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This paper deals with the design of a fractional-order chaotic secure communication scheme. On the emitter side, a fractional-order Chua’s system is used as the drive system to generate the encrypted message signal. The input secret message is modulated in the chaotic dynamics by inclusion rather than being directly added to the chaotic signal on the transmission line. A single channel is used for transmission of the encrypted signal. At the receiver side, a step-by-step sliding mode fractional-order chaotic observer subject to unknown input is proposed as the response system to obtain robust synchronization between the emitter and the receiver. After chaos synchronization is achieved at the receiver side, an estimation of the state variables is obtained and the plaintext is recovered. Finite-time convergence of both state and unknown input estimation errors is established. The efficiency of this proposed secure communication scheme is illustrated by numerical simulations.

In this paper, a fractional order control law is proposed and implemented for the evaluation of trajectory tracking performance of a rotary flexible-joint system. A state feedback based fractional integral control scheme is used in this proposed method. In this scheme, state feedback is responsible for stabilizing the system. The compensator, in series with the fractional integrator leads to obtain a similar closed-loop transient response like Bode’s ideal transfer function. The effectiveness of the proposed controller in tracking and being robust against parameter uncertainties is demonstrated through simulation. In addition, to show the usefulness of the proposed control scheme, the fractional controller is compared to an integer state feedback control by simulation and through experimentation on the Quanser’s rotary flexible-joint system.

In this study, a high gain observer with delayed driving control signal is designed for synchronisation of fractional-order chaotic systems. The method consists in using two cascade high gain observers in order to compensate for the delay transmission signal from the transmitter to the receiver. For large delay, a fractional-order chain observer composed by high gain cascade delayed observers is proposed. The last observer of this chain estimates the state at the current time while previous observers estimate delayed states. Convergence of the proposed observer is proven. Application to the synchronisation of fractional-order chaotic systems is given. Computer simulations show the effectiveness of the proposed approach.

It is generally known that model-based estimation algorithms (such as Kalman filter and its family) perform better than the non-model-based algorithms [such as least mean square (LMS), recursive least squares] due to extra information available in terms of system dynamics (which can be used to provide state space model of the system). However, the computational complexity of the model based algorithms is very high. On the other hand, the convergence performance of model based least mean type algorithms [such as state space least mean (SSLM) algorithms] is slower and highly dependent on the step-size choice. Thus, the larger step size can provide faster convergence but gives poor steady-state excess mean square error (EMSE). To meet this conflicting demand, we propose to employ the q-calculus to minimize the generalized least mean cost function. The main advantage of using the q-calculus is that it can provide a nonlinear correction term in the adaptation of the state estimate vector. Consequently, this results in an intelligent adaptation by providing both faster convergence in the initial phase of adaptation and a lower steady-state EMSE in the final phase. The developed algorithms are termed as q-state space least mean (q-SSLM) algorithms. The performance of the proposed q-state space least mean square (q-SSLMS) algorithm is also investigated both in terms of convergence in the mean and the mean square sense. The supremacy of the proposed algorithm is validated by performing several simulations and it is also contrasted with the performance of the well-known Kalman filter. Finally, the theoretical convergence analysis is also validated via simulations.

Objective: To provide coverage analysis of Multi-user Multi-antenna systems with spatial combining. Specifically, our objective is to analyze the coverage probability of uplink communication where a base station equipped with multiple antennas is communicating with many single antenna mobile stations via independent Rayleigh fading channels. Methods: We formulate the outage probability by utilizing the expression for the Signal-to-Interference-Noise-Ratio (SINR). The SINR expression is a function of channel vector, spatial combining vector, number of users and the noise power. Findings: The coverage probability is then obtained as the complementary of outage probability. Monte-Carlo simulations are presented by varying number of base station antenna size, the number of users and the noise power. This analysis provides a framework for system designers to set the system parameters in order to achieve the desired coverage performance. Results: The results show that the coverage probability decreases by increasing the number of users and the noise power. On the other hand, the coverage probability increases as the size of base station antenna increases.

