Universal Function Research Articles

Association of diabetes risk with changes in memory, working memory, and processing speed among older adults

BackgroundThis study investigated the risk of diabetes by examining changes in memory, working memory, and processing speed among older adults to provide evidence on how each cognitive domain is associated with the risk of diabetes in older adults.MethodsThis study used Health and Retirement Study data and tracked the respondents from 2012 to 2020 (n = 5,748). The Telephone Interview for Cognitive Status-27 includes three cognitive tests (recall, seven subtraction, and counting backward tests) to assess each cognitive domain. A Cox proportional hazard regression was used to calculate the changes in the odds ratio (OR) of diabetes by increasing each cognitive function and the parameter in covariates.ResultsWe found that the OR of diabetes decreased with increasing universal cognitive function, increasing memory, working memory, and processing speed, and that age increased the OR in all analysis models.ConclusionThe findings of this study contribute to filling gaps in the literature by exploring: (a) the association between each cognitive function and the decline in diabetes risk and (b) the varying patterns of change in diabetes risk with increasing cognitive function.

Non-planar corrections in ABJM theory from quantum M2 branes

The quantization of semiclassical strings in AdS spacetimes yields predictions for the strong-coupling behaviour of the scaling dimensions of the corresponding operators in the planar limit of the dual gauge theory. Finding non-planar corrections requires computing string loops (corresponding to torus and higher genus surfaces), which is a challenging task. It turns out that in the case of the Uk(N) × U−k(N) ABJM theory there is an alternative approach: one may semiclassically quantize M2 branes in AdS4 × S7/ℤk which are wrapped around the 11d circle of radius 1/k = λ/N . Such M2 branes are the M-theory generalization of the strings in AdS × CP3. In this work, we show that by expanding in large M2 brane tension T2 ~ kN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{kN} $$\\end{document} for fixed k, followed by an expansion in large k, we can predict the large λ asymptotics of the non-planar corrections to the dimensions of the dual ABJM operators. As a specific example, we consider the M2 brane configuration that generalizes the long folded string with large spin in AdS4, and compute the 1-loop correction to its energy. This calculation allows us to determine non-planar corrections to the universal scaling function or cusp anomalous dimension. We extend our analysis to the semiclassical M2 branes that generalize the “short” and “long” circular strings with two equal angular momenta in CP3. The “short” M2 brane corresponds to a dual operator whose dimension at strong coupling scales as ∆ ∼ λ1/4 + …, and we derive the leading non-planar correction to it.

Intelligent design of steel–concrete composite beams based on deep reinforcement learning

In this work, an automated member design method is proposed based on deep reinforcement learning (DRL). Using steel–concrete composite beam design as a case study, the design procedure is conceptualized as a sequential optimization process and modeled as a Markov Decision Process (MDP). A design agent equipped with two deep neural networks, is trained using the proximal policy optimization (PPO) method to complete the complex design task of steel–concrete composite beams, adhering to the Chinese standard for design of steel structures GB50017-2017 provisions. The structural provisions are integrated into a simulated design environment, which can respond to the agent’s actions. A universal reward shaping function is introduced to guide the agent towards success and minimize material cost. The design quality and generation performance of trained PPO agent are compared with those of the Differential Evolution (DE) in 100 random training cases, 100 random testing cases, and 95 real-world engineering cases, demonstrating significant promise and reduced time consumption for automated steel–concrete composite beam design. An approach combining PPO with DE is proposed to enhance the robustness and reliability of the original agent. Finally, a brief discussion is conducted on the essence and prospects of the proposed method.

