Modified Cost Function Research Articles

Sparsity aware affine-projection-like filtering integrated with robust set membership and M-estimate approach for acoustic feedback cancellation in hearing aids

This paper introduces a new adaptive feedback cancellation technique for hearing aid employing robust upper error bound of set membership filtering in the M-estimate function and applied for affine-projection-like algorithm. Additionally a l1 norm based sparsity term is appended in the cost function which takes care of the convergence while estimating feedback path of the hearing aid exhibiting sparse characteristics. The proposed method of sparsity aware affine-projection-like robust set membership M-estimate (SAPL-RSM) filtering has been utilized for alleviating the impact of impulsive noise on the adaptation of feedback canceler’s weights. The SAPL-RSM technique is derived by minimizing a modified cost function involving M-estimate function constrained by a robust error bound and sparsity dependent penalty term with the motive of enhancing the convergence and lowering the computational expenses involved in the weight update process. The validation of the proposed method is carried out in the context of adaptive feedback cancellation in hearing aids. Simulations assess the efficacy of the proposed technique as an adaptive feedback canceler in terms of misalignment, added stable gain and sound quality deliverable at the user end.

Block-sparsity regularized maximum correntropy criterion for structured-sparse system identification

This work deals with the block-sparse system identification problem on the basis of the maximum correntropy criterion (MCC). The MCC is known for its robustness against non-Gaussian noise and interference in many signal processing applications. With the aim of exploiting the block-sparse property of the system, we introduce a regularization function into the standard cost function of MCC. Based on the modified cost function, an online kernel adapting strategy is developed to further improve the estimation accuracy. Steady-state performance analysis is conducted to explore the behavior of the proposed method. The simulation results illuminate the validity of the theoretical analysis and confirm the superiority of the proposed method in block-sparse system identification through comparisons with state-of-the-art MCC techniques.

A constraint-separation principle in model predictive control

In this brief, we consider the constrained optimization problem underpinning model predictive control (MPC). We show that this problem can be decomposed into an unconstrained optimization problem with the same cost function as the original problem and a constrained optimization problem with a modified cost function and dynamics that have been precompensated according to the solution of the unconstrained problem. In the case of linear systems subject to a quadratic cost, the unconstrained problem has the familiar LQR solution and the constrained problem reduces to a minimum-norm projection. This implies that solving linear MPC problems is equivalent to precompensating a system using LQR and applying MPC to penalize only the control input. We propose to call this a constraint-separation principle and discuss the utility of both constraint separation and general decomposition in the design of MPC schemes and the development of numerical solvers for MPC problems.

Model Predictive Two-Target Current Control for OW-PMSM

Open-winding permanent magnet synchronous machine (OW-PMSM) could obtain the higher bus voltage utilization and more robustness against the component damage and faults. However, the additional torque ripples and total harmonic distortion (THD) caused by zero-sequence current would limit the further applications of OW-PMSM. In this article, a novel model predictive two-target current control (MPTCC) scheme is presented to deal with such problem through model predictive control concept. First, a basic model predictive current control is proposed to deal with the torque production in fundamental components. Then, another modified cost function is proposed to provide more precise voltage vectors in torque production. After that, the deadbeat predictive control concept is proposed to calculate the required voltage vectors in zero-sequence loop. This zero-sequence voltage is injected in the voltage vectors, which are responsible for torque production. It needs to be mentioned that the limitation of inverter is analyzed. And the real-time judgment is proposed to assess the performance of MPTCC in some work conditions. Finally, both simulation and experiments have been both applied to assess the performances of the proposed control scheme. Comparing with those existing q-axis current injection methods and modified space vector pulse width modulation (SVPWM) technologies, the proposed control scheme could eliminate the torque ripple and THD at the same time and thus possess the better performances.

