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We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…

The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…

This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…

Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically…

Learning-based control of linear systems received a lot of attentions recently. In popular settings, the true dynamical models are unknown to the decision-maker and need to be interactively learned by applying control inputs to the systems.…

Training Neural ODEs requires backpropagating through an ODE solve. The state-of-the-art backpropagation method is recursive checkpointing that balances recomputation with memory cost. Here, we introduce a class of algebraically reversible…

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This problem is rather common especially in population dynamics models. Precisely, a particular solution of a…

This paper discusses stability and robustness properties of a recently proposed observer algorithm for linear time varying systems. The observer is based on the approximation and subsequent modification of the non-negative Lyapunov…

This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…

A dynamic backstepping method is proposed to design controllers for nonlinear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit nonlinear algebraic equation. The idea of this…

Incremental stability is a property of dynamical systems ensuring the uniform asymptotic stability of each trajectory rather than a fixed equilibrium point or trajectory. Here, we introduce a notion of incremental stability for stochastic…

We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The required stabilizing algebra depends…

Optimizing non-convex functions is of primary importance in the vast majority of machine learning algorithms. Even though many gradient descent based algorithms have been studied, successive convex approximation based algorithms have been…

In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…

We deduce stability results for finite control set and mixed-integer model predictive control with a downstream oversampling phase. The presentation rests upon the inherent robustness of model predictive control with stabilizing terminal…

We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…

We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily…

Inverse design of slender elastic structures underlies a wide range of applications in computer graphics, flexible electronics, biomedical devices, and soft robotics. Traditional optimization-based approaches, however, are often orders of…