Related papers: Boundary Stabilization with restricted observabili…
The problem of formulating self-consistent local and global stability exponents is shown to require global separation of variables. Posing the separation of variable problem, we see that many such separations are possible, but only one is…
Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems.…
In the stability analysis of an equilibrium, given by a stationary point of a functional F[n] (free energy functional, e.g.), the second derivative of F[n] plays the essential role. If the system in equilibrium is subject to the…
This work presents the continuation of the recent article "The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension", published in the Nonlinear Dynamics journal. In this work, in comparison with the results for…
Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…
In this paper, we improve the known estimates for the invariance entropy of a nonlinear control system. For sets of complete approximate controllability we derive an upper bound in terms of Lyapunov exponents and for uniformly hyperbolic…
Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust…
We apply a Lyapunov function to obtain conditions for the existence and uniqueness of small classical time-periodic solutions to first order quasilinear 1D hyperbolic systems with (nonlinear) nonlocal boundary conditions in a strip. The…
Lyapunov stability theory is the bedrock of direct adaptive control. Fundamentally, Lyapunov stability requires constructing a distance-like function which must decrease with time to ensure stability. Feedback linearization, backstepping,…
In this paper we study the long time dynamics of the solutions to the initial-boundary value problem for a scalar conservation law with a saturating nonlinear diffusion. After discussing the existence of a unique stationary solution and its…
A hyperbolic group acts by homeomorphisms on its Gromov boundary. We use a dynamical coding of boundary points to show that such actions are topologically stable in the dynamical sense: any nearby action is semi-conjugate to (and an…
We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…
Polarized ferrofluids, lipid monolayers and magnetic bubbles form domains with deformable boundaries. Stability analysis of these domains depends on a family of nontrivial integrals. We present a closed form evaluation of these integrals as…
This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…
This paper addresses the challenge of safe stabilization, ensuring the system state reach the origin while avoiding unsafe regions. Existing approaches relying on smooth Lyapunov barrier functions often fail to guarantee a feasible…
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…
In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of…
We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation…
In a complex real-time operating environment, external disturbances and uncertainties adversely affect the safety, stability, and performance of dynamical systems. This paper presents a robust stabilizing safety-critical controller…