Adaptive Dynamic Programming-Based Decentralized Guaranteed Cost Control for Reconfigurable Manipulators with Uncertain Environments

In this paper, a novel decentralized guaranteed cost control method is designed for reconfigurable manipulators with uncertain environments based on the adaptive dynamic programming (ADP) approach. Each joint module, which is the basic unit for constructing the reconfigurable manipulators, is regarded as a subsystem with model uncertainties that include the error of frictional modeling and the interconnection dynamic coupling (IDC) effect. Then, by employing a robust controller and a neural network (NN) identifier-based compensation controller, the decentralized guaranteed cost control issue with uncertain environments can be changed into the optimal control issue of reconfigurable manipulators. Based on ADP algorithm, the critic neural network is introduced to approximate the modified cost function, and then the Hamilton–Jacobi–Bellman equation is addressed by the policy iterative algorithm, thus making the obtention of approximate optimal control policy doable. The stability of the robotic system under the proposed control policy is demonstrated by employing the Lyapunov theory. Finally, the effectiveness of the proposed control policy for reconfigurable manipulators with different configurations is verified by simulation experiments.

Output Feedback Control for Irregular LQ Problem

In this letter, we study the irregular output feedback linear quadratic (LQ) control problem where the state is measured through a linear system with noise. It is interesting to show that the irregular output feedback control with the standard average LQ cost is unsolvable even if the state feedback LQ control is solvable, which is completely different from the classical regular output feedback LQ control. In order to guarantee the solvability of the irregular output feedback control, the LQ cost is modified at the terminal time with the expectation of terminal state in this letter. In the framework of the modified cost function, it is shown that the separation principle holds and the explicitly optimal controller is given in the feedback form of the Kalman filtering. In particular, the feedback gain is calculated by two Riccati equations, independently of the Kalman filtering. The key technique is the analytical solution of the forward and backward differential equations (FBDEs). We also emphasize that the optimal controller at the terminal time is required to be deterministic.

Blind Adaptive Low-Complexity Time-Domain Equalizer for 100-Gb/s Direct-Detection Optical OFDM Systems Over Long-Reach SSMF

In this article, we report a low-complexity blind adaptive time-domain equalizer (TEQ) to reduce the cyclic prefix (CP) length for 100-Gb/s direct-detection optical orthogonal frequency-division multiplexing (OFDM) system combined with wavelength-division multiplexing system over 400-km standard single-mode fiber length. We show that a significant complexity reduction can be achieved by designing a modified cost function of multicarrier equalization based on orthogonality restoration (MERO) algorithm on one hand, and on deploying the symmetrical TEQ property on the other hand. Our article shows that the reduction of the system adaptation complexity can be realized up to 50% when designing and optimizing the stated system parameters. Our low-complexity MERO simulation model exhibits better performance, for a shorter CP length equal to $0.39$ % of the OFDM symbol duration, than the existing conventional algorithms in term of bit error rate versus optical signal-to-noise ratio with a much lower complexity.

Lyapunov-based finite control-set model predictive control for nested neutral point-clamped converters without weighting factors

This paper presents a novel finite control-set model predictive control (FCS-MPC) strategy for solving the well-known challenges in predictive control regulated NNPCs, which aims to avoid the tedious online adjustment of weighting factors and to achieve the flexible power regulation. Firstly, a modified cost function, which is inspired by Lyapunov control theory, is formulated from system stability point of view. As such, the designed Lyapunov-based cost function has a good potential to avoid the selection of weighting factors for the conventional FCS-MPC scheme, especially in the presence of multiple control objectives. Next, in order to achieve satisfactory regulation performance, a dynamic reference design technique is introduced as an alternative solution to serve this purpose. Worth to note that the computational complexity will be increased while applying the proposed design methodology to the control of NNPCs. In this sense, a computationally efficient FCS-MPC strategy based on Lyapunov theory is presented here. Therefore, the overall computational burden is significantly decreased while maintaining fast transient performance and flying capacitor voltages balancing. Finally, compared with the state-of-the-art FCS-MPC strategies, the effectiveness and feasibility of the proposed methodology for NNPCs are confirmed through comprehensive simulation and experimental results.

Recursive-Biased-Generalized-Inverse Method for Thrust Allocation for Dynamic Positioning Vessels with Non-Rotatable Thrusters and Force Constraints

This paper presents a novel method for thrust allocation for DP vessels with non-rotatable thrusters and force constraints. It uses a modified cost function of the thrust allocation problem for non-rotatable thruster and without force constraints, such that the force constraint can be handled. The proposed method runs in a recursive way to minimize the allocation error. The proposed method is different from the known methods in the literature. The completeness and continuity of the proposed algorithm are studied to verify the effectiveness of the proposed method.