Implementation of a non-standard system for simplifying Peirce-Webb functions

The object of research are models of optimal logic circuits based on universal Peirce-Webb functions. The problem solved is the efficiency of the technique for simplifying the Peirce-Webb functions. The extension of the non-standard system to the simplification of Peirce-Webb functions makes it possible to discover new rules of equivalent transformations of Boolean functions, and to complete the simplification procedure in one step. A feature of the simplification of functions in the Peirce-Webb basis by a non-standard system is fixing the digital project at the level of abstraction, followed by the application of the mechanism of logical synthesis to generate the corresponding equivalent at the level of gates of the logic circuit. The result of the transformation of the terms of the binary matrix in the end is some combinatorial system, metadata that can explain other data, for example, determine the minimum function for another logical basis. The interpretation of the result consists in the use of combinatorial properties of binary structures of functions in the Peirce-Webb basis and binary structures of functions in the basic basis. These properties do not depend on the selected logical basis, which makes it possible to carry out equivalent transformations on binary matrices of Peirce-Webb functions according to the rules of the algebra of the main basis. It has been experimentally confirmed that a non-standard system enables: – to reduce the algorithmic complexity of simplifying the Peirce-Webb functions; – to increase the performance of the simplification of Peirce-Webb functions by 200–300 %; – to demonstrate the visibility of the process of simplifying functions. In terms of application, the non-standard system of simplifying the Peirce-Webb functions could ensure the transfer of innovations to material production: from conducting fundamental research, expanding the capabilities of digital component design technology to organizing serial or mass production of novelties.

Universal dynamical function behind all genetic codes: [formula omitted]-adic attractor dynamical model

The genetic code is a map which gives the correspondence between codons in DNA and amino acids. In the attractor dynamical model (ADM), genetic codes can be described as the sets of the cyclic attractors of discrete dynamical systems - the iterations of functions acting in the ring of 2-adic integers Z2. This ring arises from representation of nucleotides by binary vectors and hence codons by triples of binary vectors. We construct a Universal Function B such that the dynamical functions for all known genetic codes can be obtained from B by simple transformations on the set of codon cycles - the “Addition” and “Division” operations. ADM can be employed for study of phylogenetic dynamics of genetic codes. One can speculate that the “common ancestor genetic code” was caused by B. We remark that this function has 24 cyclic attractors which distribution coincides with the distribution for the hypothetical pre-LUCA code. This coupling of the Universal Function with the pre-LUCA code assigns the genetic codes evolution perspective to ADM. All genetic codes are generated from B through the special chains of the “Addition” and “Division” operations. The challenging problem is to assign the biological meaning to these mathematical operations.

A comprehensive framework for 5G indoor localization

Localization inside legacy private 5G networks is a daunting task that involves solving the problem of indoor localization using commercial off-the-shelf proprietary hardware. While some previous work has focused on experimental analysis, none has undertaken to develop a realistic solution based on commercial equipment. In this study, we present the first comprehensive and concrete 5G framework that combines fingerprinting with the 3GPP Enhanced Cell ID (E-CID) approach. Our methodology consists of a machine-learning model to deduce the user’s position by comparing the signal strength received from the User Equipment (UE) with a reference radio power map. To achieve this, the 3GPP protocols and functions are improved to provide open, centralized, and universal localization functions. A new reference map paradigm named Optical Radio Power Estimation using Light Analysis (ORPELA) is introduced. Real-world experiments prove that it is reproducible and more accurate than state-of-the-art radio-planning software. Machine-learning models are then designed, trained, and optimized for an ultra-challenging radio context. Finally, a large-scale experimental campaign encompassing a wide range of cases, including line-of-sight or mobility, is being conducted to demonstrate expected location performance within realistic 5G private networks.

The universal multiplicity function: counting haloes and voids

We present a novel combination of the excursion-set approach with the peak theory formalism in Lagrangian space and provide accurate predictions for halo and void statistics over a wide range of scales. The set-up is based on an effective moving barrier. Besides deriving the corresponding numerical multiplicity function, we introduce a new analytical formula reaching the percent level agreement with the exact numerical solution obtained via Monte Carlo realisations down to small scales, ∼ 1012 h -1M⊙. In the void case, we derive the dependence of the effective moving barrier on the void formation threshold, δ v, by comparison against the Lagrangian void size function measured in the DEMNUni simulations. We discuss the mapping from Lagrangian to Eulerian space for both haloes and voids; adopting the spherical symmetry approximation, we obtain a strong agreement at intermediate and large scales. Finally, using the effective moving barrier, we derive Lagrangian void density profiles accurately matching measurements from cosmological simulations, a major achievement towards using void profiles for precision cosmology with the next generation of galaxy surveys.

