Uncertain Function Research Articles

Time-varying formation of uncertain nonlinear multi-agent systems via adaptive feedback control approach with event-triggered impulsive estimator

The time-varying formation problem under directed topology is investigated for the uncertain nonlinear multi-agent systems (MASs) via the neural networks-based adaptive feedback control (NNAFC). Compared with the simple adaptive control, the designed control protocol consists of two parts: NNAFC and the event-triggered impulsive estimator. To save communication costs, communications among followers are only carried out at discrete instants determined by the event-triggered impulsive rule. Two kinds of estimators and controllers are designed for two cases with or without communication delay, respectively. Further, NNAFC can be further improved to eliminate errors due to uncertain function approximation for some special cases. Utilizing the Lyapunov stability theory and impulsive control theory, we obtain some sufficient conditions to implement time-varying formation task. Finally, three examples are given to show the feasibility of theoretical analysis.

Constructing order-2 information granules of linguistic expressions with the aid of the principle of justifiable granularity

To capture collective opinions/evaluations in a collection of individual linguistic expressions, this study proposes an approach to construct order-2 information granules by extending the numerical data-based principles of justifiable granularity to a linguistic data-based one. First, the two key criteria of the principle of justifiable granularity, namely coverage and specificity, are formally defined in the context of order-2 information granules. Second, three order-2 information granules construction models by maximizing the product of coverage and specificity are developed for coping with one-dimensional direct linguistic expressions, linguistic preference relations, and multi-dimensional direct linguistic expressions, respectively. Third, considering that the developed order-2 information granules construction models exhibit a non-linear uncertain objective function and equality constraints, the constrained multi-swarm PSO without velocity is improved with the use of the ε constrained handling technique for effectively solving the models. Case studies on the considered three types of linguistic expressions show the applicability of the proposed models and ensuing algorithm. The superiority of the improved algorithm in handling the proposed models is demonstrated by comparison with the original one. The effectiveness of the proposed models in terms of abnormal corrective ability and balance of coverage and specificity is verified by comparing with a family of Top-n methods. The originality of this study lies in the construction of an operational entity, namely order-2 information granule, that reflects the group opinion without specifying the formalism of individual linguistic expressions, which provides an effective and efficient way to aggregate ubiquitous linguistic information for subsequent computation, reasoning and decision-making.

Adaptive fixed-time dynamic surface tracking control for high-order nonstrict-feedback nonlinear switched systems

This paper considers the adaptive fixed-time neural tracking dynamic surface control (DSC) for high-order nonlinear switched systems. The uncertain nonlinear functions are approximated by neural networks (NNs). And the obstacles of high-order terms are eliminated by the adding a power integrator. A novel fixed-time convergence filter is proposed to refrain from the problem of repeated differentiation of virtual controllers. On the basis of the backstepping control algorithm and the common Lyapunov function (CLF) method, a novel adaptive fixed-time neural DSC strategy is developed. It is proven that the states in the closed-loop system are bounded and the tracking error converges to an area of zero in fixed time. The simulation experiments further verify the feasibility of the mentioned method.

Event-Triggered Adaptive Fuzzy Control for Strict-Feedback Nonlinear FOSs Subjected to Finite-Time Full-State Constraints

In this article, an event-triggered adaptive fuzzy finite-time dynamic surface control (DSC) is presented for a class of strict-feedback nonlinear fractional-order systems (FOSs) with full-state constraints. The fuzzy logic systems (FLSs) are employed to approximate uncertain nonlinear functions in the backstepping process, the dynamic surface method is applied to overcome the inherent computational complexity from the virtual controller and its fractional-order derivative, and the barrier Lyapunov function (BLF) is used to handle the full-state constraints. By introducing the finite-time stability criteria from fractional-order Lyapunov method, it is verified that the tracking error converges to a small neighborhood near the zero and the full-state constraints are satisfied within a predetermined finite time. Moreover, reducing the communication burden can be guaranteed without the occurrence of Zeno behavior, and the example is given to demonstrate the effectiveness of the proposed controller.

