Cloud computing applications must be allocated sufficient resources to comply with Service Level Agreements (SLAs). This paper considers data-driven probabilistic modeling of application resource demand for resource allocation. The modeling method is focused on peak demand and SLA violations and relies on a branch of statistics known as extreme value theory (EVT). Rigorous statistical validation of the proposed model shows that it generalizes better than the alternative. The paper presents a resource allocation algorithm using the model to ensure a given small SLA violation rate. For resource allocation in Yahoo data center, over 50 percent savings are demonstrated using the proposed approach.

This letter develops a method for estimating trends of extreme events statistics across multiple time periods. Some of the periods might have no extreme events and some might have much data. The extreme event distribution is modeled with a Pareto or exponential tail. The method requires selecting an extreme event threshold and then solving two convex problems for the tail parameters. Solving one provides a smoothed tail rate trend, solving another, the smoothed trend of the tail quantile level. The approach is illustrated by trending the 10-year extreme event risks for S&P 500 index daily losses and for peak power load in electrical utility data.

We consider a discrete-time dynamical system with Boolean and continuous states, with the continuous state propagating linearly in the continuous and Boolean state variables, and an additive Gaussian process noise, and where each Boolean state component follows a simple Markov chain. This model, which can be considered a hybrid or jump-linear system with very special form, or a standard linear Gauss-Markov dynamical system driven by a Boolean Markov process, arises in dynamic fault detection, in which each Boolean state component represents a fault that can occur. We address the problem of estimating the state, given Gaussian noise corrupted linear measurements. Computing the exact maximum a posteriori (MAP) estimate entails solving a mixed integer quadratic program, which is computationally difficult in general, so we propose an approximate MAP scheme, based on a convex relaxation, followed by rounding and (possibly) further local optimization. Our method has a complexity that grows linearly in the time horizon and cubicly with the state dimension, the same as a standard Kalman filter. Numerical experiments suggest that it performs very well in practice.

This paper presents a new paradigm for model-free design of a trajectory tracking controller and its experimental implementation in control of a direct-drive manipulator. In accordance with the paradigm, a nonlinear approximation for the feedforward control is used. The input to the approximation scheme are task parameters that define the trajectory to be tracked. The initial data for the approximation is obtained by performing learning control iterations for a number of selected tasks. The paper develops and implements practical approaches to both the approximation and learning control. We propose a new learning control algorithm based on the online Levenberg-Marquardt minimization of a regularized tracking error index. The paper demonstrates an experimental application of the paradigm to trajectory tracking control of fast (1.25 s) motions of a direct-drive industrial robot AdeptOne. In our experiments, the learning control converges in five to six iterations for a given set of the task parameters.

This paper considers a problem of nonholonomic motion planning. A practical paradigm for planning and stabilization of motion in a class of multivariate nonlinear (nonholonomic) systems is presented and applied to a planar free-floating manipulator system. The controller architecture designed in the paper is based on the radial basis function approximation of an optimal control program for any desired motion. This architecture also incorporates a sampled-data feedback stabilization algorithm. The proposed control technique overcomes certain problems associated with other control approaches available for nonholonomic systems. The presented simulation results reveal a promising potential of the proposed control paradigm. This paradigm can be extended to a broader class of nonlinear control problems.

The paper describes a novel approach to accurate positioning control of mechanical devices with nonlinear (stick-slip) friction. The controller applies narrow torque pulses to achieve the desired displacement of the mechanism. The pulse shapes are computed through fuzzy logic approximation of the dependence between the desired displacement and the pulse shape. The stability conditions of the proposed controller are derived taking into account an influence of random variation of the friction properties. A detailed experimental study of the system response to the torque pulses of different shapes and a detailed controller design are presented for a direct-drive manipulator setup. It is experimentally demonstrated that the developed controller achieves positioning precision up to the limits of the position encoder resolution.

Considers radial basis function (RBF) network approximation of a multivariate nonlinear mapping as a linear parametric regression problem. Linear recursive identification algorithms applied to this problem are known to converge, provided the regressor vector sequence has the persistency of excitation (PE) property. The main contribution of this paper is formulation and proof of PE conditions on the input variables. In the RBF network identification, the regressor vector is a nonlinear function of these input variables. According to the formulated condition, the inputs provide PE, if they belong to domains around the network node centers. For a two-input network with Gaussian RBF that have typical width and are centered on a regular mesh, these domains cover about 25% of the input domain volume. The authors further generalize the proposed solution of the standard RBF network identification problem and study affine RBF network identification that is important for affine nonlinear system control. For the affine RBF network, the author formulates and proves a PE condition on both the system state parameters and control inputs.

In this paper, we present a technique for planning and stabilization of motion in a class of multivariable nonlinear (nonholonomic) systems, and apply this technique to the free-flying manipulators. The controller architecture designed in the paper is based on the radial basis function (RBF) network approximation of an optimal control program for any desired motion. An additional control level for sampled feedback compensation of the approximation errors is also proposed. The presented RBF-based control technique overcomes certain problems associated with other control approaches recently proposed for nonholonomic systems. An example and numerical simulations are provided for illustration.>

This paper compares the application of five different methods for the approximation of the inverse kinematics of a manipulator arm from a number of joint angle/Cartesian coordinate training pairs. The first method is a standard feedforward neural network with error backpropagation learning. The next two methods are derived from an extended Kohonen Map algorithm that we combine with Shepard interpolation for the forward computation. We compare the method of Ritter et al. for the learning of the extended Kohonen Map to our own scheme based on gradient descent optimization. We also study three scattered data approximation algorithms. They include two variants of the Radial Basis Function (RBF) method: Hardy's multiquadrics and gaussian RBF. We further develop our own Local Polynomial Fit method that could be considered as a modification of McLain's method. We propose extensions to the considered scattered data approximation algorithms to make them suitable for vector-valued multivariable functions, such as the mapping of Cartesian coordinates into joint angle coordinates.