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Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…
We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential equations defining a flow on a three-dimensional manifold.…
This paper presents basis parts of a new method to synthesize a return trajectory for a reactive process from a default mode to one of the nominal modes. The process is modeled with a hybrid automata. The purpose consists of doing a…
We consider the parameter synthesis problem of parametric timed automata (PTAs). The problem is, given a PTA and a property, to compute the set of valuations of the parameters under which the resulting timed automaton satisfies the…
Most passivity based trajectory tracking algorithms for mechanical systems can only stabilise reference trajectories that have constant energy. This paper overcomes this limitation by deriving a single variable Hamiltonian model for the…
Reactive synthesis is a technology for the automatic construction of reactive systems from logical specifications. In these lecture notes, we study different algorithms for the reactive synthesis problem of linear-time temporal logic (LTL).…
We propose an example of smooth autonomous system governed by differential delay equation manifesting chaotic dynamics apparently associated with hyperbolic attractor of Smale - Williams type. The general idea is to depart from a system…
The effect of noise is studied in one-dimensional maps undergoing transcritical, tangent, and pitchfork bifurcations. The attractors of the noiseless map become metastable states in the presence of noise. In the weak-noise limit, a…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…
System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback…
We consider how breakdown of the quasistatic approximation for attractors can lead to rate-induced tipping, where a qualitative change in tracking/tipping behaviour of trajectories can be characterised in terms of a critical rate.…
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the…
We describe some recent results on the dynamics of singular-hyperbolic (or Lorenz-like) attractors: attractors in this class are expansive and so sensitive with respect to initial data; they admit a unique physical measure whose support is…
In this work, we propose novel LMI-based controller synthesis frameworks for periodically time-varying Markov-jump linear systems. We first discuss the necessary conditions for mean square stability and derive Lyapunov-like conditions for…
Reactive synthesis is a class of methods to construct a provably-correct control system, referred to as a robot, with respect to a temporal logic specification in the presence of a dynamic and uncontrollable environment. This is achieved by…
We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orbits of a given dynamical system. We develop theory for it…
In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart…
The paper presents a novel approach to synthesize robust controllers for nonlinear systems along perturbed trajectories. The approach linearizes the system with respect to a reference trajectory. In contrast to existing methods rooted in…
Systems of dense spheres interacting through very short-ranged attraction are known from theory, simulations and colloidal experiments to exhibit dynamical reentrance. The liquid state can thus be fluidized to higher densities than…
The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem $u_t= u_{xx} + \lambda u - \beta(t)u^3$ when the parameter $\lambda > 0$ varies. Also, we answer a question proposed in…