonstrated on a
single-integrator, two-tank system, and building example.Comment: Submitted to Automatic
Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach
We develop a novel form of differentiable predictive control (DPC) with
safety and robustness guarantees based on control barrier functions. DPC is an
unsupervised learning-based method for obtaining approximate solutions to
explicit model predictive control (MPC) problems. In DPC, the predictive
control policy parametrized by a neural network is optimized offline via direct
policy gradients obtained by automatic differentiation of the MPC problem. The
proposed approach exploits a new form of sampled-data barrier function to
enforce offline and online safety requirements in DPC settings while only
interrupting the neural network-based controller near the boundary of the safe
set. The effectiveness of the proposed approach is demonstrated in simulation.Comment: Accepted to IEEE Conference on Decision and Control Conference 202