In-Motion Alignment for Doppler Velocity Log-Aided SINS Based on Initial Velocity Error Estimation

Inertial frame alignment (IFA) for strapdown inertial navigation systems is widely considered to be a promising method due to its robustness to disturbances and noise. By using the velocity data from a Doppler velocity log (DVL), the IFA can be performed while the vehicle is in motion. However, this article reveals that the initial velocity error of the DVL at the startup continuously and considerably affects the precision of the in-motion IFA. Based on the formula derived with other sensor errors isolated, the azimuth error is proportional to the initial velocity error and is inversely proportional to the square of time, e.g., a 0.3 m/s measurement error in the initial velocity from the Doppler velocity log leading to a considerable azimuth error of more than 1.78° in five minutes. Moreover, the azimuth error becomes bulky if the latitude is high. The modified cost function with a constant vector is used to replace the cost function from the well-known Wahba’s problem. Thus, an alignment result with a much higher precision and with the initial velocity error suppressed can be obtained in a short period of time. The vehicular experimental results further verify the error analysis and the improved method.

The Global Geometry of Centralized and Distributed Low-rank Matrix Recovery Without Regularization

Low-rank matrix recovery is a fundamental problem in signal processing and machine learning. A recent very popular approach to recovering a low-rank matrix X is to factorize it as a product of two smaller matrices, i.e., X = UV^T, and then optimize over U, V instead of X. Despite the resulting non-convexity, recent results have shown that many factorized objective functions actually have benign global geometry---with no spurious local minima and satisfying the so-called strict saddle property---ensuring convergence to a global minimum for many local-search algorithms. Such results hold whenever the original objective function is restricted strongly convex and smooth. However, most of these results actually consider a modified cost function that includes a balancing regularizer. While useful for deriving theory, this balancing regularizer does not appear to be necessary in practice. In this work, we close this theory-practice gap by proving that the unaltered factorized non-convex problem, without the balancing regularizer, also has similar benign global geometry. Moreover, we also extend our theoretical results to the field of distributed optimization.

Minimum BER Criterion and Adaptive Moment Estimation Based Enhanced ICA for Wireless Communications

This paper concentrates on investigating an enhanced independent component analysis (ICA) method for blind separation of signals corrupted by noise in wireless communications. Because of the traditional classical ICA methods that always have an inadequate capacity of anti-noise or insufficient separable ability in noise circumstance without satisfying practical application requirements. For this reason, two mechanisms are conducted to establish the modified cost function and fulfill the optimization assignment in the process of constituting an enhanced ICA algorithm. This proposed algorithm can benefit tremendously from the derived minimum bit error rate (BER) criterion and the novel adaptive moment estimation (Adam) optimization approach. In this work, firstly, the novel cost function is obtained according to minimum BER fused into maximum likelihood (ML) principle-based ICA cost function. Furthermore, by utilizing Adam processing, the task of blind separation of mixed signals is implemented via optimizing this modified cost function. Lastly, theoretical analysis and experiment results corroborate the better effectiveness and robustness of the proposed enhanced ICA algorithm compared with a series of popular representative ICA methods.

Consensus Algorithm-Based Distributed Operation of Microgrids During Grid-Connected and Islanded Modes

The existing distributed operation schemes for microgrids lack the ability to determine the power selling to the grid during normal operation mode and are unable to provide service reliability to critical loads, during islanded operation mode. In order to overcome these issues, in this study, we have proposed a distributed operation method for both grid-connected and islanded modes of microgrids. Unlike the existing studies, where the utility grid is considered as a dispatchable generator, the bi-directional flow of power with the grid is considered in this study. Similarly, different load agents are considered for different priority loads to assure the service reliability to the critical loads during islanding. A two-step operation method is proposed for both grid-connected and islanded mode operations. During the first step, each agent in the network shares information with its neighboring agents to determine the total load and available renewable power in the network. Whereas, in the second step, each agent in the network determines the optimal operation points based on the local information received from the neighboring agents. Moreover, a modified cost function for the battery is also proposed in this study, which utilizes the information of market price and load to enhance the battery operation. A comparison is made between the centralized method, conventional distributed method, and the proposed distributed operation method. Simulation results have proved the effectiveness of the proposed method for realizing distributed operation for microgrids in both grid-connected and islanded modes.