This paper characterizes the performance metrics of MU-MIMO systems under Rayleigh fading channels in the presence of both cochannel interference and additive noise with unknown channel state information and known correlation matrices. In the first task, we derive analytical expressions for the cumulative distribution function of the instantaneous signal-to-interference-plus-noise ratio (SINR) for any deterministic beamvectors. As a second task, exact closed-form expressions are derived for the instantaneous capacity, the upper bound on ergodic capacity, and the Gram-Schmidt orthogonalization-based ergodic capacity for similar intra-cell correlation coefficients. Finally, we present the utility of several structured-diagonalization techniques, which can achieve the tractability for the approximate solution of ergodic capacity for both similar as well as different intra-cell correlation matrices. The novelty of this paper is to formulate the received SINR in terms of indefinite quadratic forms, which allows us to use complex residue theory to characterize the system behavior. The analytical expressions obtained closely match simulation results.

Herein, we propose a new class of stochastic gradient algorithm for channel identification. The proposed q-least mean fourth (q-LMF) is an extension of the least mean fourth (LMF) algorithm and it is based on the q-calculus which is also known as Jackson’s derivative. The proposed algorithm utilizes a novel concept of error correlation energy and normalization of signal to ensure a high convergence rate, better stability, and low steady-state error. Contrary to conventional LMF, the proposed method has more freedom for large step sizes. Extensive experiments show significant gain in the performance of the proposed q-LMF algorithm in comparison to the contemporary techniques.

Artificial neural networks have proven to be one of the most effective algorithms for learning and predicting information from data. Data come in many formats depending on the source and the nature of the phenomenon they pertain to. Numerous neural network models were proposed to handle the different data formats as efficiently as possible. One of the more abstract data format is graph structured data. We propose the Combined Graph Diffusion Embedding Network (CGDEN). The model combines two diffusion models to exploit the features of the graph nodes as well as the underlying structure of the graph. The model’s performance was test in a node classification problem in semi-supervised setting, where only a fraction on the node labels were available in the training phase. Two benchmarking citation network datasets (Cora and Citeseer) were used to validate the model. The accuracy of the proposed model in node classification exceeded that of the previous models.

Rotary double inverted pendulum is a highly nonlinear complex system and requires a high performance controller for its control. Using gain matrix which is obtained through state feedback technique may create complexity while removing the steady-state error for all states. Incorporating an integral action can be an alternative for these errors. Therefore, a state space–based fractional order controller with fractional integral action is designed and tested on a rotary double inverted pendulum in this article. The fractional integral controller is designed based on Bode’s ideal transfer function. Two degree of freedom is considered for tuning purpose as well. The integer order controller based on the state space approach is also shown for comparison. Simulation and experimental results are presented for both controllers of this rotary double inverted pendulum system.

This paper will illustrate the application of constraint based Robust Generalized Dynamic Inversion (RGDI) control for balancing the Rotary Inverted Pendulum system. The proposed control law is established by hybridizing the equivalent control (conventional GDI) and the robust control. The equivalent control is constructed by formulating the dynamical constraints, based on the attitude deviation functions of the rotary arm and the vertical pendulum. The constraint dynamics are then inverted using dynamically scaled Moore-Penrose Generalized Inverse to solve for the equivalent control. For the robust term, sliding mode control is utilized, that will provide robustness against parametric uncertainties, system nonlinearities, such that semi-global practically stable angular position tracking is guaranteed. The controller's capability is verified through computer simulation and experimental studies on the Quanser's SRV02 Rotary Inverted Pendulum system.

As one of the most promising topics in complex control processes, data-driven techniques have been widely used in numerous industrial sectors and have developed over the past two decades. In addition, the fractional-order controller has become more attractive in applied studies. In this article, a fractional integral control is implemented for a rotary flexible joint system. Moreover, an adjusted virtual reference feedback tuning (VRFT) technique is used to tune the fractional-order integrator. In this method, fractional integral control is designed based on state feedback control. Then, VRFT is adjusted and applied to the fractional integral controller. The effectiveness of the proposed adjusted VRFT method is discussed and presented through simulation and experimental results. The tracking performance of the rotary arm and the minimization of the vibration tip is evaluated based on the proposed method. In this article, the comparison of our proposed VRFT fractional scheme is made with the classical state feedback as well as a recently developed state feedback-based fractional order integral (SF-FOI) controller. The current investigations determine the performance improvement of our proposed scheme of comparable structure to the recent SF-FOI, with the introduction of the VRFT to the SF-FOI scheme.

