We consider an experimental system consisting of a pendulum, which is free to rotate 360 degrees, attached to a cart. The cart can move in one dimension. We describe a model for this system and use it to design a feedback control law that stabilizes the pendulum in the upright position. We then introduce a time delay into the feedback and prove that for values of the delay below a critical dela...

Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Due to limited energy budgets and limited control authority, these “disturbances” cannot always be canceled out with high-gain feedback. Minimally-actuated walking machines subject to stochastic disturbances no longer satisfy strict conditions for limit-cycle...

Statistical estimation theory determines the optimal way of estimating parameters of a fluctuating noisy signal. However, if the estimation is performed on unreliable hardware, a sub-optimal estimation procedure can outperform the previously optimal procedure. Here, we compare classes of circadian clocks by viewing them as phase estimators for the periodic day-night light signal. We find that c...

—Based on the classic SIR model, this paper proposes a new rumor spreading model which considers the transition probability of nodes from S to I as a variable instead of a constant. This paper firstly studies the nonlinear phenomena in the new model, such as balance node, Hopf bifurcation, limit cycle. Secondly, this paper studies how to control the range of limit cycle. Finally, this paper st...

We propose a quantitative approach to some high frequency trading problematics. We are interested in several aspects of this field, from minimizing indirect trading costs to market making, and more generally in profit maximization strategies over a finite time horizon. We build an original framework that reflects specificities of high frequency trading, and especially the distinction between pa...

Seminal works in biped walking such as [1] had assumed favorable initial conditions on a limit cycle to start with. A more practical approach would be to start the biped from a static resting position. This paper proposes a simplified and straightforward approach for taking a biped robot from an initial resting position to a stable walking limit cycle. The biped model selected for the study is ...

Unlike input deadband, the sandwiched deadband between actuator and plant dynamics is very difficult to be explicitly compensated for due to the proceeding actuator dynamics whose effect may not be negligible. The paper presents a practical way to overcome the design conservativeness of existing methods in dealing with sandwiched deadband. Specifically, a describing function based nonlinear ana...

An adaptive control system using extremum-seeking optimization is developed to suppress subsonic cavity flow oscillations. The overall control system is developed by following two steps. First, a simple linear control law which uses measurements of wall pressure fluctuations at two different locations in the cavity is developed, and the effect on the magnitude of the limit cycle produced by tun...

This paper studies the optimal control of an animal-vegetation system where growth in the animal stock is density independent. The ecological system is shown to have a limit cycle, under certain parameter values, but can also be stabilized by a simple harvesting rule. The managing unit maximizes profits from selling the meat, over an infinite planning horizon. With a domestic animal stock, cost...