Autonomous system (mathematics)

About: Autonomous system (mathematics) is a research topic. Over the lifetime, 1648 publications have been published within this topic receiving 38373 citations.

Kernel methods for the approximation of discrete-time linear autonomous and control systems

Abstract: Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate relevant matrices and some relevant quantities such as the topological entropy. An application to stabilization via algebraic Riccati equations is included by viewing a control system as an autonomous system in an extended space of states and control inputs. Kernel methods are the main techniques used in this paper and the approach is illustrated via a series of numerical examples. The advantage of using kernel methods is that they allow to perform function approximation from data and, as illustrated in this paper, allow to approximate linear discrete-time autonomous and control systems from data.

Pseudo-reference for motion transfer based on autonomous control system with an orbit attractor

Abstract: Skill or motion transfer from someone to other persons is always required for dance teaching, rehabilitation, sports and so on. For teaching or transfer of motion, a dance notation and display of sequence of motion are often used effectively. However, these contain only the instantaneous postures of motion or professional subjective sense, it is not easy for beginners to understand the dynamical knack of motion. In this paper, we propose “pseudo-reference” that is a virtual target posture in the human motion. The pseudo-reference is developed based on the modeling of the human motion by the attractor design method which realizes an autonomous system. By comparing the nonlinear controller with conventional control systems (1DOF and 2DOF control system), the pseudo-reference is obtained as an embodiment of the implicit reference. The proposed method is performed with the inverted pendulum system and the tap dancing robot, and the validity and feasibility for motion transfer of the pseudo-reference are evaluated.

Towards autonomous cruising on highways

Abstract: The objectives of this paper are to discuss how vehicle automation technology can be used to benefit car drivers and also to propose a concept of an autonomous highway vehicle which improves highway driving safety.

The autonomous system derived from Van der Pol-Mathieu equation

Abstract: This work is devoted to the autonomous system derived from Van der Pol-Mathieu equation which was applied to the study the dynamics of dusty plasmas. In this work we shall investigate mathematically this autonomous system and shall find how large region of the plane will be attracted to the equilibrium point.