In this paper, an original model-based analytical method is developed to design a fractional order controller combined with a Smith predictor and a modified Smith predictor that yield control systems which are robust to changes in the process parameters. This method can be applied for integer order systems and for fractional order ones. Based on the Bode's ideal transfer function, the fractional order controllers are designed via the internal model control principle. The simulation results demonstrate the successful performance of the proposed method for controlling integer as well as fractional order linear stable systems with long time delay.

In this paper, fractional-order controller designs for integer first-order plus time delay systems are investigated. Based on Bode’s ideal transfer function as a reference model, a new structure of the fractional-order controller is proposed. The internal model control principle is used to design the controllers. The effectiveness of the controllers is demonstrated through simulations and their efficiency is validated through experimentation on a heat flow platform.

Integration of low-cost Micro-Electro-Mechanical Systems (MEMS) in the design of Inertial Navigation Systems (INS) for real-time guidance, navigation, and control of flying vehicles often results in low precision, poor accuracy, and degraded performance. Most of existing filtering and data fusion methods that have been applied to the problem of attitude estimation with use of low-cost MEMS-based INS fail in cases that have highly nonlinear process dynamics, nonlinear measurement models, and long-range navigation. This paper presents two nonlinear filtering algorithms for low-cost Unmanned Aerial Vehicles (UAVs) attitude and measurement biases estimation. An Unscented Kalman Filter (UKF) and a Minimum Energy Kalman Filter (MEKF) are designed using two different attitude parameterizations i.e. Euler Angle (EA) and Unit Quaternion (UQ). The two filters AE-UKF and UQ-MEKF use highly nonlinear process and measurements estimators, zero-mean Gaussian noises, and first-order Gauss-Markov biases models. Field experiments, adding systems, and data fusion algorithms are used to achieve real-time tracking and estimation. The results show that both AE-UKF and UQ-MEKF demonstrate high accuracy estimation and robustness for UAVs attitude as well as MEMS biases filtering.

In this paper, a fixed-time terminal synergetic observer for synchronization of fractional-order nonlinear chaotic systems is proposed. First, fixed-time terminal attractors for fractional-order nonlinear systems are introduced on the basis of fixed-time stability of integer-order nonlinear differential equations and on defining particular fractional-order macro-variables. Second, a new synergetic observer dedicated to the synchronization of fractional-order chaotic systems is developed. The proposed observer converges in a predefined fixed-time uniformly bounded with respect to initial conditions. Thanks to the step-by-step procedure, only one communication channel is used to achieve the synchronization. Third, a fixed-time synergetic extended observer with unknown input is constructed to simultaneously estimate the state variables and to recover the unknown input. Finally, computer simulations are performed to illustrate the efficiency of the proposed synchronization method and its application in a secure communication scheme.

This paper presents the balance control design using Robust Generalized Dynamic Inversion (RGDI) for Rotary Double Inverted Pendulum (RDIP) system. The RGDI control comprised of the particular part and the robust control element. The particular part is responsible to enforce the constraint dynamics based on the attitude deviation functions, and is inverted using Moore-Penrose Generalized Inverse (MPGI) to obtain the control law. An additional robust term based on the concept of sliding mode is integrated to enhance the robust characteristics against system nonlinearities, uncertainties and disturbances. The singularity problem is addressed by incorporating a dynamic scale factor in the expression of MPGI. The proposed RGDI control will guarantee semi-global practically stable angular position tracking of the horizontal rotary arm and the stabilization of the two pendulums at the upright position. Numerical simulations are carried out on the RDIP simulator to analyze the controller performance.

Recently, CNNs have become very popular in the machine learning field, due to their high predictive power in classification problems that involve very high dimensional data with tens of hundreds of different classes. CNN is a natural extension to MLP with few modifications which resulted in a breakthrough. Mainly, the MLP algebraic dot product as a similarity function was replaced with 2-d convolution; in addition to a pooling layer which reduces parameter dimensions making the model equi-variant to translations, distortions, and transformations. The sparse connectivity nature of CNN is also a variation to the MLP. The two models were implemented on the EMNIST dataset which was used as 50% and 100% of its capacity. The models were trained with fixed and flexible number of epochs in two runs. Using 100% of EMNIST; for the fixed run CNN achieved test accuracy of 92% and MLP 31.43%, where in the flexible run the CNN achieved 92% and MLP 89.47%. Using 50% of EMNIST; for the fixed run CNN achieved test accuracy of 92.9% and MLP 33.75%, where in the flexible run of 92.9% and MLP 88.20%. The CNN demonstrated a good maintenance of high accuracy for image like inputs and also proved to be a better candidate for big data applications.