PCLOS based fractional-order sliding mode stochastic path following control for underactuated marine vehicles with multiple disturbances and constraints

This paper investigates the stochastic path following control of underactuated marine vehicles (UMVs) subject to multiple disturbances and constraints. Firstly, the complex marine environment in which UMVs navigate typically contains stochastic components, thus the multiple disturbances are categorized as slow-varying deterministic disturbances and stochastic disturbances. Secondly, a position-constrained line-of-sight (PCLOS) based fractional-order sliding mode stochastic (FSMS) control strategy is established to achieve path following control of UMVs. A PCLOS guidance law based on universal barrier Lyapunov function is proposed to ensure that the position errors remain within the constraint ranges, which is versatile for systems with symmetric constraints or without constraints. An FSMS controller based on fractional-order theory and sliding mode control is designed to improve the dynamic response speed of the system and effectively attenuate chattering phenomenon. A stochastic disturbance observer is developed to estimate the slow-varying deterministic disturbances in the stochastic system, and auxiliary dynamic compensators are used to mitigate the impact of input constraints. Lastly, theoretical analysis indicates that the closed-loop system is stable and the position constraint requirements are satisfied. Comparative simulations illustrate the effectiveness of the proposed control strategy.

Fuzzy adaptive finite-time formation control of unmanned ground vehicles with performance and feasibility constraints

This paper investigates the problem of fuzzy adaptive finite-time formation tracking control for unmanned ground vehicles (UGVs) systems with two different constraints. By utilizing the distance tracking error between the actual trajectory and the desired trajectory of each UGV, as well as the constraints of bearing angle, to achieve the performance and feasibility constraints, respectively. Furthermore, the fuzzy logic systems (FLSs) are used to approximate unknown nonlinear functions. Due to the limitations of the field of view and communication distance of UGVs, the controller is designed by using finite time stability theory and universal barrier function. Under the proposed control scheme, the stability of the closed-loop system can be ensured, feasibility and performance constraints are also achieved. Finally, the effectiveness of the proposed control design is verified through simulation results.

Health status and disability in persons with spinal cord injuries in South Africa and Kenya

Background: There is a lack of understanding regarding the nature of disabilities and functioning limitations associated with spinal cord injuries (SCI) in developing economies given limited healthcare resources.Aim: Our purpose was to assess and compare SCI-related disability among individuals with SCI in South Africa and Kenya to inform rehabilitation service planning.Settings: Two hundred individuals from South Africa and 90 from Kenya with SCI took part in this cross-sectional survey study, examining the comprehensive functioning of individuals with long-term SCI.Methods: This study utilised the International SCI (InSCI) Community Survey questionnaire. Subsections of the questionnaire were used to investigate the differences in the period-prevalence of secondary medical conditions, activity limitations and participation restrictions in persons with SCI.Results: In both countries, sexual dysfunction (55% – 57%), pain (48% – 49%), spasticity (41% – 42%) and bladder dysfunction (27% – 60%) emerged as the predominant secondary medical complications, with sexual dysfunction and pain showing overlap. There was no notable superiority in terms of treatment rates for secondary medical conditions between countries; however, exceptions were found. Both countries experienced similar overlaps in prevalent activity limitations and participation restrictions, including standing unsupported, using the toilet, bladder and bowel impairments, using public transport and reaching destinations. However, the Kenyan cohort showed significantly higher prevalence rates compared to the South African cohort for challenges related to carrying out daily routines, getting to destinations and using public transportation, while maintaining intimate relationships was more prevalent in South Africa.Conclusion: This study provides insight into the similarities and differences in both the nature and prevalence of disability in two developing economies. It appears that universal functioning patterns after SCI exist in the two countries, and a further need emerged to examine these functioning problems on other major life areas.Contribution: While some functioning problems could be addressed through healthcare and rehabilitation alone, others will require improved coordination and a whole-of-government approach, namely issues related to participation, community integration and inclusion.