Adaptive event‐triggered output‐feedback control for p‐normal stochastic nonlinear systems with uncertain output function and time‐varying delays

AbstractThis paper designs an adaptive event‐triggered output‐feedback controller for a class of ‐normal switched SNS with uncertain output function and time‐varying delays. Firstly, a Lyapunov function and reduced‐order observer using the output signal are constructed for nominal system by virtue of sign function and API technique. Then a dynamic gain and time‐decaying parameter are introduced into the event‐triggered mechanism to reduce the number of control updates. Next, by virtue of LKF and stochastic Barbalat's Lemma, it is proved that all the signals are bounded and system states asymptotically converge to zero in probability, and Zeno behavior is excluded. Finally, a numerical example and practical one are given to show the effectiveness of the proposed method.

Bacterial hypothetical proteins may be of functional interest

Genomic analysis is part of the daily routine for many microbiology researchers. These analyses frequently unveil genes that encode proteins with uncertain functions, and for many bacterial species, these unknown genes constitute a significant proportion of their genomic coding sequences. Because these genes do not have defined functions, they are often overlooked in analyses. Experimentally determining the function of a gene can be challenging; however, ongoing advancements in bioinformatics tools, especially in protein structural analysis, are making it progressively easier to assign functions to hypothetical sequences. Leveraging various complementary tools and automated pipelines for annotating hypothetical sequences could ultimately enhance our comprehension of microbial functions and provide direction for new laboratory experiments.

POBO: Safe and Optimal Resource Management for Cloud Microservices

Resource management in microservices is challenging due to the uncertain latency-resource relationship, dynamic environment, and strict Service-Level Agreement (SLA) guarantees. This paper presents a Pessimistic and Optimistic Bayesian Optimization framework, named POBO, for safe and optimal resource configuration for microservice applications. POBO leverages Bayesian learning to estimate the uncertain latency-resource functions and combines primal-dual and penalty-based optimization to maximize resource efficiency while guaranteeing strict SLAs. We prove that POBO can achieve sublinear regret and SLA violation compared with the optimal resource configuration in hindsight. We have implemented a prototype of POBO and conducted extensive experiments on a real-world microservice application. Our results show that POBO can find the safe and optimal configuration efficiently, outperforming Kubernetes' built-in auto-scaling module and the state-of-the-art algorithm.

Improving the Quality of Industrial Robot Control Using an Iterative Learning Method with Online Optimal Learning and Intelligent Online Learning Function Parameters

It is inevitable that the characteristics of a robot system change inaccurately or cannot be accurately determined during movement and are affected by external disturbances. There are many adaptive control methods, such as the exact linearization method, sliding control, or neural control, to improve the quality of trajectory tracking for a robot’s motion system. However, those methods require a great deal of computation to solve the constrained nonlinear optimization problem. This article first presents some techniques for determining the online learning function parameters of an intelligent controller, including two circuits: the inner circuit is an uncertain function component estimator to compensate for the robot’s input, and the outer circuit is an iterative learning controller and does not use a mathematical model of the robot with optimal online learning function parameters. The optimal condition is based on the model in the time domain to determine the learning function parameters that change adaptively according to the sum of squared tracking errors of each loop. As for the intelligent online learning function parameters, they closely follow the general model to stabilize the robot system, based on the principle of intelligent estimation of the uncertainty component and total noise. This method is built on Taylor series analysis for the state vector and does not use a mathematical model of the system at all. It allows feedback linearization, as well as intelligent stabilization of the system. This article’s content uses a 2-DOF flat robot implemented on MatlabR2022b software to verify the theory. These findings indicate that superior tracking performance is achievable.

A stochastic optimization technique for hyperparameter tuning in reservoir computing

This paper presents a new approach to reservoir computing (RC) optimization. Reservoir computing (RC) is a framework for building recurrent neural networks (RNNs) that alleviates the well-known learning difficulties in such neural networks by training only the output layer. While the weights of the input and the nonlinear hidden layers are randomly generated, the adjustment of critical hyperparameters, such as the input and the feedback scaling factor, is essential for optimal performance in RC. While recent hardware implementations of RC are crucial for high-speed processing, standard gradient-based hyperparameter optimization is often irrelevant due to potentially uncertain or time-varying internal functions and parameters. In this work, we propose and analyze a stochastic optimization approach using gradient approximations based solely on noisy measurements of the loss function to circumvent this problem. Our numerical and experimental results confirm that the proposed method can provide near-optimal RC hyperparameters with substantial complexity reduction compared to competing methods, validating its potential for RC optimization.