Currently the fractional order controller becomes much more popular in automation engineering due its flexible tuning technique of control parameters. Moreover, it may not be possible to remove the steady-state errors for every states by using traditional sate feedback integer control approach. Therefore, in this paper a state feedback based fractional order controller is designed for rotary flexible link system. In this scheme, Bode's ideal transfer function is considered as a bench mark to obtain similar transient response of closed-loop system. Based on these idea, trajectory tracking performance of a rotary flexible link is demonstrated through computer simulation program. Effectiveness and usefulness of the proposed fractional control scheme is shown as well.

In this paper, an impulsive observer for fractional-order linear continuous-time systems is proposed. The observer converges exactly in finite time and the time of convergence can be chosen a priori. Two cases are considered. In the first case, the system is not subject to any unknown input. In the second case, the presence of an unknown input that affects the system dynamics is studied. In both cases, the finite-time convergence is established. Numerical simulations performed with different fractional derivative order and different times of convergence are given to illustrate the efficiency of proposed observer.

The Least Mean Square (LMS) algorithm inherits slow convergence due to its dependency on the eigenvalue spread of the input correlation matrix. In this work, we resolve this problem by developing a novel variant of the LMS algorithms based on the q-derivative concept. The q-gradient is an extension of the classical gradient vector based on the concept of Jackson?s derivative. Here, we propose to minimize the LMS cost function by employing the concept of q-derivative instead of the convent ional derivative. Thanks to the fact that the q-derivative takes larger steps in the search direction as it evaluates the secant of the cost function rather than the tangent (as in the case of a conventional derivative), we show that the q-derivative gives faster convergence for q 1 when compared to the conventional derivative. Then, we present a thorough investigation of the convergence behavior of the proposed q-LMS algorithm and carry out different analyses to assess its performance. Consequently, new explicit closed-form expressions for the mean-square-error (MSE) behavior are derived. Simulation results are presented to corroborate our theoretical findings. HighlightsDevelopment of the q-gradient.Development of the q-LMS algorithm.Derivation of closed-form expressions for the mean-square-error for the proposed algorithm.Extensive simulation results are carried out to corroborate the theoretical findings.

State feedback technique through a gain matrix has been a well-known method for pole assignment of a linear system. The technique could encounter a difficulty in eliminating the steady-state errors in some states. Introducing an integral element can effectively eliminate these errors. State feedback with fractional integral control is proposed, in this work, for pole placement of a linear time invariant system. The proposed method yields simple gain formulae. The paper presents the derivation of the design formulae. The method is applied to stabilise an inherently unstable inverted pendulum-cart system. Simulation and experimental results show the effectiveness of the proposed method for set-point tracking, disturbance rejection and stabilising the inverted pendulum. Comparison with the results obtained from applying Achermann’s formula is also presented.

In this paper, we derive Outage Probability in closed form for a Multi-user Multi-polarized antenna in an uplink communication. The derived expression is generalized and valid for polarized antenna of any polarization order. This analytical expression is then validated through extensive simulations for different system parameters. Moreover, the analysis is used to investigate the effect of various system properties, such as Cross Polarization Discrimination (XPD) and noise variance. Finally, we compared the performance of Dual and Triple Polarized antennas in terms of Outage Probability, which provides us a good measure for the selection of these polarized antennas.

This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u(t)=K(p)x(t)+K(I)I(α)(x(t)). The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n-1 (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments.

In this work an optimum error nonlinearity is derived for the channel estimation in the existence of class-A impulsive noise. The main idea of the design is based on minimizing the steady-state error to reach the limit dictated by the Cramer-Rao Lower Bound (CRLB) of the implicit estimation process. By using the proposed method, optimum error nonlinearity is devised for long adaptive filters without employing any assumption on the distribution input regressor constituents and on the noise distribution, independence input regressor assumption and any kind of linearization. Moreover, to implement the proposed design, two different methods for estimating the variance of a priori estimation error are developed. Furthermore, an intelligent switching mechanism is also introduced to efficiently utilize the designed optimum error non-linearity for the impulsive noise. The theoretical results are testify through simulations, to show the superiority of the designed optimum error nonlinearity.