Bio‐Inspired Hybrid Laser Direct Writing of Interfacial Adhesion for Universal Functional Coatings

AbstractEnhancing interfacial adhesion between functional coatings and target surfaces facilitates long‐term stable service by mitigating interferences of mechanical mismatches. Design of mechanical interlocks affords an effective strategy to strengthen the interfacial bonding with durability and compatibility, but the in‐depth investigations are still lacked. Herein, a gecko‐inspired hierarchical strategy realized by hybrid laser direct writing is proposed, which incorporates an armored frame scale for surface protection and a riveted anchor scale for interlocks. Such dual‐scale configurations endow the functional coatings with the stronger adhesion to the targets than the pristine and mono‐scale cases, resulting in 2 orders of magnitude enhancement resistant to tape peeling tests. Utilizing this scheme, a laser‐induced integrated deicing system is in situ manufactured on thermoplastics, primarily comprising superhydrophobic structures, carbon‐based sensors as well as adhesive copper (Cu) interconnects and heaters, where Cu‐based devices exhibit superior resistance to water impacts and stress fatigue. Interfacing with signal processing modules, such an all‐in‐one system demonstrates real‐time temperature monitoring and high efficiency in deicing (4.24 folds faster than the control group). The facile route for intensified adhesion holds promise in the interfaces within advanced equipment and under harsh scenarios.

Cooperative learning‐based practical formation‐containment control with prescribed performance for heterogeneous clusters of UAV/USV

SummaryIn this paper, a new approach for formation‐containment control with prescribed performances is introduced for heterogeneous autonomous vehicles involving a cluster of leader unmanned aerial vehicles (UAVs) and follower unmanned surface vessels (USVs). We introduce a two‐layer distributed control system: The upper layer focuses on guiding the UAVs to form a scalable lattice while synchronizing their movement along a predefined path, and the second layer guides the USVs to enter the convex hull formed by the UAVs, ensuring collision‐free operation with static/dynamic objects. To prevent collisions and ensure lattice formation, a set of well‐defined bump functions are utilized in the design of the backstepping control algorithm. Managing virtual controls, we incorporate a nonlinear dynamic surface control (NDSC), while a universal barrier function enhances the convergence of formation tracking errors. Furthermore, each USV employs a cooperative adaptive learning neural network to handle uncertainties in heterogeneous vehicle models. Utilizing the Lyapunov theorem, the stability of the formation‐containment of UAV/USV is achieved, and all signals in the formation‐containment systems are semiglobal uniform ultimate bounded (SGUUB). A simulation example showcases the effectiveness of our proposed approach, highlighting contributions in collision avoidance, synchronization speed, and adaptive learning. Our work advances the heterogeneous formation‐containment literature towards more realistic scenarios with safety‐critical considerations amidst multiple layers of uncertainties and unknown parameters.

Predicting Inhibition of CDK2 with SAnDReS: The Application of Machine Learning to Navigate the Scoring Function Space.

CDK2 plays a pivotal role in controlling the progression of the cell cycle and is a target for anticancer drugs. The last 30 years of structural studies focused on CDK2 provided the basis for understanding its inhibition and furnished the data to develop machine-learning models to study intermolecular interactions. This review addresses the application of computational models to estimate the inhibition of CDK2. It focuses on machine-learning models developed to predict binding affinity against CDK2 using the program SAnDReS. A search of previously published articles on PubMed showed machine-learning models built to evaluate CDK2 inhibition. BindingDB information for CDK2 furnished the data to generate updated machine-learning models to predict the inhibition of this enzyme. The application of SAnDReS to model CDK2-inhibitor interactions showed that this approach can build machine-learning models with superior predictive performance compared with classical and deep-learning scoring functions. Also, the innovative DOME analysis of the predictive performance of machine learning and universal scoring function indicates that this method is adequate to select computational models to address protein-ligand interactions. The available structural and functional data about CDK2 is a rich source of information to build machine-learning models to predict the inhibition of this protein target. SAnDReS can build superior models to predict pKi and outperform universal scoring functions, including one developed using deep learning.

On the Strong Composition Dependence of the Martensitic Transformation Temperature and Heat in Shape Memory Alloys.

General derivation of the well-known Ren-Otsuka relationship, 1αdTodx=-αβ (where To, x, α and β(>0) are the transformation temperature and composition, as well as the composition and temperature coefficient of the critical shear constant, c', respectively) for shape memory alloys, SMAs, is provided based on the similarity of interatomic potentials in the framework of dimensional analysis. A new dimensionless variable, tox=ToxTmx, describing the phonon softening (where Tm is the melting point) is introduced. The dimensionless values of the heat of transformation, ΔH, and entropy, ΔS, as well as the elastic constants c', c44, and A=c44c' are universal functions of to(x) and have the same constant values at to(0) within sub-classes of host SMAs having the same type of crystal symmetry change during martensitic transformation. The ratio of dtodx and α has the same constant value for all members of a given sub-class, and relative increase in c' with increasing composition should be compensated by the same decrease in to. In the generalized Ren-Otsuka relationship, the anisotropy factor A appears instead of c', and α as well as β are the differences between the corresponding coefficients for the c44 and c' elastic constants. The obtained linear relationship between h and to rationalizes the observed empirical linear relationships between the heat of transformation measured by differential scanning calorimetry (DSC) (QA⟶M) and the martensite start temperature, Ms.

