Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Greedy feature replacement for online value function approximation

Reinforcement learning(RL) in real-world problems requires function approximations that depend on selecting the appropriate feature representations. Representational expansion techniques can make linear approximators represent value functions more effectively; however, most of these techniques function well only for low dimensional problems. In this paper, we present the greedy feature replacement(GFR), a novel online expansion technique, for value-based RL algorithms that use binary features. Given a simple initial representation, the feature representation is expanded incrementally. New feature dependencies are added automatically to the current representation and conjunctive features are used to replace current features greedily. The virtual temporal difference(TD) error is recorded for each conjunctive feature to judge whether the replacement can improve the approximation. Correctness guarantees and computational complexity analysis are provided for GFR. Experimental results in two domains show that GFR achieves much faster learning and has the capability to handle large-scale problems.

A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS

Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.

ON APPROXIMATION OF FUNCTIONS ON SPHERE

Let f be an integrable function on the unit sphere and let be the Cesaro means of order of the Fourier-Laplace series of f.The special ualue of is known as the critical index. This paper proves that and where w (f,t)p is the lst-or der modulus of continuity of in Lp-metric which is defined in a way different than in the classical case of

A(α)-ACCEPTABILITY OF RATIONAL APPROXIMATIONS TO FUNCTION exp(z)

In this paper, two necessary and sufficient conditions, and a sufficient condition of A(α)-acceptability for (n,m) rational approximation to function exp(z) are given, where α∈(0, π/2). A necessary and sufficient condition of A-acceptability for (n,m) rational approximation to exp(z) of order p is obtained, where n≤m≤p.

ON THE BEST APPROXIMATION MATRIX PROBLEM FOR INTEGRABLE MATRIX FUNCTIONS

In this paper positive definite matrix functionals defined on a set of square integrable matrix valued func- tions are introduced and studied. The best approximation problem is solved in terms of matrix Fourier series. Riemann-Lebesgue matrix property and a Bessel-Parseval matrix inequality are given.

Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

Deep reinforcement learning using least-squares truncated temporal-difference

Policy evaluation(PE)is a critical sub-problem in reinforcement learning,which estimates the value function for a given policy and can be used for policy improvement.However,there still exist some limitations in current PE methods,such as low sample efficiency and local convergence,especially on complex tasks.In this study,a novel PE algorithm called Least-Squares Truncated Temporal-Difference learning(LST2D)is proposed.In LST2D,an adaptive truncation mechanism is designed,which effectively takes advantage of the fast convergence property of Least-Squares Temporal Difference learning and the asymptotic convergence property of Temporal Difference learning(TD).Then,two feature pre-training methods are utilised to improve the approximation ability of LST2D.Furthermore,an Actor-Critic algorithm based on LST2D and pre-trained feature representations(ACLPF)is proposed,where LST2D is integrated into the critic network to improve learning-prediction efficiency.Comprehensive simulation studies were conducted on four robotic tasks,and the corresponding results illustrate the effectiveness of LST2D.The proposed ACLPF algorithm outperformed DQN,ACER and PPO in terms of sample efficiency and stability,which demonstrated that LST2D can be applied to online learning control problems by incorporating it into the actor-critic architecture.

Chebyshev Biorthogonal Multiwavelets and Approximation

In this paper, we construct Chebyshev biorthogonal multiwavelets, and use this multiwavelets to approximate signals (functions). The convergence rate for signal approximation is derived. The fast signal decomposition and reconstruction algorithms are presented. The numerical examples validate the theoretical analysis.

Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.

NCFS:new chaotic fuzzy system as a general function approximator

Conventional fuzzy systems(type-1 and type 2)are universal approximators.The goal of this paper is to design and implement a new chaotic fuzzy system(NCFS)based on the Lee oscil-lator for function approximation and chaotic modelling.NCFS incorporates fuzzy reasoning of the fuzzy systems,self-adaptation of the neural networks,and chaotic signal generation in a unique structure.These features enable the structure to handle uncertainties by generating new information or by chaotic search among prior knowledge.The fusion of chaotic structure into the neurons of the membership layer of a conventional fuzzy system makes the NCFS more capable of confronting nonlinear problems.Based on the GFA and Stone-Weierstrass theorems,we show that the proposed model has the function approximation property.The NCFS perfor-mance is investigated by applying it to the problem of chaotic modelling.Simulation results are demonstrated to ilustrate the concept of function approximation.

The Time Asymptotic Expansion of the Bipolar Hydrodynamic Model for Semiconductors

In 2003, Gasser-Hsiao-Li [JDE(2003)] showed that the solution to the bipolar hydrodynamic model for semiconductors(HD model) without doping function time-asymptotically converges to the diffusion wave of the porous media equation(PME) for the switch-off case. Motivated by the work of Huang-Wu[arXiv:2210.13157], we will confirm that the time-asymptotic expansion proposed by Geng-Huang-Jin-Wu [arXiv:2202.13385] around the diffusion wave is a better asymptotic profile for the HD model in this paper, where we mainly adopt the approximate Green function method and the energy method.