Agents in a multi-agent system need to localize themselves and know the positions of the other agents for navigation and good coordination. In the outdoor environment, GPS can solve this problem; however indoors and in the GPS-denied situations, alternate arrangements are necessary. Most of such methods use landmarks or vision-based solutions, and are quite complex and expensive. The objective of this research is to design a simple, yet effective, sensing system for approximate localization of all the agents (or at least those in close vicinity) in a multi-agent environment. The proposed technique uses optical transmitters and receivers available with each agent. An agent transmits a signal to prompt the other agents about the "region" in which it is present. All other agents detect this signal and mark the regions (boundaries) where this agent is detected. When all other agents have marked the boundaries for the transmitting agent, the information gathered is exchanged and intersection region is calculated. The final subset region gives the approximate location of the agent that had transmitted the signal. MATLAB® simulations show the effectiveness of the proposed localization approach. The proposed system is scalable and does not require landmarks; more precise localization is possible depending on the requirements.

The Normalized Least Mean Square (NLMS) algorithm belongs to gradient class of adaptive algorithm which provides the solution to the slow convergence of the Least Mean Square (LMS) algorithm. Motivated by the recently explored q-gradient in the field of adaptive filtering, we developed here a q-gradient based NLMS algorithm. More specifically, we replace the conventional gradient by the q-gradient to derive the NLMS weight update recursion. We also provide a detailed mean-square-error (MSE) analysis of the proposed algorithm for both the transient and the steady-state scenarios. Consequently, we derive the closed form expressions for the MSE learning curve and the steady-state excess MSE (EMSE). Simulation results are provided to show the superiority of the proposed algorithm over the conventional NLMS algorithm and to validate the theoretical analysis.

A Flight Control System (FCS) of an autonomous Unmanned Aerial Vehicle (UAV) is highly time sensitive as it is required to efficiently integrate various sub-systems running at different speeds. Moreover, functional accuracy has to be maintained while sharing the memory, computing and peripheral resources. A real-time implementation of a complete FCS in a tight closed loop on a TI® DSP microcontroller (Delfino® Dual-Core F28377D) without kernel support is described. The bare-metal embedded code developed for this application achieves the required timing constraints through efficient use of flexible memory organization, timer interrupts and CPU resource sharing. The developed system has been functionally verified to autonomously control the intended UAV in the desired manner through extensive real-time Hardware-In-Loop (HIL) simulations. The current archetype can run at 50 Hz with extensive data logging, communication, navigation and control algorithms engaging only one DSP core.

This work gives an insight into Beamforming scheme employed to Massive multi-user multiple-input multiple-output MU-MIMO Cellular System under stochastic geometry approach. A particular case envisioned for 5G; where a cellular network comprises of a number of antennas at Base Station that forms a beamforming projection on a single antenna user or Mobile Station. Under the auspices of stochastic geometry approach; a new theorem for outage probability under aggregate interference settings is derived that is generalized from recent works in beamforming and Massive MU-MIMO Heterogeneous Cellular Networks. Outage probability is characterized for three different reuse factors for the case of orthogonal pilots and results are verified by means of Monte Carlo simulations.

Vehicle navigation systems rely on the correct positioning information and GPS is the best solution. However, in situations of GPS outage, like in tunnels and dense woods, the vehicle can lose track quickly. Modern vehicle navigation systems are mostly based on the vehicle dynamics; proprietary algorithms keep navigating for quite some time. But these solutions are expensive and add much to a vehicle's cost. This paper proposes a Kalman filter based dead-reckoning algorithm that fuses GPS information with the orientation information from a cheap IMU/INS, and the vehicle's speed accessed from its ECU. This low-cost system uses GPS and IMU/INS in a loosely coupled manner along with vehicle's speed and keeps supplying a quite accurate position information with GPS outage for significantly long intervals. With proper tuning and initialization, the proposed scheme has a potential to keep working in a completely GPS-denied situation.

