1,806 research outputs found
Singularly Perturbed Stochastic Hybrid Systems: Stability and Recurrence via Composite Nonsmooth Foster Functions
We introduce new sufficient conditions for verifying stability and recurrence
properties in singularly perturbed stochastic hybrid dynamical systems.
Specifically, we focus on hybrid systems with deterministic continuous-time
dynamics that exhibit multiple time scales and are modeled by constrained
differential inclusions, as well as discrete-time dynamics modeled by
constrained difference inclusions with random inputs. By assuming regularity
and causality of the dynamics and their solutions, respectively, we propose a
suitable class of composite nonsmooth Lagrange-Foster and Lyapunov-Foster
functions that can certify stability and recurrence using simpler functions
related to the slow and fast dynamics of the system. We establish the stability
properties with respect to compact sets, while the recurrence properties are
studied only for open sets
Online Optimization of Switched LTI Systems Using Continuous-Time and Hybrid Accelerated Gradient Flows
This paper studies the design of feedback controllers that steer the output
of a switched linear time-invariant system to the solution of a possibly
time-varying optimization problem. The design of the feedback controllers is
based on an online gradient descent method, and an online hybrid controller
that can be seen as a regularized Nesterov's accelerated gradient method. Both
of the proposed approaches accommodate output measurements of the plant, and
are implemented in closed-loop with the switched dynamical system. By design,
the controllers continuously steer the system output to an optimal trajectory
implicitly defined by the time-varying optimization problem without requiring
knowledge of exogenous inputs and disturbances. For cost functions that are
smooth and satisfy the Polyak-Lojasiewicz inequality, we demonstrate that the
online gradient descent controller ensures uniform global exponential stability
when the time-scales of the plant and the controller are sufficiently separated
and the switching signal of the plant is slow on the average. Under a strong
convexity assumption, we also show that the online hybrid Nesterov's method
guarantees tracking of optimal trajectories, and outperforms online controllers
based on gradient descent. Interestingly, the proposed hybrid accelerated
controller resolves the potential lack of robustness suffered by standard
continuous-time accelerated gradient methods when coupled with a dynamical
system. When the function is not strongly convex, we establish global practical
asymptotic stability results for the accelerated method, and we unveil the
existence of a trade-off between acceleration and exact convergence in online
optimization problems with controllers using dynamic momentum. Our theoretical
results are illustrated via different numerical examples
Online Optimization of LTI Systems Under Persistent Attacks: Stability, Tracking, and Robustness
We study the stability properties of the interconnection of an LTI dynamical
plant and a feedback controller that generates control signals that are
compromised by a malicious attacker. We consider two classes of controllers: a
static output-feedback controller, and a dynamical gradient-flow controller
that seeks to steer the output of the plant towards the solution of a convex
optimization problem. We analyze the stability of the closed-loop system under
a class of switching attacks that persistently modify the control inputs
generated by the controllers. The stability analysis leverages the framework of
hybrid dynamical systems, Lyapunov-based arguments for switching systems with
unstable modes, and singular perturbation theory. Our results reveal that under
a suitable time-scale separation, the stability of the interconnected system
can be preserved when the attack occurs with "sufficiently low frequency" in
any bounded time interval. We present simulation results in a power-grid
example that corroborate the technical findings
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