Low-delay, high-rate, non-square STBCs from scaled complex orthogonal designs

Space-time block codes (STBCs) obtained from non-square complex orthogonal designs are bandwidth efficient compared to those from square real/complex orthogonal designs for colocated coherent MIMO systems and has other applications in (i) non-coherent MIMO systems with non-differential detection, (ii) Space-Time-Frequency codes for MIMO-OFDM systems and (iii) distributed space-time coding for relay channels. Liang (IEEE Trans. Inform. Theory, 2003) has constructed maximal rate non-square designs for any number of antennas, with rates given by [(a+1)/(2a)] when number of transmit antennas is 2a-1 or 2a. However, these designs have large delays. When large number of antennas are considered this rate is close to 1/2. Tarokh et al (IEEE Trans. Inform. Theory, 1999) have constructed rate 1/2 non-square CODs using the rate-1 real orthogonal designs for any number of antennas, where the decoding delay of these codes is less compared to the codes constructed by Liang for number of transmit antennas more than 5. In this paper, we construct a class of rate-1/2 codes for arbitrary number of antennas where the decoding delay is reduced by 50% when compared with the rate-1/2 codes given by Tarokh et al. It is also shown that even though scaling the variables helps to lower the delay it can not be used to increase the rate.

A homotopy approach for stabilizing single-input systems with control structure constraints

A linear state feedback gain vector used in the control of a single input dynamical system may be constrained because of the way feedback is realized. Some examples of feedback realizations which impose constraints on the gain vector are: static output feedback, constant gain feedback for several operating points of a system, and two-controller feedback. We consider a general class of problems of stabilization of single input dynamical systems with such structural constraints and give a numerical method to solve them. Each of these problems is cast into a problem of solving a system of equalities and inequalities. In this formulation, the coefficients of the quadratic and linear factors of the closed-loop characteristic polynomial are the variables. To solve the system of equalities and inequalities, a continuous realization of the gradient projection method and a barrier method are used under the homotopy framework. Our method is illustrated with an example for each class of control structure constraint.

Relationship Between The Impedance Matrix And The Transfer Matrix With Specific Reference To Symmetrical, Reciprocal And Conservative Systems

Impedance matrix and transfer matrix methods are often used in the analysis of linear dynamical systems. In this paper, general relationships between these matrices are derived. The properties of the impedance matrix and the transfer matrix of symmetrical systems, reciprocal systems and conservative systems are investigated. In the process, the following observations are made: (a) symmetrical systems are not a subset of reciprocal systems, as is often misunderstood; (b) the cascading of reciprocal systems again results in a reciprocal system, whereas cascading of symmetrical systems does not necessarily result in a symmetrical system; (c) the determinant of the transfer matrix, being ±1, is a property of both symmetrical systems and reciprocal systems, but this condition, however, is not sufficient to establish either the reciprocity or the symmetry of the system; (d) the impedance matrix of a conservative system is skew-Hermitian.

Multi-agent Search using Voronoi partitions

This paper addresses the problem of multiagent search in an unknown environment. The agents are autonomous in nature and are equipped with necessary sensors to carry out the search operation. The uncertainty, or lack of information about the search area is known a priori as a probability density function. The agents are deployed in an optimal way so as to maximize the one step uncertainty reduction. The agents continue to deploy themselves and reduce uncertainty till the uncertainty density is reduced over the search space below a minimum acceptable level. It has been shown, using LaSalle’s invariance principle, that a distributed control law which moves each of the agents towards the centroid of its Voronoi partition, modified by the sensor range leads to single step optimal deployment. This principle is now used to devise search trajectories for the agents. The simulations were carried out in 2D space with saturation on speeds of the agents. The results show that the control strategy per step indeed moves the agents to the respective centroid and the algorithm reduces the uncertainty distribution to the required level within a few steps.

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.

On the study of a third-order mechanical oscillator

In this paper, the study of a third-order mechanical oscillator is presented by demonstrating its equivalence to the well-known R.C. multivibrator with two additional reactive elements. The conditions for the oscillator's possession of periodic solutions are presented. It is also shown that under certain conditions, the study of the given third-order autonomous system can be reduced to the study of an equivalent second-order, non-autonomous system.

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.