This article deals with a special type of Lyapunov functions, namely the solution of Zubov's
equation. Such a function can be used to characterize the exact boundary of the domain of …

We propose a deep neural network architecture and a training algorithm for computing
approximate Lyapunov functions of systems of nonlinear ordinary differential equations …

We propose a deep neural network architecture for storing approximate Lyapunov functions
of systems of ordinary differential equations. Under a small-gain condition on the system, the …

In this paper, we consider nonlinear control systems and discuss the existence of a
separable control Lyapunov function. To this end, we assume that the system can be …

Because of the unavoidable use of numerical integration methods, such as Runge--Kutta or
finite elements, the numerical solution of optimal control problems, with either ODE or PDE …

Complex systems are pervasive in many areas of science. With the increasing requirement
for high levels of system performance, complex systems has become an important area of …

We briefly review recent work where deep learning neural networks have been interpreted
as discretisations of an optimal control problem subject to an ordinary differential equation …

SOLVING an optimal control problem using a digital computer implies discrete
approximations. Since the 1960s, there have been well-documented [1–3] naïve …

Abstract The Region of Attraction of an equilibrium point is the set of initial conditions whose
trajectories converge to it asymptotically. This article, building on a recent work on positively …

Distributed optimization increasingly plays a central role in economical and sustainable
operation of cyber-physical systems. Nevertheless, the complete potential of the technology …