A regeneratable dynamic differential evolution algorithm for neural networks with integer weights

Neural networks with integer weights are more suited for embedded systems and hardware implementations than those with real weights. However, many learning algorithms, which have been proposed for training neural networks with float weights, are inefficient and difficult to train for neural networks with integer weights. In this paper, a novel regeneratable dynamic differential evolution algorithm (RDDE) is presented. This algorithm is efficient for training networks with integer weights. In comparison with the conventional differential evolution algorithm (DE), RDDE has introduced three new strategies: (1) A regeneratable strategy is introduced to ensure further evolution, when all the individuals are the same after several iterations such that they cannot evolve further. In other words, there is an escape from the local minima. (2) A dynamic strategy is designed to speed up convergence and simplify the algorithm by updating its population dynamically. (3) A local greedy strategy is introduced to improve local searching ability when the population approaches the global optimal solution. In comparison with other gradient based algorithms, RDDE does not need the gradient information, which has been the main obstacle for training networks with integer weights. The experiment results show that RDDE can train integer-weight networks more efficiently.

Kernel-blending connection approximated by a neural network for image classification

This paper proposes a kernel-blending connection approximated by a neural network(KBNN)for image classification.A kernel mapping connection structure,guaranteed by the function approximation theorem,is devised to blend feature extraction and feature classification through neural network learning.First,a feature extractor learns features from the raw images.Next,an automatically constructed kernel mapping connection maps the feature vectors into a feature space.Finally,a linear classifier is used as an output layer of the neural network to provide classification results.Furthermore,a novel loss function involving a cross-entropy loss and a hinge loss is proposed to improve the generalizability of the neural network.Experimental results on three well-known image datasets illustrate that the proposed method has good classification accuracy and generalizability.

Small-world Neural Network and Its Performance for Wind Power Forecasting

A small-world neural network has stronger generalization ability with high transfer efficiency than that of the regular neural networks.This paper presents two novel smallworld neural networks,the Watts-Strogatz small-world based on a BP neural network(WSBP)and a Newman-Watts smallworld neural network based on a BP neural network(NWBP),related to previous research of complex networks.The algorithms are developed separately by adopting WS and NW small-world networks as their topological structures,and their derivation and convergence criterion are progressively discussed.After that,the proposed models are subsequently tested by two typical nonlinear functions which confirm their significant improvement over the regular BP networks and other algorithms.Finally,a wind power prediction system is advanced to verify their generalization abilities,and show that the models are practically feasible and effective with improved accuracy and acceptable forecasting errors caused by wind fluctuation and randomness with a time scale up to 24 h.

Hierarchical fuzzy ART for Q-learning and its application in air combat simulation

Value function approximation plays an important role in reinforcement learning(RL)with continuous state space,which is widely used to build decision models in practice.Many traditional approaches require experienced designers to manually specify the formulization of the approximating function,leading to the rigid,non-adaptive representation of the value function.To address this problem,a novel Q-value function approximation method named‘Hierarchical fuzzy Adaptive Resonance Theory’(HiART)is proposed in this paper.HiART is based on the Fuzzy ART method and is an adaptive classification network that learns to segment the state space by classifying the training input automatically.HiART begins with a highly generalized structure where the number of the category nodes is limited,which is beneficial to speed up the learning process at the early stage.Then,the network is refined gradually by creating the attached subnetworks,and a layered network structure is formed during this process.Based on this adaptive structure,HiART alleviates the dependence on expert experience to design the network parameter.The effectiveness and adaptivity of HiART are demonstrated in the Mountain Car benchmark problem with both fast learning speed and low computation time.Finally,a simulation application example of the one versus one air combat decision problem illustrates the applicability of HiART.

Regularized machine learning through constraint swarm and evolutionary computation applied to regression problems

