Model-following Neuro-adaptive approach for robust control of high performance aircrafts

Based on dynamic inversion, a relatively straightforward approach is presented in this paper for nonlinear flight control design of high performance aircrafts, which does not require the normal and lateral acceleration commands to be first transferred to body rates before computing the required control inputs. This leads to substantial improvement of the tracking response. Promising results are obtained from six degree-offreedom simulation studies of F-16 aircraft, which are found to be superior as compared to an existing approach (which is also based on dynamic inversion). The new approach has two potential benefits, namely reduced oscillatory response (including elimination of non-minimum phase behavior) and reduced control magnitude. Next, a model-following neuron-adaptive design is augmented the nominal design in order to assure robust performance in the presence of parameter inaccuracies in the model. Note that in the approach the model update takes place adaptively online and hence it is philosophically similar to indirect adaptive control. However, unlike a typical indirect adaptive control approach, there is no need to update the individual parameters explicitly. Instead the inaccuracy in the system output dynamics is captured directly and then used in modifying the control. This leads to faster adaptation, which helps in stabilizing the unstable plant quicker. The robustness study from a large number of simulations shows that the adaptive design has good amount of robustness with respect to the expected parameter inaccuracies in the model.

Non-linear electrical response of chalcogenide glasses: Memory state phenomena

Investigations on the switching behaviour of arsenic-tellurium glasses with Ge or Al additives, yield interesting information about the dependence of switching on network rigidity, co-ordination of the constituents, glass transition & ambient temperature and glass forming ability.

Random vibration testing with controlled samples

This paper proposes a novel experimental test procedure to estimate the reliability of structural dynamical systems under excitations specified via random process models. The samples of random excitations to be used in the test are modified by the addition of an artificial control force. An unbiased estimator for the reliability is derived based on measured ensemble of responses under these modified inputs based on the tenets of Girsanov transformation. The control force is selected so as to reduce the sampling variance of the estimator. The study observes that an acceptable choice for the control force can be made solely based on experimental techniques and the estimator for the reliability can be deduced without taking recourse to mathematical model for the structure under study. This permits the proposed procedure to be applied in the experimental study of time-variant reliability of complex structural systems that are difficult to model mathematically. Illustrative example consists of a multi-axes shake table study on bending-torsion coupled, geometrically non-linear, five-storey frame under uni/bi-axial, non-stationary, random base excitation. Copyright (c) 2014 John Wiley & Sons, Ltd.

Bayesian parameter identification in dynamic state space models using modified measurement equations

When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. The present study proposes strategies based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples cover laboratory studies on a time variant dynamical system and a bending-torsion coupled, geometrically non-linear building frame under earthquake support motions. (C) 2015 Elsevier Ltd. All rights reserved.

Topology-based denoising of chaos

In this article, we propose a denoising algorithm to denoise a time series y(i) = x(i) + e(i), where {x(i)} is a time series obtained from a time- T map of a uniformly hyperbolic or Anosov flow, and {e(i)} a uniformly bounded sequence of independent and identically distributed (i.i.d.) random variables. Making use of observations up to time n, we create an estimate of x(i) for i<n. We show under typical limiting behaviours of the orbit and the recurrence properties of x(i), the estimation error converges to zero as n tends to infinity with probability 1.

A semi-analytical particle filter for identification of nonlinear oscillators

Particle filters find important applications in the problems of state and parameter estimations of dynamical systems of engineering interest. Since a typical filtering algorithm involves Monte Carlo simulations of the process equations, sample variance of the estimator is inversely proportional to the number of particles. The sample variance may be reduced if one uses a Rao-Blackwell marginalization of states and performs analytical computations as much as possible. In this work, we propose a semi-analytical particle filter, requiring no Rao-Blackwell marginalization, for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. Through local linearizations of the nonlinear drift fields in the process/observation equations via explicit Ito-Taylor expansions, the given nonlinear system is transformed into an ensemble of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. This information is further exploited within the particle filter algorithm for obtaining samples from the optimal posterior density of the states. The potential of the method in state/parameter estimations is demonstrated through numerical illustrations for a few nonlinear oscillators. The proposed filter is found to yield estimates with reduced sample variance and improved accuracy vis-a-vis results from a form of sequential importance sampling filter.

Design of a FIR filter for image restoration using principal component neural networks

The neural network finds its application in many image denoising applications because of its inherent characteristics such as nonlinear mapping and self-adaptiveness. The design of filters largely depends on the a-priori knowledge about the type of noise. Due to this, standard filters are application and image specific. Widely used filtering algorithms reduce noisy artifacts by smoothing. However, this operation normally results in smoothing of the edges as well. On the other hand, sharpening filters enhance the high frequency details making the image non-smooth. An integrated general approach to design a finite impulse response filter based on principal component neural network (PCNN) is proposed in this study for image filtering, optimized in the sense of visual inspection and error metric. This algorithm exploits the inter-pixel correlation by iteratively updating the filter coefficients using PCNN. This algorithm performs optimal smoothing of the noisy image by preserving high and low frequency features. Evaluation results show that the proposed filter is robust under various noise distributions. Further, the number of unknown parameters is very few and most of these parameters are adaptively obtained from the processed image.