Iterative Feedback Tuning of Cascade Control for Position and Velocity of Two-Mass System

The inaccuracy of position and velocity controllers due to the vibration in the two-mass system in industrial robots cause devastating problems in both safety and productivity. To solve this problem, a method for tuning a cascade controller applied to two-mass systems based on Iterative Feedback Tuning (IFT) is proposed. The proposed new iterative feedback tuning method utilized a modified cost function to optimize the gains in a cascade control system and to address the complexity of the two-mass system due to higher-order dynamics. The performance of the proposed iterative feedback tuning method is verified through several simulations.

Adaptive Fourier linear combiner based on modified least mean Kurtosis algorithm for the processing of sinusoidal signals

This study introduces an adaptive Fourier linear combiner (FLC) based on a modified least mean kurtosis (LMK) algorithm in order to effectively process sinusoidal signals, which we call FLC-LMK algorithm. In the design procedure of the proposed FLC-LMK algorithm, the classical kurtosis-based cost function is first modified for only sinusoidal signal distributions instead of Gaussian. Then, the FLC-LMK algorithm is derived from the minimization of this cost function and thus updates the weight coefficients of the FLC structure so as to directly process sinusoidal signals. Moreover, in this study, the convergence in the mean of the proposed FLC-LMK algorithm is analysed in order to determine the lower and upper bounds of its step size parameter. The most important contributions of the use of the proposed algorithm in the FLC structure are that it increases the convergence rate, decreases the steady-state error level and also has a robust behaviour against sinusoidal signal distributions due to its modified cost function. The performance of the proposed FLC-LMK algorithm is evaluated on the synthetic and real-world pathological hand tremor data by comparing with that of the FLC based on the classical least mean square (LMS) (FLC-LMS) algorithm. The simulation results support the mentioned properties of the proposed FLC-LMK algorithm.

Predictive Torque Control Algorithm for a Five-Phase Induction Motor Drive for Reduced Torque Ripple With Switching Frequency Control

This article presents a progressive comparison of predictive torque control (PTC) algorithms for a five-phase induction motor fed with a two-level five-phase inverter. The extension of three-phase PTC to the five-phase motor, introduces current harmonics of the order 10n $\pm$ 3 (n = 0, 1, 2.. .), which are not responsible for torque/flux production. The inherent disadvantage of PTC is being a variable frequency algorithm, which adds complexity to the design of magnetic components. This disadvantage of PTC can be overcome by applying dwell time ( $t_{s}$ ) to the voltage vectors obtained through a minimum torque ripple condition, which is determined based on the ripple equation. In the proposed algorithm, a set of synthetic voltage vectors are generated and used for reducing flux and torque error through cost function. The use of synthetic voltage vector simplifies the cost function and further reduces the computation time. A two-step delay compensation is adopted to improve the precision of the control algorithm further. In each control cycle, an optimal switching time is calculated to reduce the torque ripple and to maintain the constant switching frequency. In this article, a modified PTC is proposed, which targets to achieve constant switching frequency, eliminate the xy-subspace current harmonics, reduce the torque ripple, and minimize the computational burden involved in the conventional predictive torque control algorithm. The experimental study is carried out on a laboratory prototype. The results show compliance with all the experimental study with different PTC algorithms with different sampling frequencies, and the modified cost function.