Dynamic fluctuations of current and mass in nonequilibrium mass transport processes

We study steady-state dynamic fluctuations of current and mass in several variants of random average processes on a ring of L sites. These processes violate detailed balance in the bulk and have nontrivial spatial structures: their steady states are not described by the Boltzmann–Gibbs distribution and can have nonzero spatial correlations. Using a microscopic approach, we exactly calculate the second cumulants, or the variance, ⟨Qi2(T)⟩c and ⟨Qsub2(l,T)⟩c , of cumulative (time-integrated) currents up to time T across the ith bond and across a subsystem of size l (summed over bonds in the subsystem), respectively. We also calculate the (two-point) dynamic correlation function of the subsystem mass. In particular, we show that, for large L≫1 , the second cumulant ⟨Qi2(T)⟩c of the cumulative current up to time T across the ith bond grows linearly as ⟨Qi2⟩c∼T for initial times T∼O(1) , subdiffusively as ⟨Qi2⟩c∼T1/2 for intermediate times 1≪T≪L2 , and then again linearly as ⟨Qi2⟩c∼T for long times T≫L2 . The scaled cumulant liml→∞,T→∞⟨Qsub2(l,T)⟩c/2lT of current across the subsystem of size l and up to time T converges to the density-dependent particle mobility χ(ρ) when the large subsystem-size limit is taken first, followed by the large-time limit; when the limits are reversed, it simply vanishes. Remarkably, regardless of the dynamical rules, the scaled current cumulant D⟨Qi2(T)⟩c/2χL≡W(y) as a function of scaled time y=DT/L2 can be expressed in terms of a universal scaling function W(y) , where D is the bulk-diffusion coefficient; interestingly, the intermediate-time subdiffusive and long-time diffusive growths can be connected through a single scaling function W(y) . The power spectra for current and mass are also exactly characterized by the respective scaling functions. Furthermore, we provide a microscopic derivation of equilibrium-like Green–Kubo and Einstein relations that connect the steady-state current fluctuations to an ‘operational’ mobility (i.e. the response to an external force field) and mass fluctuation, respectively.

Towards circular economy of wasted printed circuit boards of mobile phones fuelled by machine learning and robust mathematical optimization framework

Estimating the operating conditions using conventional process analysis techniques for the maximum metal extraction from the wasted printed circuit boards (WPCB) can provide sub-optimal solutions leading to the low yield of the process. In this paper, we present a closed-loop methodological framework built on machine learning and robust mathematical optimization technique, that offers the mathematical rigour, to determine the optimum operating conditions for the maximum Cu and Ni recovery from the WPCB. Alkali leaching based novel metals recovery process from the WPCB is designed, and the experiments are conducted to collect the data on the percentage recovery of Cu and Ni against the operating levels of the process input variables (ammonia concentration (NH3 conc. (g/L)), ammonium sulfate concentration ((NH4)2SO4 conc. (g/L)), H2O2 concentration (H2O2 conc. (M)), time (h), liquid to solid ratio (L/S ratio, (mL/g)), temperature (Temp. (°C)), and stirring speed (rpm)). The experimental data is deployed to construct the functional mapping between the nonlinear output variables of metals recovery process with the hyperdimensional input space through artificial neural network (ANN) based modelling algorithm – a powerful universal function approximator. Well-predictive ANN models for Cu and Ni recovery are developed having co-efficient of determination (R2) value more than 0.90. Partial derivative-based sensitivity analysis is then carried out to establish the order of the significance of the input variables that is backed by the domain knowledge, thus promotes the interpretability of the trained ANN models. The hybridization of ANN with NLP (nonlinear programming) framework is implemented for the determination of optimized operating conditions to extract maximum Cu and Ni under separate and combined model of metal extraction. The robustness of the determined solutions is verified, the determined optimized solutions for the metal recovery are validated in the lab, and the maximum metal recovery, i.e., 100 % Cu and 90 % Ni is extracted from the WPCB. This research demonstrates the effective utilization of ANN model-based robust optimization approach for the metal recovery from the WPCB that supports the circular economy for the metal extraction industry.

