If the dynamics of an evolutionary differential equation system possess a lowdimensional, attracting, slow manifold, there are many advantages to using this manifold to perform computations for long term dynamics, locating features such as stationary points, limit cycles, or bifurcations. Approximating the slow manifold, however, may be computationally as challenging as the original problem. If...

Reinforcement learning (RL) has become a central paradigm for solving learning-control problems in robotics and artificial intelligence. R L researchers have focussed almost exclusively on problems where the controller has to maximize the discounted sum of payoffs. However, as emphasized by Schwartz (1$X)3), in many problems, e.g., those for which the optimal behavior is a limit cycle, it is mo...

INTRODUCTION Precision positioning systems are essential in precision industry. These positioning systems often have one or more elements that introduce friction. Friction is well known to cause steadystate errors and limit cycles, and to slow the motion of the mechanism. Thus, it is important to consider friction compensation in controller design. Simple controllers like PID controllers do not...

Currently, reset control focuses on using structures which allow new resetting rules in order to avoid limit cycle to be caused and improve the performance of the system. This paper investigates the properties of some reset strategies, of integer and fractional order, which reset controller states to fixed or variable non-zero values and are able to eliminate or reduce the overshoot in first an...

This paper considers the optimal control problem of connecting two periodic trajectories with maximal persistence. A maximally persistent trajectory is close to the periodic type in the sense that the norm of the image of this trajectory under the operator defining the periodic type is minimal among all trajectories. A solution is obtained in this paper for the case when the two trajectories ha...

¥ This research was supported in part by DARPA contracts/grants N66001-97-C-8522 and N66001-97-C-8523, by NSF grants CCR-9876217 and by Tektronix Inc., and Intel Corporation. Abstract – Experimentally, we show that Transmission Control Protocol (TCP)’s congestion control algorithm results in dynamic behavior similar to a stable limit cycle (attractor) when data from TCP flow into a fixed-size b...

Solar photovoltaics is one of the most promising technologies for the non-carbon based electricity production. Power electronics is therefore necessary. In this paper a converter is analyzed which makes it possible to control the mean value of the output voltage, this is e.g. the voltage across a DC machine (and therefore the speed) from zero up to three times of the input voltage. The converte...

An iterative scheme is set up for solving the loop equation of the hermitian one-matrix model with a multi-cut structure. Explicit results are presented for genus one for an arbitrary but finite number of cuts. Due to the complicated form of the boundary conditions, the loop correlators now contain elliptic integrals. This demonstrates the existence of new universality classes for the hermitian...

In [17] it was suggested that the number of limit cycles in a piecewise-linear system could be closely related to the number of zones, that is the number of parts of the phase plane where the system is linear. In this note we construct an example of a class of perturbed piecewise systems with n zones such that the first variation of the displacement function is identically zero. Then we conject...

In this paper we consider the classical and quantum control of squeezed states of harmonic oscillators. This provides a method for reducing noise below the quantum limit and provides an example of the control of under-actuated systems in the stochastic and quantum context. We consider also the interaction of a squeezed quantum oscillator with an external heat bath.