Improved stochastic fractal search algorithm and modified cost function for automatic generation control of interconnected electric power systems

An improved stochastic fractal search algorithm (ISFS) and a modified cost function are proposed in this paper to skillfully handle the issue of automatic generation control (AGC) of power systems. Most employed power system models namely two-area non-reheat thermal power system with and without governor dead band nonlinearity, and three-area hydro-thermal power plant with generation rate constraints are considered to be controlled by a PID controller. Then the gains of this controller are optimized with SFS and ISFS individually by minimizing the value of cost function proposed. This function consists in minimizing the integral time absolute error (ITAE) and also the time rates of frequency and tie-line power deviations. After recognizing the supremacy of SFS tuned PID controller over some existing methods in improving settling time and oscillations of frequency and tie-line power deviations, ISFS tuned PID controller is shown to promote the system performance further to compete with some other control schemes of higher degree and complexity available in the literature. This outcome has unveiled the superior tuning ability of ISFS over the original version of SFS. Also, convergence curves of the algorithms are analyzed from which it is observed that the speed of convergence for ISFS is remarkable.

Event-Driven Guaranteed Cost Control Design for Nonlinear Systems With Actuator Faults via Reinforcement Learning Algorithm

This article presents a novel event-driven guaranteed cost control method for nonlinear systems subject to actuator faults. For the purpose of handling the problem of actuator faults and obtaining the event-driven approximate optimal guaranteed cost control approach for general nonlinear dynamics, the reinforcement learning (RL) algorithm is utilized to develop a sliding-mode control (SMC) strategy. To begin with, the unknown faults can be estimated by designing a fault observer. Meanwhile, an SMC technique is presented aiming at countering the effect of abrupt faults. In addition, the optimal performance of the equivalent sliding mode dynamics is considered, then an event-driven guaranteed cost control mechanism is implemented by using RL principle. In the control process, a general cost function, which has a simpler structure, is given to reduce the computation complexity. At the same time, a modified cost function is approximated to obtain optimal guaranteed cost control by using a single critic neural network (NN). In addition, a modified weight update law for critic NN is presented to relax the persistence of excitation (PE) condition. Moreover, a newly triggering condition, which is easy to be implemented, is designed, and the critic NN update law makes sure that the system states are stable. Furthermore, in light of the Lyapunov analysis, it is demonstrated that the developed event-driven control method guarantees the uniformly ultimately bounded (UUB) property of all the signals. Finally, three simulation results are given to validate the designed control method.

Full Information Estimation for Time-Varying Systems Subject to Round-Robin Scheduling: A Recursive Filter Approach

The full information estimation (FIE) problem is addressed for discrete time-varying systems (TVSs) subject to the effects of a round-Robin (RR) protocol. A shared communication network is adopted for data transmissions between sensor nodes and the state estimator. In order to avoid data collisions in signal transmission, only one sensor node could have access to the network and communicate with the state estimator per time instant. The so-called RR protocol, which is also known as the token ring protocol, is employed to orchestrate the access sequence of sensor nodes, under which the chosen sensor node communicating with the state estimator could be modeled by a periodic function. A novel recursive FIE scheme is developed by defining a modified cost function and using a so-called “backward-propagation-constraints.” The modified cost function represents a special global estimation performance. The solution of the proposed FIE scheme is achieved by solving a minimization problem. Then, the recursive manner of such a solution is studied for the purpose of online applications. For the purpose of ensuring the estimation performance, sufficient conditions are obtained to derive the upper bound of the norm of the state estimation error (SEE). Finally, two illustrative examples are proposed to demonstrate the effectiveness of the developed estimation algorithm.

A Novel Nine-Level Quadruple Boost Inverter With Inductive-Load Ability

A novel single-phase nine-level switched-capacitor inverter (9LSCI) is presented with quadruple boost ability and reduced components. The proposed topology with single dc source employs only eight switches to realize nine-level output, self-voltage balance of capacitors, quadruple boost and inductive-load ability, thus, the effective cost is cut down compared to other switched-capacitor multilevel inverters (SCMLIs). Different from other SCMLIs, the proposed 9LSCI has no need for back-end H-bridge, of which four switches need to withstand the peak voltage of output. Hence, total standing voltage can be reduced. The operation principles containing the self-voltage balance of capacitors are described in detail. The quantitative comparisons, modified cost function, as well as the loss evaluations are examined in depth. Finally, multicarrier phase disposition pulsewidth modulation method is adopted and a laboratory prototype is implemented with the rated output of 220 V–500 W. The experimental results also verify the feasibility of the proposed topology.