Corrections to Diffusion in Interacting Quantum Systems

The approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative universality class, the most prevalent one being diffusion. In this paper, we use the effective field theory (EFT) of diffusion to systematically obtain universal power-law corrections to diffusion. We then employ large-scale simulations of classical and quantum systems to explore their validity. In particular, we find universal scaling functions for the corrections to the dynamical structure factor ⟨n(x,t)n⟩, in the presence of a single U(1) or SU(2) charge in systems with and without particle-hole symmetry, and present the framework to generalize the calculation to multiple charges. Classical simulations show remarkable agreement with EFT predictions for subleading corrections, pushing precision tests of effective theories for thermalizing systems to an unprecedented level. Moving to quantum systems, we perform large-scale tensor-network simulations in unitary and noisy 1D Floquet systems with conserved magnetization. We find a qualitative agreement with EFT, which becomes quantitative in the case of noisy systems. Additionally, we show how the knowledge of EFT corrections allows for fitting methods, which can improve the estimation of transport parameters at the intermediate times accessible by simulations and experiments. Finally, we explore nonlinear response in quantum systems and find that EFT provides an accurate prediction for its behavior. Our results provide a basis for a better understanding of the nonlinear phenomena present in thermalizing systems. Published by the American Physical Society 2024

Agent-based simulation model of micro-mobility trips in heterogeneous and perceived unsafe road environments

Safety concerns expressed by micro-mobility users seem to practically constrain the use and flexibility of these new modes. This paper introduces a new, parametric agent-based modeling approach for simulating micro-mobility, using MATSim as a platform. Perceived safety is introduced as a factor, which affects travel behavior of micro-mobility modes in a car-dominated, heterogeneous, and perceived unsafe road network. To meet the research objectives, different scenarios are simulated, using the city of Athens, Greece as a test bed, to examine the model performance and applicability. A universal scoring function based on travel time, cost, and safety, is proposed. This study also discusses the concept of unsafe discontinuities. Simulation results show that an unsafe road segment of 500 m long is sufficient to induce evident behavioral variations and hinder the practical use of e-bikes and e-scooters in the base scenario. The establishment of a cycle-friendly road network leads to significant changes in the chosen routes and decreases the average trip distance for micro-mobility users. In this case, the simulation process is guided by perceived safety, primarily focusing on formulating safer paths for micro-mobility mode users. Nevertheless, the routing behavior of car users is not modified due to the spatial uniformity of safety perceptions in a car-dominated road environment.

Robustness of the hedgehog Skyrmion

We investigate the radial profile function of the hedgehog Skyrmion with unit baryon number in generic EFTs (effective field theories) of pions. The analysis assumes chiral symmetry and ignores the pion mass term. The Skyrmion is always smooth, because it has no point source at the origin, and terms in the EFT with higher numbers of pion derivatives do not result in uncontrolled large corrections or singularities there. The profile varies in quite a limited way as the terms in the EFT change, and a universal profile function is proposed.

Inverse Optimal Adaptive Neural Control for State-Constrained Nonlinear Systems.

Optimizing a performance objective during control operation while also ensuring constraint satisfactions at all times is important in practical applications. Existing works on solving this problem usually require a complicated and time-consuming learning procedure by employing neural networks, and the results are only applicable for simple or time-invariant constraints. In this work, these restrictions are removed by a newly proposed adaptive neural inverse approach. In our approach, a new universal barrier function, which is able to handle various dynamic constraints in a unified manner, is proposed to transform the constrained system into an equivalent one with no constraint. Based on this transformation, a switched-type auxiliary controller and a modified criterion for inverse optimal stabilization are proposed to design an adaptive neural inverse optimal controller. It is proven that optimal performance is achieved with a computationally attractive learning mechanism, and all the constraints are never violated. Besides, improved transient performance is obtained in the sense that the bound of the tracking error could be explicitly designed by users. An illustrative example verifies the proposed methods.