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements m in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes' theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito-Taylor's discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplifiedmby considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations. (C) 2010 Elsevier Ltd. All rights reserved.

A Comparative Study of Liapunov Stability Analyses of Flexible Damped Satellites

A literal Liapunov stability analysis of a spacecraft with flexible appendages often requires a division of the associated dynamic potential into as many dependent parts as the number of appendages. First part of this paper exposes the stringency in the stability criteria introduced by such a division and shows it to be removable by a “reunion policy.” The policy enjoins the analyst to piece together the sets of criteria for each part. Employing reunion the paper then compares four methods of the Liapunov stability analysis of hybrid dynamical systems illustrated by an inertially coupled, damped, gravity stabilized, elastic spacecraft with four gravity booms having tip masses and a damper rod, all skewed to the orbital plane. The four methods are the method of test density function, assumed modes, and two and one-integral coordinates. Superiority of one-integral coordinate approach is established here. The design plots demonstrate how elastic effects delimit the satellite boom length.

Formation and propagation of bands in jerky flow:a coupled lattice map description

There has been revival of interest in Jerky flow from the point of view of dynamical systems. The earliest attempt in this direction was from our group. One of the predictions of the theory is that Jerky flow could be chaotic. This has been recently verified by us. We have recently extended the earlier model to account for the spatial aspect as well. Both these models are in the form of coupled set of nonlinear differential equations and hence, they are complicated in their structure. For this reason we wish to devise a model based on the results of these two theories in the form of coupled lattice map for the description of the formation and propagation of dislocation bands. We report here one such model and its results.

Topological phases, Majorana modes and quench dynamics in a spin ladder system

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z(2) symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce and employ a new topological invariant for explicitly determining the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder and, in particular, the post-quench dynamics governed by tuning through a quantum critical point.

Fault-Tolerant Average Execution Time Optimization for General Purpose Multi-Processor System-on Chips

Fault-tolerance is due to the semiconductor technology development important, not only for safety-critical systems but also for general-purpose (non-safety critical) systems. However, instead of guaranteeing that deadlines always are met, it is for general-purpose systems important to minimize the average execution time (AET) while ensuring fault-tolerance. For a given job and a soft (transient) error probability, we define mathematical formulas for AET that includes bus communication overhead for both voting (active replication) and rollback-recovery with checkpointing (RRC). And, for a given multi-processor system-on-chip (MPSoC), we define integer linear programming (ILP) models that minimize AET including bus communication overhead when: (1) selecting the number of checkpoints when using RRC, (2) finding the number of processors and job-to-processor assignment when using voting, and (3) defining fault-tolerance scheme (voting or RRC) per job and defining its usage for each job. Experiments demonstrate significant savings in AET.

Two-timescale Q-learning Algorithms with an Application to Routing in Networks

We propose two variants of the Q-learning algorithm that (both) use two timescales. One of these updates Q-values of all feasible state-action pairs at each instant while the other updates Q-values of states with actions chosen according to the ‘current ’ randomized policy updates. A sketch of convergence of the algorithms is shown. Finally, numerical experiments using the proposed algorithms for routing on different network topologies are presented and performance comparisons with the regular Q-learning algorithm are shown.

Bidding Dynamics of Rational Advertisers in Sponsored Search Auctions on the Web

In this paper, we address a key problem faced by advertisers in sponsored search auctions on the web: how much to bid, given the bids of the other advertisers, so as to maximize individual payoffs? Assuming the generalized second price auction as the auction mechanism, we formulate this problem in the framework of an infinite horizon alternative-move game of advertiser bidding behavior. For a sponsored search auction involving two advertisers, we characterize all the pure strategy and mixed strategy Nash equilibria. We also prove that the bid prices will lead to a Nash equilibrium, if the advertisers follow a myopic best response bidding strategy. Following this, we investigate the bidding behavior of the advertisers if they use Q-learning. We discover empirically an interesting trend that the Q-values converge even if both the advertisers learn simultaneously.

Incentive Compatible Mechanisms for Resource Procurement in Computational Grids with Rational resource Providers

In a computational grid, the presence of grid resource providers who are rational and intelligent could lead to an overall degradation in the efficiency of the grid. In this paper, we design incentive compatible grid resource procurement mechanisms which ensure that the efficiency of the grid is not affected by the rational behavior of resource providers.In particular, we offer three elegant incentive compatible mechanisms for this purpose: (1) G-DSIC (Grid-Dominant Strategy Incentive Compatible) mechanism (2) G-BIC (Grid-Bayesian Nash Incentive Compatible) mechanism (3) G-OPT(Grid-Optimal) mechanism which minimizes the cost to the grid user, satisfying at the same time, (a) Bayesian incentive compatibility and (b) individual rationality. We evaluate the relative merits and demerits of the above three mechanisms using game theoretical analysis and numerical experiments.