Ernest Barany

Global regulation of uncertain manipulators using bounded controls

This paper considers the position regulation problem for uncertain robot manipulators in the presence of constraints on the available actuator torques, and proposes two new controllers as solutions to this problem. The first controller is derived under the assumption that the manipulator state is measurable, while the second strategy is developed for those applications in which only position measurements are available. Each scheme consists of a nonadaptive component for gross position control and an adaptive component to ensure convergence to the desired position. The controllers are computationally simple, require very little information regarding the manipulator model or the payload, and ensure that the position error is globally convergent. The capabilities of the proposed control strategies are illustrated though both computer simulations and laboratory experiments with an IMI Zebra Zero manipulator.

Adaptive regulation of manipulators using only position measurements

This article considers the motion-control problem for uncertain robot manipulators in the case where only joint-position mea surements are available, and proposes an adaptive controller as a solution to this problem. The proposed control strategy is general and computationally effrcient, requires very little infor mation regarding the manipulator model or the payload, and ensures that the position-regulation error possesses desirable convergence properties: semiglobal asymptotic convergence if no external disturbances are present, and semiglobal con vergence to an arbitrarily small neighborhood of zero in the presence of bounded disturbances. It is shown that the adaptive controller can be modified to provide accurate trajectory track ing control through the introduction of feedforrvard elements in the control law. The adaptive regulation and tracking schemes have been implemented in laboratory experiments with an IMI Zebra Zero manipulator. These experiments demonstrate that accurate and robust motion control can be achieved by using the proposed approach.

Adaptive control of nonholonomic mechanical systems

This paper considers the problem of controlling nonholonomic mechanical systems in the presence of incomplete information concerning the system model and state, and presents a class of adaptive controllers as a solution to this problem. The proposed control strategies provide simple and robust solutions to a number of important nonholonomic system control problems, including stabilization to an equilibrium manifold, stabilization to an equilibrium point, and trajectory tracking control. All of the schemes are computationally efficient, are implementable without system dynamic model or rate information, and ensure uniform boundedness of all signals and accurate motion control.

Adaptive output stabilization of manipulators

This paper considers the position regulation problem for rigid robots for the case in which only joint position measurements are available, and proposes two adaptive controllers as solutions to this problem. The first controller is developed by assuming that the structure of the vector of gravity torques is known, but that the inertial parameters for the manipulator and payload are unknown; it is shown that this scheme ensures semiglobal stability and convergence of the position error to zero. Alternatively, the second adaptive strategy is derived under the assumption that no information is available concerning the manipulator model, and in this case it is shown that the controller provides uniform boundedness of all signals and exponential convergence of the position error to a set which can be made arbitrarily small. Experimental results are presented for a Zebra Zero manipulator and demonstrate that the proposed approach provides a simple and effective means of obtaining high performance position regulation.<<ETX>>

Global stabilization of uncertain manipulators using bounded controls

This paper considers the position stabilization problem for uncertain robot manipulators in the presence of constraints on the available actuator torques, and proposes two new controllers as solutions to this problem. The first controller is derived under the assumption that the manipulator state is measurable, while the second strategy is developed for those applications in which only position measurements are available. Each scheme consists of a nonadaptive component for gross position control and an adaptive component to ensure convergence to the desired position. The controllers are computationally simple, require very little information regarding the manipulator model or the payload, and ensure that the position error is globally convergent.

Detecting market crashes by analysing long-memory effects using high-frequency data

It is well known that returns for financial data sampled with high frequency exhibit memory effects, in contrast to the behavior of the much celebrated log-normal model. Herein, we analyse minute data for several stocks over a seven-day period which we know is relevant for market crash behavior in the US market, March 10–18, 2008. We look at the relationship between the Lévy parameter α characterizing the data and the resulting H parameter characterizing the self-similar property. We give an estimate of how close this model is to a self-similar model.

Nonlinear controllability of singularly perturbed models of power flow networks

A method based on differential geometric control theory is presented intended to provide insight into how the nodes of a power network can affect each other. In this preliminary report, we consider a simple model of a power system derived from singular perturbation of the power flow equations. It is shown that such a model is accessible, and that for simple chain topology the network is actually feedback linearizable. The result is illustrated numerically. This simple example is a precursor for more interesting models of networks.

Evolutionary dynamics through multispecies competition

Disruptive selection, emerging from frequency-dependent intraspecific competition can have very exciting evolutionary outcomes. One such outcome is the origin of new species through an evolutionary branching event. Literature on theoretical models investigating the emergence of disruptive selection is vast, with some investigating the sensitivity of the models on assumptions of the competition and carrying capacity functions’ shapes. What is seldom modeled is what happens once the population escapes its effect via increase phenotypic or genotypic variance. The expectation is mixed: disruptive selection could diminish and ultimately disappear or it could still exist leading to further speciation events through multiple evolutionary branching events. Here, we derive the conditions under which disruptive selection drives two subpopulations that originated at a branching point to other points in trait space where each subpopulation again experiences disruptive selection. We show that the general pattern for further branchings require that the competition function to be even narrower than what is required for the first evolutionary branching. However, we also show that the existence of disruptive selection in higher dimensional systems is also sensitive to the shapes of the functions used.

Stabilization of chemostats using feedback linearization

Stabilization via feedback linearization of two-species competition models based in the chemostat is considered. Competition is for a single growth-limiting resource in the first model, and for two perfectly substitutable resources in the second. The dilution rate and the input concentration of one nutrient are taken as input controls in each model. The main issues we investigate are limitations on stabilizable states and stabilizer design due to the structure of the linearized system. It is shown that determination of feasible stabilizable states requires computation of an equilibrium submanifold in the state space. Once this is accomplished, the potential exists for failure of a proportional-derivative stabilizer strategy due to singular structure in the resulting closed-loop dynamics caused by failure of the linearizing coordinate transformation to be a global diffeomorphism. This is exhibited explicitly in the three-dimensional model, and it is shown numerically that similar phenomena persist in four dimensions.

Control of nonholonomic mechanical systems using reduction and adaptation

This paper considers the problem of controlling the motion of nonholonomic mechanical systems in the presence of uncertainty regarding the system model and state. It is proposed that a simple and effective solution to this problem can be obtained by first using a reduction procedure to obtain a lower dimensional system which retains the mechanical system structure of the original system, and then adaptively controlling the reduced system in such a way that the complete system is driven to the goal configuration. This approach is shown to be easy to implement and to ensure accurate motion control despite measurement and model uncertainty. The efficacy of the proposed control strategy is illustrated through computer simulations and preliminary hardware experiments with nonholonomic mechanical systems arising from both explicit kinematic constraints and symmetries of the system dynamics.