Related papers: Asymptotics of motion planning complexity for cont…

We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…

In normal on-road situations, autonomous vehicles will be expected to have smooth trajectories with relatively little demand on the vehicle dynamics to ensure passenger comfort and driving safety. However, the occurrence of unexpected…

Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…

Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…

This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…

The main objective of this paper is to show that two asymptotically stable steady states which belong to an analytic path of asymptotically stable steady states can be gradually transferred one to the other by successive changes of the…

This paper addresses the three-dimensional path-following guidance problem for unmanned aerial vehicles under explicit actuator constraints. Unlike conventional approaches that assume unbounded control inputs or handle saturation…

This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise…

This paper examines impulsive controls related to nonautonomous impulsive integro-differential equations in Hilbert space, highlighting their significance. We establish the existence of the mild solution by using fixed point approach and…

This paper concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear…

We study the dynamics of pairs of connected masses in the plane, when nonholonomic (knife-edge) constraints are realized by forces of viscous friction, in particular its relation to constrained dynamics, and its approximation by the method…

In the dynamics of open quantum systems, the interaction with the external environment usually leads to a contraction of the set of reachable states for the system as time increases, eventually shrinking to a single stationary point. In…

We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of…

We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…

We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…

The problem of suboptimality under bounded disturbances for the adaptive systems based on speed-graadient approach is discussed. A formulation of the estimated optimality of nonlinear nonlinearly parametrized adaptive control systems is…

We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…

For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control…

It has been observed that the very important motion planning problem of robotics mathematically speaking boils down to the problem of finding a section to the path-space fibration, raising the notion of topological complexity, as introduced…

In this paper approximations of the set of trajectories and integral funnel of the control system described by nonlinear ordinary differential equation with integral constraint on the control functions are considered. The set of admissible…