Related papers: Distributionally Robust Lyapunov Function Search U…
We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…
Stochastic Optimization (SO) is a classical approach for optimization under uncertainty that typically requires knowledge about the probability distribution of uncertain parameters. As the latter is often unknown, Distributionally Robust…
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…
This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with…
In the dynamical systems approach to describing turbulent or otherwise chaotic flows, an important quantity is the Lyapunov exponents and vectors that characterize the strange attractor of the flow. In particular, knowledge of the Lyapunov…
Stability margins for linear time-varying (LTV) and switched-linear systems are traditionally computed via quadratic Lyapunov functions, and these functions certify the stability of the system under study. In this work, we show how the more…
In this work we addressed the problem of stability analysis for an uncertain piecewise affine model of a genetic regulatory network. In particular we considered polytopic parameter uncertainties on the proteins production rate functions,…
This paper presents a data-driven framework for uncertainty propagation under unmeasured or statistically unmodeled (unstructured) disturbances. We consider residual disturbances, which consolidate all unstructured disturbances into a…
We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially nonlinear systems…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at…
We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are…
This paper studies Markov Decision Processes under parameter uncertainty. We adapt the distributionally robust optimization framework, and assume that the uncertain parameters are random variables following an unknown distribution, and…
We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation,…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…