Abstract. The paper presents an analysis of a mathematical model of the human arm dynamics in terms of observability. The purpose of the performed experiments is the selection of an observer for the possibility of arm tracking. The arm model is based on the two-link manipulator moving horizontally and vertically. For the study a model was linearized and the model part responsible for the work of human muscles was omitted. The experimental part involved simulated measurements of the motion parameters that imitate real-IMU (Inertial Measurement Unit) measurements. Finally, the simulation results using the observer in the form of a Kalman filter and the particle filter have been presented.
Abstract. The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.
The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder's fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.
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