Finite‐time stabilization for a class of more general p‐normal nonlinear systems with input and output nonlinearities

AbstractThis study investigates the global finite‐time state feedback stabilization for a class of more general p‐normal nonlinear systems subjects to input time‐delay and uncertain output function under rational powers. A novel control input compensation signal comprising a finite integral of previous control values is presented, and an equivalent system with control input dependent‐free time delay is obtained by introducing a variable transformation technique that includes the compensation signal. A suitable controller is designed in line with the homogeneous domination method to ensure the globally finite‐time stability of the closed‐loop system. Finally, the effectiveness of the proposed control scheme is verified through a numerical simulation and an induction heater circuit system.

Синтез адаптивной робастной системы управления трикоптером с поворотными винтами в условиях неопределенных аэродинамических коэффициентов, частично неопределенной матрицы входа, влияния внешних возмущений и ограничения входных воздействий

In this article, an adaptive robust control system for a tricopter equipped with three rotary propellers is developed and studied under the following conditions: a) uncertain aerodynamic coefficients; b) partially uncertain input matrix; c) influence of unknown external disturbances; and d) input constraints. When constructing a complete nonlinear mathematical model of the dynamics of a tricopter with rotary propellers in the form of Lagrange-Euler equations, the input constraints are taken into account. The synthesis of an adaptive robust control system for a tricopter with rotary propellers is carried out on the basis of the modified computed torque control (Li–Slotine method) and the function approximation technique to eliminate the influence of uncertainty. Unknown external disturbances are compensated by a smooth sliding mode control using an adaptive estimate of the upper bound of the sum of external disturbances and approximation errors of uncertain functions in the mathematical model. To compensate for the negative effects of input constraints, an auxiliary dynamic system is constructed, the state variables of which are used to synthesize the control law. The robustness of the adaptive system and the desired tracking accuracy of the reference signals are proven using the Lyapunov function method. Simulation results using MatLab/Simulink are presented to illustrate the effectiveness of the proposed control law.

Adaptive fuzzy fixed time formation control of state constrained nonlinear multi-agent systems against FDI attacks.

In this manuscript, based on nonlinear multi-agent systems (MASs) with full state constraints and considering security control problem under false data injection (FDI) attacks, the fixed-time formation control (FTFC) protocol was designed, which can ensure that all agents follow the required protocol within a fixed time. Fuzzy logic system (FLS) was used to compensate and approximate the uncertain function, which improved safety and robustness of the formation process. Finally, the fixed-time theory and Lyapunov stability theory were addressed to prove the effectiveness of the proposed method, and simulation examples verified the effectiveness of the theory.

Neural-Network-Based Adaptive Fixed-Time Control for Nonlinear Multiagent Non-Affine Systems.

In this research, the adaptive neural network consensus control problem is addressed for a class of non-affine multiagent systems (MASs) with actuator faults and stochastic disturbances. To overcome difficulties associated with actuator faults and uncertain functions of the designed MAS, a neural network fault-tolerant control scheme is developed. Moreover, an adaptive backstepping controller is developed to solve the non-affine appearance in multiagent stochastic non-affine systems using the mean value theorem. Being different from the existing control methods, the developed adaptive fixed-time control approach can ensure that the outputs of all followers track the reference signal synchronously in the fixed time, and all signals of the controlled system are semi-globally uniformly fixed-time stable. The simulation results confirm that the presented control strategy is effective in achieving control goals.

