Related papers: Global Dynamical Solvers for Nonlinear Programming…
A dynamic method to solve the Non-linear Programming (NLP) problem with Equality Constraints (ECs) and Inequality Constraints (IECs) is proposed. Inspired by the Lyapunov continuous-time dynamics stability theory in the control field, the…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
A general model of age-structured population dynamics is developed and the fundamental properties of its solutions are analyzed. The model is a semilinear partial differential equation with a nonlinear nonlocal boundary condition.…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential…
This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…
Identifying the dynamic precompensator that renders a nonlinear control system feedback linearizable is a challenging problem. Researchers have explored the problem -- dynamic feedback linearization -- and produced existence conditions and…
The notion of the relaxed Robust Control Lyapunov Function (relaxed RCLF) is introduced and is exploited for the design of robust feedback stabilizers for nonlinear systems. Particularly, it is shown for systems with input constraints that…
The aim of this survey is to present the main important techniques and tools from variational analysis used for first and second order dynamical systems of implicit type for solving monotone inclusions and non-smooth optimization problems.…
This paper develops a direct data-driven framework for infinite networks with unknown nonlinear polynomial subsystems, enabling the synthesis of controllers that ensure the entire network is uniformly globally asymptotically stable (UGAS).…
We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to…
In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an…
Conceptual framework is laid out of a deterministic program capable of obtaining optimum solutions with or without constraints for any reasonably behaved analytical system. Recipe implementable as a well-behaved Runge-Kutta procedure is…
Given a dynamical system with constrained outputs, the maximal admissible set (MAS) is defined as the set of all initial conditions such that the output constraints are satisfied for all time. It has been previously shown that for…
This work has the goal of briefly surveying some key stabilization techniques for general nonlinear systems, for which, as it is well known, a smooth control Lyapunov function may fail to exist. A general overview of the situation with…
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…