A global convergence criterion for discrete-time multivariable adaptive systems

The paper deals with the basic problem of adjusting a matrix gain in a discrete-time linear multivariable system. The object is to obtain a global convergence criterion, i.e. conditions under which a specified error signal asymptotically approaches zero and other signals in the system remain bounded for arbitrary initial conditions and for any bounded input to the system. It is shown that for a class of up-dating algorithms for the adjustable gain matrix, global convergence is crucially dependent on a transfer matrix G(z) which has a simple block diagram interpretation. When w(z)G(z) is strictly discrete positive real for a scalar w(z) such that w-1(z) is strictly proper with poles and zeros within the unit circle, an augmented error scheme is suggested and is proved to result in global convergence. The solution avoids feeding back a quadratic term as recommended in other schemes for single-input single-output systems.

A Pulsewidth Modulated Control of Induction Motor Drive Using Multilevel 12-Sided Polygonal Voltage Space Vectors

In this paper, a novel 12-sided polygonal space vector structure is proposed for an induction motor drive. The space vector pattern presented in this paper consists of two 12-sided concentric polygons with the outer polygon having a radius double the inner one. As compared to previously reported 12-sided polygonal space vector structures, this paper subdivides the space vector plane into smaller sized triangles. This helps in reducing the switching frequency of the inverters without deteriorating the output voltage quality. It also reduces the device ratings and dv/dt stress on the devices to half. At the same time, other benefits obtained from the existing 12-sided space vector structure, such as increased linear modulation range and complete elimination of 5th and 7th order harmonics in the phase voltage, are also retained in this paper. The space vector structure is realized by feeding an open-end induction motor with two conventional three-level neutral point clamped (NPC) inverters with asymmetric isolated dc link voltage sources. The neutral point voltage fluctuations in the three-level NPC inverters are eliminated by utilizing the switching state multiplicities for a space vector point. The pulsewidth modulation timings are calculated using sampled reference waveform amplitudes and are explained in detail in this paper. Experimental verification on a laboratory prototype shows that this configuration may be considered suitable for high power drives.

Observers for linear systems with unknown inputs

This paper presents a constructive solution to the problem of designing a reduced-order Luenberger observer for linear systems subject to arbitrary unknown inputs.

Identification of a class of non-linear systems

This paper considers the on-line identification of a non-linear system in terms of a Hammerstein model, with a zero-memory non-linear gain followed by a linear system. The linear part is represented by a Laguerre expansion of its impulse response and the non-linear part by a polynomial. The identification procedure involves determination of the coefficients of the Laguerre expansion of correlation functions and an iterative adjustment of the parameters of the non-linear gain by gradient methods. The method is applicable to situations involving a wide class of input signals. Even in the presence of additive correlated noise, satisfactory performance is achieved with the variance of the error converging to a value close to the variance of the noise. Digital computer simulation establishes the practicability of the scheme in different situations.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

Stabilization of linear and nonlinear dynamical systems using an observer-controller configuration

In this paper the problem of stabilization of systems by means of stable compensations is considered, and results are derived for systems using observer�controller structures, for systems using a cascade structure, and for nonlinear systems

Constrained linear minimax filter for systems with large plant uncertainties

This paper presents a method of designing a minimax filter in the presence of large plant uncertainties and constraints on the mean squared values of the estimates. The minimax filtering problem is reformulated in the framework of a deterministic optimal control problem and the method of solution employed, invokes the matrix Minimum Principle. The constrained linear filter and its relation to singular control problems has been illustrated. For the class of problems considered here it is shown that the filter can he constrained separately after carrying out the mini maximization. Numorieal examples are presented to illustrate the results.

An approach for sensitivity-reduced design of linear regulators

A now procedure for the design of sensitivity-reduced control for linear regulators is described. The control is easily computable and implementable since it requires neither the solution of an increased-order augmented system nor the generation and feedback of a trajectory sensitivity vector. The method provides a trade-off between reduction in sensitivity measure and increase in performance index.

