相关论文: Switching between Limit Cycles in a Model of Runni…

This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from…

This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…

In this paper we provide a method to generate a continuum of limit cycles using a single precomputed exponentially stable limit cycle designed within the Hybrid Zero Dynamics framework. Guarantees for existence and stability of these limit…

We present a new Lyapunov-based switching attitude controller for energy-efficient real-time selection of the torque inputted to an uncrewed aerial vehicle (UAV) during flight. The proposed method, using quaternions to describe the attitude…

This paper presents the design of a control model to navigate the differential mobile robot to reach the desired destination from an arbitrary initial pose. The designed model is divided into two stages: the state estimation and the…

We study the occurrence of limit cycles from a point on the discontinuity hyperplane $L$ between two smooth vector fields where the two vector fields both point towards one another. Generically, such a point (called switched equilibrium in…

This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the "rimless wheel", and the "compass…

Complex motions for robots are frequently generated by switching among a collection of individual movement primitives. We use this approach to formulate robot motion plans as sequences of primitives to be executed one after the other. When…

Although the limit cycle have been studied for more than 100 years, the existence of its Lyapunov function is still poorly understood. By considering a common limit cycle system, a puzzle related to the existence of Lyapunov functions for…

The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…

Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…

We present a switching scheme, which uses both the attitude-error quaternion (AEQ) and the angular-velocity error, for controlling the rotational degrees of freedom of an uncrewed aerial vehicle (UAV) during flight. In this approach, the…

This paper studies the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. By analyzing the obtained first order Melnikov function, we give an upper bound of the number of limit cycles…

Soft and soft-rigid hybrid robots are inherently underactuated and operate under tight actuator limits, making task-space control with stability guarantees challenging. Common nonlinear strategies for soft robots (e.g., those based on PD…

Safety is essential for autonomous systems, in particular for interconnected systems in which the interactions among subsystems are involved. Motivated by the recent interest in cyber-physical and interconnected autonomous systems, we…

In this paper, we apply a Control Lyapunov Function methodology to design two families of cruise controllers for the two-dimensional movement of autonomous vehicles on lane-free roads using the bicycle kinematic model. The control Lyapunov…

Robust stabilization conditions for uncertain switched affine systems subject to a unitary input delay are presented. They are obtained through the Lyapunov framework and a min-switching state-feedback predictive control law. The result…

This paper studies the family of piecewise linear differential systems in the plane with two pieces separated by a switching curve $y=x^{m}$, where $m>1$ is an arbitrary positive. By analysing the first order Melnikov function, we give an…

This paper deals with the problem of limit cycle bifurcations for a piecewise near-Hamilton system with four regions separated by algebraic curves $y=\pm x^2$. By analyzing the obtained first order Melnikov function, we give an upper bound…

Growing penetration of renewable generation in power systems brings more challenges in transient stability assessment using direct methods. One of the reasons is the inability to assess the risk of instability brought by tripping of a large…