A novel robust disturbance rejection anti-windup framework

This is an Author's Original Manuscript of an article submitted for consideration in the International Journal of Control [copyright Taylor & Francis] and is available online at http://www.tandfonline.com/10.1080/00207179.2010.542774In this article, we propose a novel anti-windup (AW) framework for coping with input saturation in the disturbance rejection problem of stable plant systems. This framework is based on the one developed by Weston and Postlethwaite (W&P) (Weston, P.F., and Postlethwaite, I. (2000), ‘Linear Conditioning for Systems Containing Saturating Actuators’, Automatica, 36, 1347–1354). The new AW-design improves the disturbance rejection performance over the design framework usually suggested for the coprime-factorisation based W&P-approach. Performance improvement is achieved by explicitly incorporating a transfer function, which represents the effect of the disturbance on the nonlinear loop, into the AW compensator synthesis. An extra degree of freedom is exploited for the coprime factorisation, resulting in an implicitly computed multivariable algebraic loop for the AW-implementation. Suggestions are made to overcome the algebraic loop problem via explicit computation. Furthermore, paralleling the results of former work (Turner, M.C., Herrmann, G., and Postlethwaite, I. (2007), ‘Incorporating Robustness Requirements into Antiwindup Design’, IEEE Transactions on Automatic Control, 52, 1842–1855), the additive plant uncertainty is incorporated into the AW compensator synthesis, by using a novel augmentation for the disturbance rejection problem. In this new framework, it is shown that the internal model control (IMC) scheme is optimally robust, as was the case in Turner, Herrmann, and Postlethwaite (2007) and Zheng and Morari (Zheng, A., and Morari, M. (1994), ‘Anti-windup using Internal Model Control’, International Journal of Control, 60, 1015–1024). The new AW approach is applied to the control of dynamically substructured systems (DSS) subject to external excitation signals and actuator limits. The benefit of this approach is demonstrated in the simulations for a small-scale building mass damper DSS and a quasi-motorcycle DSS

Externally positive linear systems from transfer function properties

The characterisation of single-input-single-output externally positive linear systems is considered. A complete characterisation of the class of externally positive second-order and a class of underdamped third-order systems is given and connections to negative-imaginary systems are highlighted. It is shown that negative-imaginary systems have non-negative step responses, leading to a condition for external positivity based on negative imaginary systems theory. Finally, a class of externally positive systems which can be verified using the developed results but which fail a recently developed numerical test for external positivity based upon linear matrix inequalities are introduced. These results extend the class of system for which external positivity can be verified, facilitating large-scale control and less conservative absolute stability analysis

Reduced-order neural network synthesis with robustness guarantees

In the wake of the explosive growth in smartphones and cyber-physical systems, there has been an accelerating shift in how data are generated away from centralized data toward on-device-generated data. In response, machine learning algorithms are being adapted to run locally on board, potentially hardware-limited, devices to improve user privacy, reduce latency, and be more energy efficient. However, our understanding of how these device-orientated algorithms behave and should be trained is still fairly limited. To address this issue, a method to automatically synthesize reduced-order neural networks (having fewer neurons) approximating the input-output mapping of a larger one is introduced. The reduced-order neural network's weights and biases are generated from a convex semidefinite program that minimizes the worst case approximation error with respect to the larger network. Worst case bounds for this approximation error are obtained and the approach can be applied to a wide variety of neural networks architectures. What differentiates the proposed approach to existing methods for generating small neural networks, e.g., pruning, is the inclusion of the worst case approximation error directly within the training cost function, which should add robustness to out-of-sample data points. Numerical examples highlight the potential of the proposed approach. The overriding goal of this article is to generalize recent results in the robustness analysis of neural networks to a robust synthesis problem for their weights and biases

Exponential input-to-state stability for Lur’e systems via Integral Quadratic Constraints and Zames–Falb multipliers

Absolute stability criteria that are sufficient for global exponential stability are shown, under a Lipschitz assumption, to be sufficient for the a priori stronger exponential input-to-state stability property. Important corollaries of this result are as follows: (i) absolute stability results obtained using Zames–Falb multipliers for systems containing slope-restricted nonlinearities provide exponential input-to-state-stability under a mild detectability assumption; and (ii) more generally, many absolute stability results obtained via Integral Quadratic Constraint methods provide, with the additional Lipschitz assumption, this stronger property

Palatini approach to 1/R gravity and its implications to the late Universe

By applying the Palatini approach to the 1/R-gravity model it is possible to explain the present accelerated expansion of the Universe. Investigation of the late Universe limiting case shows that: (i) due to the curvature effects the energy-momentum tensor of the matter field is not covariantly conserved; (ii) however, it is possible to reinterpret the curvature corrections as sources of the gravitational field, by defining a modified energy-momentum tensor; (iii) with the adoption of this modified energy-momentum tensor the Einstein's field equations are recovered with two main modifications: the first one is the weakening of the gravitational effects of matter whereas the second is the emergence of an effective varying "cosmological constant"; (iv) there is a transition in the evolution of the cosmic scale factor from a power-law scaling $a\propto t^{11/18}$ to an asymptotically exponential scaling $a\propto \exp(t)$; (v) the energy density of the matter field scales as $\rho_m\propto (1/a)^{36/11}$; (vi) the present age of the Universe and the decelerated-accelerated transition redshift are smaller than the corresponding ones in the $\Lambda$CDM model.Comment: 5 pages and 2 figures. Accepted in PR

A model for interacting instabilities and texture dynamics of patterns

A simple model to study interacting instabilities and textures of resulting patterns for thermal convection is presented. The model consisting of twelve-mode dynamical system derived for periodic square lattice describes convective patterns in the form of stripes and patchwork quilt. The interaction between stationary zig-zag stripes and standing patchwork quilt pattern leads to spatiotemporal patterns of twisted patchwork quilt. Textures of these patterns, which depend strongly on Prandtl number, are investigated numerically using the model. The model also shows an interesting possibility of a multicritical point, where stability boundaries of four different structures meet.Comment: 4 pages including 4 figures, page width revise

Problems with Time-Varying Extra Dimensions or "Cardassian Expansion" as Alternatives to Dark Energy

It has recently been proposed that the Universe might be accelerating as a consequence of extra dimensions with time varying size. We show that although these scenarios can lead to acceleration, they run into serious difficulty when taking into account limits on the time variation of the four dimensional Newton's constant. On the other hand, models of ``Cardassian'' expansion based on extra dimensions which have been constructed so far violate the weak energy condition for the bulk stress energy, for parameters that give an accelerating universe.Comment: 8 pages, minor changes. To appear in Physical Review

Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator

We investigate the quasiparticle density of states in disordered d-wave superconductors. By constructing a quantum map describing the quasiparticle dynamics in such a medium, we explore deviations of the density of states from its universal form ($\propto E$), and show that additional low-energy quasiparticle states exist provided (i) the range of the impurity potential is much larger than the Fermi wavelength [allowing to use recently developed semiclassical methods]; (ii) classical trajectories exist along which the pair-potential changes sign; and (iii) the diffractive scattering length is longer than the superconducting coherence length. In the classically chaotic regime, universal random matrix theory behavior is restored by quantum dynamical diffraction which shifts the low energy states away from zero energy, and the quasiparticle density of states exhibits a linear pseudogap below an energy threshold $E^* \ll \Delta_0$.Comment: 4 pages, 3 figures, RevTe