Positional Consensus in Multi-Agent Systems using a Broadcast Control Mechanism

In this paper a strategy for controlling a group of agents to achieve positional consensus is presented. The proposed technique is based on the constraint that every agents must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming formulation that is computationally less intensive than earlier proposed methods. Moreover, we introduce a random perturbation input in the control command that helps us to achieve perfect consensus even for a large number of agents, which was not possible with the existing strategy in the literature. Moreover, we extend the method to achieve positional consensus at a pre-specified location. The effectiveness of the approach is illustrated through simulation results.

Trajectory sensitivity modification in optimal linear systems

A new procedure for reducing trajectory sensitivity for the optimal linear regulator is described. The design is achieved without increase in the order of optimization and without the feedback of trajectory sensitivity. The procedure is also used in the input signal design problem for linear system identification by interpreting it as increasing trajectory sensitivity with respect to parameters to be estimated.

Application of optimization methods to vibration control of stretched strings

In this paper, non-linear programming techniques are applied to the problem of controlling the vibration pattern of a stretched string. First, the problem of finding the magnitudes of two control forces applied at two points l1 and l2 on the string to reduce the energy of vibration over the interval (l1, l2) relative to the energy outside the interval (l1, l2) is considered. For this problem the relative merits of various methods of non-linear programming are compared. The more complicated problem of finding the positions and magnitudes of two control forces to obtain the desired energy pattern is then solved by using the slack unconstrained minimization technique with the Fletcher-Powell search. In the discussion of the results it is shown that the position of the control force is very important in controlling the energy pattern of the string.

Formation of linear plasmid multimers promoted by the phage lambda Red-system in lon mutants of Escherichia coli

We report here the formation of plasmid linear multimers promoted by the Red-system of phage lambda using a multicopy plasmid comprised of lambda red alpha and red beta genes, under the control of the lambda cI857 repressor. Our observations have revealed that the multimerization of plasmid DNA is dependent on the red beta and recA genes, suggesting a concerted role for these functions in the formation of plasmid multimers. The formation of multimers occurred in a recBCD+ sbcB+ xthA+ lon genetic background at a higher frequency than in the isogenic lon+ host cells. The multimers comprised tandem repeats of monomer plasmid DNA. Treatment of purified plasmid DNA with exonuclease III revealed the presence of free double-chain ends in the molecules. Determination of the size of multimeric DNA, by pulse field gel electrophoresis, revealed that the bulk of the DNA was in the range 50-240 kb, representing approximately 5-24 unit lengths of monomeric plasmid DNA. We provide a conceptual framework for Red-system-promoted formation and enhanced accumulation of plasmid linear multimers in lon mutants of E. coli.

On the PAPR of cosets of linear codes

Employing an error control code is one of the techniques to reduce the Peak-to-Average Power Ratio (PAPR) in a Orthogonal Frequency Division Multiplexing system, a well known class of such codes being the cosets of Reed-Muller codes. In this paper, we consider the class of such coset-codes of arbitrary linear codes and present a method of doubling the size of such a code without increasing the PAPR, by combining two such binary coset-codes. We identify the conditions under which we can employ this doubling more than once with no marginal increase in the PAPR value. Given a PAPR and length, our method has enabled to get the best coset-code (in terms of the size). Also, we show that the PAPR information of the coset-codes of the extended codes is obtainable from the PAPR of the corresponding coset-codes of the parent code. We have also shown a special type of lengthening is useful in PAPR studies.

Optimal resource allocation in conflicts with the Lanchester linear law (2,1) model

This paper presents a detailed analysis of a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts in an area fire situation. Lanchester linear law attrition model is used to develop the dynamical equations governing the variation in force strength. Here we address a static resource allocation problem namely, Time-Zero-Allocation (TZA) where the resource allocation is done only at the initial time. Numerical examples are given to support the analytical results.