Purpose–The purpose of this paper is to demonstrate the applicability of swarm and evolutionary techniques for regularized machine learning.Generally,by defining a proper penalty function,regularization laws are embedded into the structure of common least square solutions to increase the numerical stability,sparsity,accuracy and robustness of regression weights.Several regularization techniques have been proposed so far which have their own advantages and disadvantages.Several efforts have been made to find fast and accurate deterministic solvers to handle those regularization techniques.However,the proposed numerical and deterministic approaches need certain knowledge of mathematical programming,and also do not guarantee the global optimality of the obtained solution.In this research,the authors propose the use of constraint swarm and evolutionary techniques to cope with demanding requirements of regularized extreme learning machine(ELM).Design/methodology/approach–To implement the required tools for comparative numerical study,three steps are taken.The considered algorithms contain both classical and swarm and evolutionary approaches.For the classical regularization techniques,Lasso regularization,Tikhonov regularization,cascade Lasso-Tikhonov regularization,and elastic net are considered.For swarm and evolutionary-based regularization,an efficient constraint handling technique known as self-adaptive penalty function constraint handling is considered,and its algorithmic structure is modified so that it can efficiently perform the regularized learning.Several well-known metaheuristics are considered to check the generalization capability of the proposed scheme.To test the efficacy of the proposed constraint evolutionary-based regularization technique,a wide range of regression problems are used.Besides,the proposed framework is applied to a real-life identification problem,i.e.identifying the dominant factors affecting the hydrocarbon emissions of an automotive engine,for further assurance on the performance of the proposed scheme.Findings–Through extensive numerical study,it is observed that the proposed scheme can be easily used for regularized machine learning.It is indicated that by defining a proper objective function and considering an appropriate penalty function,near global optimum values of regressors can be easily obtained.The results attest the high potentials of swarm and evolutionary techniques for fast,accurate and robust regularized machine learning.Originality/value–The originality of the research paper lies behind the use of a novel constraint metaheuristic computing scheme which can be used for effective regularized optimally pruned extreme learning machine(OP-ELM).The self-adaption of the proposed method alleviates the user from the knowledge of the underlying system,and also increases the degree of the automation of OP-ELM.Besides,by using different types of metaheuristics,it is demonstrated that the proposed methodology is a general flexible scheme,and can be combined with different types of swarm and evolutionary-based optimization techniques to form a regularized machine learning approach.

Simultaneous knowledge-based identification and optimization of PHEV fuel economy using hyper-level Pareto-based chaotic Lamarckian immune algorithm, MSBA and fuzzy programming

Purpose–The purpose of this paper is to probe the potentials of computational intelligence(CI)and bio-inspired computational tools for designing a hybrid framework which can simultaneously design an identifier to capture the underlying knowledge regarding a given plug-in hybrid electric vehicle’s(PHEVs)fuel cost and optimize its fuel consumption rate.Besides,the current investigation aims at elaborating the effectiveness of Pareto-based multiobjective programming for coping with the difficulties associated with such a tedious automotive engineering problem.Design/methodology/approach–The hybrid intelligent tool is implemented in two different levels.The hyper-level algorithm is a Pareto-based memetic algorithm,known as the chaos-enhanced Lamarckian immune algorithm(CLIA),with three different objective functions.As a hyper-level supervisor,CLIA tries to design a fast and accurate identifier which,at the same time,can handle the effects of uncertainty as well as use this identifier to find the optimum design parameters of PHEV for improving the fuel economy.Findings–Based on the conducted numerical simulations,a set of interesting points are inferred.First,it is observed that CI techniques provide us with a comprehensive tool capable of simultaneous identification/optimization of the PHEV operating features.It is concluded that considering fuzzy polynomial programming enables us to not only design a proper identifier but also helps us capturing the undesired effects of uncertainty and measurement noises associated with the collected database.Originality/value–To the best knowledge of the authors,this is the first attempt at implementing a comprehensive hybrid intelligent tool which can use a set of experimental data representing the behavior of PHEVs as the input and yields the optimized values of PHEV design parameters as the output.

A numerical study for off-centered stagnation flow towards a rotating disc

In this investigation,a semi-numerical method based on Bernstein polynomials for solving off-centered stagnation flow towards a rotating disc is introduced.This method expands the desired solutions in terms of a set of Bernstein polynomials over a closed interval and then makes use of the tau method to determine the expansion coefficients to construct approximate solutions.This method can satisfy boundary conditions at infinity.The properties of Bernstein polynomials are presented and are utilized to reduce the solution of governing nonlinear equations and their associated boundary conditions to the solution of algebraic equations.Graphical results are presented to investigate the influence of the rotation ratioαon the radial velocity,azimuthal velocity and the induced velocities.A comparative study with the previous results of viscous fluid flow in the literature is made.

On increasing of integration rate of elements in a multi-level inverter

Purpose–The purpose of this paper is to analyze the redistribution of dopant and radiation defects to determine conditions which correspond to decreasing of elements in the considered inverter and at the same time to increase their density.Design/methodology/approach–In this paper,the authors introduce an approach to increase integration rate of elements in a three-level inverter.The approach is based on decrease in the dimension of elements of the inverter(diodes and bipolar transistors)due to manufacturing of these elements by diffusion or ion implantation in a heterostructure with specific configuration and optimization of annealing of dopant and radiation defects.Findings–The authors formulate recommendations to increase density of elements of the inverter with a decrease in their dimensions.Practical implications–Optimization of manufacturing of integrated circuits and their elements.Originality/value–The results of this paper are based on original analysis of transport of dopant with account transport and interaction of radiation defects.