A Newton algorithm for invariant subspace computation with large basins of attraction

We study the global behaviour of a Newton algorithm on the Grassmann manifold for invariant subspace computation. It is shown that the basins of attraction of the invariant subspaces may collapse in case of small eigenvalue gaps. A Levenberg-Marquardt-like modification of the algorithm with low numerical cost is proposed. A simple strategy for choosing the parameter is shown to dramatically enlarge the basins of attraction of the invariant subspaces while preserving the fast local convergence.

Stabilising terminal cost and terminal controller for ℓasso- MPC: Enhanced optimality and region of attraction

In recent literature, ℓ1-regularised MPC, or ℓasso-MPC, has been recommended for control tasks involving complex requirements on the control signals, for instance, the simultaneous solution of regulation and sharp control allocation for redundantly-actuated systems. This is due to the implicit thresholding ability of LASSO regression. In this paper, a stabilising terminal cost featuring a mixed ℓ1/ℓ2 2 penalty is presented. Then, a candidate terminal controller is computed, with the aim of enlarging the region of attraction. © 2013 EUCA.

Unified modelling in support of organization design and change

The aim of this research is to provide a unified modelling-based method to help with the evaluation of organization design and change decisions. Relevant literature regarding model-driven organization design and change is described. This helps identify the requirements for a new modelling methodology. Such a methodology is developed and described. The three phases of the developed method include the following. First, the use of CIMOSA-based multi-perspective enterprise modelling to understand and capture the most enduring characteristics of process-oriented organizations and externalize various types of requirement knowledge about any target organization. Second, the use of causal loop diagrams to identify dynamic causal impacts and effects related to the issues and constraints on the organization under study. Third, the use of simulation modelling to quantify the effects of each issue in terms of organizational performance. The design and case study application of a unified modelling method based on CIMOSA (computer integrated manufacturing open systems architecture) enterprise modelling, causal loop diagrams, and simulation modelling, is explored to illustrate its potential to support systematic organization design and change. Further application of the proposed methodology in various company and industry sectors, especially in manufacturing sectors, would be helpful to illustrate complementary uses and relative benefits and drawbacks of the methodology in different types of organization. The proposed unified modelling-based method provides a systematic way of enabling key aspects of organization design and change. The case company, its relevant data, and developed models help to explore and validate the proposed method. The application of CIMOSA-based unified modelling method and integrated application of these three modelling techniques within a single solution space constitutes an advance on previous best practice. Also, the purpose and application domain of the proposed method offers an addition to knowledge. © IMechE 2009.

Rhythmic stabilization of periodic orbits in a wedge

The paper addresses the rhythmic stabilization of periodic orbits in a wedge billiard with actuated edges. The output feedback strategy, based on the sole measurement of impact times, results from the combination of a stabilizing state feedback control law and a nonlinear deadbeat state estimator. It is shown that the robustness of both the control law and the observer leads to a simple rhythmic controller achieving a large basin of attraction. Copyright © 2005 IFAC.

Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Use of vertically-aligned carbon nanotube array to enhance the performance of electrochemical capacitors

In the domain of energy storage, electrochemical capacitors have numerous applications ranging from hybrid vehicles to consumer electronics, with very high power density at the cost of relatively low energy storage. Here, we report an approach that uses vertically aligned carbon nanotube arrays as electrodes in electrochemical capacitors. Different electrolytes were used and multiple parameters of carbon nanotube array were compared: carbon nanotube arrays were shown to be two to three times better than graphite in term of specific capacitance, while the surface functionalization was demonstrated to be a critical factor in both aqueous and nonaqueous solutions to increase the specific capacitance. We found that a maximum energy density of 21 Wh/kg at a power density of 1.1 kW/kg for a hydrophilic electrode, could be easily achieved by using tetraethylammonium tetrafluoroborate in propylene carbonate. These are encouraging results in the path of energy-storage devices with both high energy density and power density, using only carbon-based materials for the electrodes with a very long lifetime, of tens of thousands of cycles. © 2011 IEEE.

Minimalistic control of biped walking in rough terrain

Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this article, we tackle with the problem of bipedal locomotion in rough terrains by using a minimalistic control architecture for the compass gait walking model. This controller utilizes an open-loop sinusoidal oscillation of hip motor, which induces basic walking stability without sensory feedback. A set of simulation analyses show that the underlying mechanism lies in the "phase locking" mechanism that compensates phase delays between mechanical dynamics and the open-loop motor oscillation resulting in a relatively large basin of attraction in dynamic bipedal walking. By exploiting this mechanism, we also explain how the basin of attraction can be controlled by manipulating the parameters of oscillator not only on a flat terrain but also in various inclined slopes. Based on the simulation analysis, the proposed controller is implemented in a real-world robotic platform to confirm the plausibility of the approach. In addition, by using these basic principles of self-stability and gait variability, we demonstrate how the proposed controller can be extended with a simple sensory feedback such that the robot is able to control gait patterns autonomously for traversing a rough terrain. © 2010 Springer Science+Business Media, LLC.