Robotic air vehicles are used increasingly in delivering goods especially for safety-of-life applications. This paper discusses a guidance module for trajectory generation of such vehicles. An offline algorithm is developed using a navigation model to produce the required trajectory in the form of time-tagged longitude, latitude and altitude. The process is an essential requirement when an operator has to program a robotic vehicle to travel on the desired course. This problem is addressed scarcely in the relevant literature. The waypoints are generated for all phases of flight and then modified to cater for the wind disturbance parameters obtained from current meteorological information. The waypoints are uploaded to the vehicle's flight control system memory and reside there for the vehicle to follow. This paper also renders the generated trajectory on Google Earth® using Matlab/Simulink® to test the closed-loop performance. Furthermore, a Dryden wind model is utilized to generate a modified trajectory for turbulent conditions. An operator can make adjustments in the required initial heading angle so the vehicle lands at its destination even in turbulent weather. An empirical formula is also proposed for this purpose. Further work includes design of a control system to follow the generated waypoints.

An analytical design for proportional integral derivative (PID) controller cascaded with a fractional-order filter is proposed for first-order unstable processes with time delay. The design algorithm is based on the internal model control (IMC) paradigm. A two degrees-of-freedom (2DOF) control structure is used to improve the performance of the closed-loop system. In the 2DOF control structure, an integer order controller is used to stabilize the inner-loop, and a fractional-order controller for the stabilized system is employed to improve the performance of the closed-loop system. The Walton–Marshall's method, which is applicable to quasi-polynomials, is then used to establish the internal stability condition of the closed-loop system (the fractional part of the controller in particular) and to seek the set of stabilizing proportional (P) or proportional-derivative (PD) controller parameters.

Analytical methods are usually applied for tuning fractional controllers. The present paper proposes an empirical method for tuning a new type of fractional controller known as PID-Fractional-Order-Filter (FOF-PID). Indeed, the setpoint overshoot method, initially introduced by Shamsuzzoha and Skogestad, has been adapted for tuning FOF-PID controller. Based on simulations for a range of first order with time delay processes, correlations have been derived to obtain PID-FOF controller parameters similar to those obtained by the Internal Model Control (IMC) tuning rule. The setpoint overshoot method requires only one closed-loop step response experiment using a proportional controller (P-controller). To highlight the potential of this method, simulation results have been compared with those obtained with the IMC method as well as other pertinent techniques. Various case studies have also been considered. The comparison has revealed that the proposed tuning method performs as good as the IMC. Moreover, it might offer a number of advantages over the IMC tuning rule. For instance, the parameters of the fractional controller are directly obtained from the setpoint closed-loop response data without the need of any model of the plant to be controlled.

Adaptive filters generally employed for estimation purposes require high computational power when it comes to real time estimation. Therefore, in this paper we propose a computationally light yet effective estimation algorithm based on state space model. Our algorithm has been employed successfully in linear and non linear state space model based estimation problems.We investigate few examples to demonstrate the novelty of our algorithm by comparison with few existing algorithms in presence of non Gaussian noise namely uniform noise. More specifically, the state space normalized least mean squares and the Kalman filter has been compared with our algorithm.

Kalman filter and its variants are well known for the static and dynamic state estimation of power systems because of their accuracies. These adaptive filters generally employed for estimation purposes require high computational power when it comes to real time estimation. Therefore, in this paper we propose a computationally light yet effective estimation algorithm based on state space model which have not yet been applied to the problem of power system estimation. We propose the use of state space least mean square algorithms for the purpose of state estimation considering the problem of a two phase permanent magnet synchronous motor. The algorithms have been employed successfully in this paper in the state estimation of the highly non linear synchronous motor. We investigate the problem in the presence of Gaussian noise to show the novelty of the algorithms. Moreover, these algorithms are compared with the state estimation performance of the non linear Extended Kalman filter.

In this work, we propose a novel LMS type algorithm by utilizing the q-gradient. The concept of q-gradient is derived from the definition of Jacksons derivative which is also called as the q-derivative. The q-gradient based LMS algorithm results in faster convergence for q > 1 because of the fact that the q-derivative, unlike the conventional derivative which evaluates tangent, computes the secant of the cost function and hence takes larger steps towards the optimum solution. We show an important application of the proposed q-LMS algorithm in which it acts like a whitening filter. Convergence analysis of the proposed algorithm is also presented. Simulation results are presented to support our theoretical findings.

The computation of balanced-truncation reduced-order models of large-scale systems is impractical. However, for such complex systems there is typically a weak coupling between the subsystems. This is used here to derive approximate balanced-truncation reduced-order model of large-scale discrete-time systems with reliable and tractable computations. The condition for validity of the approximations and bounds on the norms of the approximation errors are also derived. These results are an extension, to the discrete-time case, of analogous results for continuous-time large-scale systems.

A new method for the approximation of bilinear systems is proposed. The reduction scheme applies to both stable and unstable bilinear systems. The technique uses generalized input normal representations to retain the dominant part of the original system. The algorithm is evaluated on a synchronous induction generator and is shown to lead to acceptable reduced approximations of the original system. A frequency weighting is also introduced in the reduction scheme to further improve the approximation.

A new technique for constructing the dynamic equivalents for power systems is developed. The technique utilizes a balanced state-space representation to determine the order, state matrix, and either the input matrix or the output matrix of the reduced-order model. The other matrix is found such that the reduced-order model matches the full-order model at both high and low frequencies. The suitability of the new technique for obtaining reduced-order models for the dynamic control of a power plant is demonstrated on a single-machine infinite-bus system.

Four relatively recent techniques for model reduction (balanced, weighted balanced, optimal Hankel and weighted optimal Hankel) are reviewed. The usefulness of these techniques for obtaining reduced-order models of power systems for dynamic control purposes, their effectiveness, and the merits of the simplified models are illustrated on a single-machine infinite-bus system. The methods are evaluated on the basis of Lα errors, transient responses, and steady-state errors. The superiority of the frequency-weighting methods is clearly demonstrated.

The complexity of a large scale system makes the computations of reduced order models based on balancing impractical. However, typically there is a weak coupling between the subsystems of a large scale system. This is used here to derive approximate balanced-truncation reduced order models for large scale systems with reliable and tractable computations.

The design of a robust digital multivariable feedback control system for the F-100 turbofan jet engine is considered. The control system design problem is posed, and conditions for satisfying performance specifications and stability robustness are stated. The discrete LQG/LTR methodology is used to design a compensator that meets the stated specifications. New results for multi-input LQR loop shaping are derived. To get a reasonably low-order compensator, frequency-weighted reduced-order models are exploited, with the reduction error treated as an uncertainty.

The relationship between subsystem interconnection of discrete balanced systems and the Hankel singular values is explored. Upper bounds on the spectral norm of the submatrices of the discrete balanced representation are derived by approximating the matrix Riccati equation by its power series expansion with respect to two scalar parameters related to the Hankel singular values. For diagonalizable symmetric discrete-time systems, the relation between the eigenvalues of the subsystems and the eigenvalues of the overall system is explored. It is shown that an upper bound on the distance between corresponding eigenvalues in these two sets is related to the ratio of the Hankel singular values. >

Robust discrete control system design techniques and model reduction are discussed. A new linear quadratic guussian/loop transfer recovery procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has the desired loop shape, and then recovered by a realizable linear quadratic gaussian controller. To do this, results that show the effects of the weighting matrices (noise intensities) on linear quadratic regulator (Kalman-Bucy filter) return difference and inverse-return difference arc derived and a procedure to recover the linear quadratic regulator loop transfer function is described. The complexity of the resulting controller is then reduced without causing closed-loop instability. Two methods for model reduction are considered. The first is the discrete balanced realization and the second is P frequency weighting technique where it is possible to vary the approximation accuracy with frequency. The controller design and re...

A new method for approximating scalar discrete linear systems is described. The method can be classified as a time domain/frequency domain technique. Two reduced order models are obtained. One is obtained when the time domain specifications are in terms of the impulse response of the error. The other is derived when the time domain specifications are in terms of the step response of the error. The technique utilizes the input normal system representation to determine the order and the denominator polynomial of the reduced order model.

Advanced controller synthesis techniques often result in high order controllers whose order exceeds the order of the plant and it is impractical to implement. The main use of the advanced synthesis techniques is to find the possible optimal performance of the system and thus to check how a practical simpler controller comes close to achieving that optimum. PID controllers are the most found in industry and here we describe a novel technique, based on approximation, to tune the parameters of PID controllers.

In [1], an algorithm is given for the design of digital controllers. The controller parameters were obtained by minimizing an objective function in terms of the controller parameters and a non-linear optimization technique was employed. Here we point out that the proposed objective function is linear in the controller parameters and the minimization problem is a standard linear least squares problem.