Solution of generalized fractional Jaulent–Miodek model with uncertain initial conditions

This paper analyses a coupled system of generalized coupled system of fractional Jaulent–Miodek equations, including uncertain initial conditions with fuzzy extension. In this regard, an extension of the homotopy with a generalized integral algorithm is adopted for a class of time-fractional fuzzy Jaulent–Miodek models by mixing the fuzzy q-homotopy analysis algorithm with a generalized integral transform and Caputo fractional derivative. The triangular fuzzy numbers (TFNs)are expressed in double parametric form using κ-cut and r-cut and utilized to explain the uncertainties arising in the initial conditions of highly nonlinear differential equations with generalized Hukuhara differentiability (gH-differentiability). The TFNs are controlled by the κ-cut and r-cut, and the variability of uncertainty is examined using a “triangular membership function” (TMF). The results are analyzed by finding the solutions for different spatial coordinate values of time with κ-cut and r-cut for both lower and upper bounds and validated through numerical and graphical representations in crisp cases. Finally, it can be seen that the uncertain probability density function rapidly decreases at the left and right edges when the fractional order is increased, and it is observed that the obtained solutions are more accurate than the existing results through the Hermite wavelet method in the literature.

Semiglobal stability of PID for uncertain nonaffine systems

Proportional–integral–derivative (PID) controller is the most widely used form of feedback control by far. However, a satisfactory theory is still lacking to explain the rationale of the widespread PID control, and the gap between theory and practice of PID needs to be filled by control scientists. It is worth noting that a recent work (Zhao and Guo, 2022) proved that the classical PID controller has the ability to globally stabilize a basic class of uncertain nonaffine nonlinear systems, while the system nonlinear function is required to have a linear growth rate with respect to the state variables. In this paper, we will consider the more general case where the system nonlinear function may have super-linear growth rates, and show that the classical PID control can always be designed to stabilize such systems in the semiglobal sense, provided that the smallest eigenvalue of the control gain matrix has a positive lower bound. Moreover, a three dimensional parameter set for the stabilizing PID parameters will be constructed. Furthermore, under some additional knowledge about the system uncertain functions, we will propose a simpler PD controller with desired compensation, and show that the proposed controllers can still be designed to achieve semiglobal stability and desired tracking targets.

Globally Adaptive Neural Network Output-Feedback Control for Uncertain Nonlinear Systems.

In this article, a globally neural-network-based adaptive control strategy with flat-zone modification is proposed for a class of uncertain output feedback systems with time-varying bounded disturbances. A high-order continuously differentiable switching function is introduced into the filter dynamics to achieve global compensation for uncertain functions, thus further to ensure that all the closed-loop signals are globally uniformity ultimately bounded (GUUB). It is proven that the output tracking error converges to the prespecified neighborhood of the origin. The effectiveness of the proposed control method is verified by two simulation examples.

Finite‐time adaptive fuzzy tracking control for high‐order nonlinear time‐delay systems with dead‐zone

AbstractIn this paper, the adaptive fuzzy finite‐time tracking control problem is studied for a class of non‐strict feedback high‐order time‐delay systems with unknown dead‐zone. The fuzzy logic systems are introduced to approximate the uncertain nonlinear functions in the system. The Lyapunov–Krasovskii (L–K) functional technology is used to compensate for the unknown time delays. In addition, based on the backstepping technique and finite‐time theory, an adaptive fuzzy finite‐time tracking controller is designed to ensure that the closed‐loop system is semi‐global practical finite‐time stability, and the tracking error can converge to a small neighbourhood around the origin within a finite time. Finally, the rationality of the proposed method is verified by simulation results.

Practical aspects of application of artifi cial intelligence in metrology

Artifi cial intelligence as one of the main elements of digital transformation and promising directions of its application in metrology are considered. The main attention is paid to the application of artifi cial neural networks as a part of measuring instruments and measurement systems for obtaining measurement results in cases when the measurement function is unknown, not suffi ciently defi ned or too complicated for algorithmic formalization. More often in practice we meet problems with partially uncertain function, when in addition to the deterministic basis there is an additional unknown component that has a signifi cant impact on the measurement result. A simulation experiment was conducted to solve such a measurement problem using a neural network model. In the experiment, a measurement function with a linear deterministic basis and an additional nonlinear component of about 10 % of the relative standard deviation, that was implied by the unknown when the model was created, was used. The results of the experiment confi rmed the practical possibility and high effi ciency of using artifi cial neural networks to solve such measurement problems. The neural network model in the conditions of a noisy training sample, corresponding to real measurement conditions, almost completely restored the measurement function despite the fact that a linear neural network model was used, and the additional component of the measurement function was nonlinear. In this particular experiment, due to the use of neural network, the accuracy of measurements was improved by about an order of magnitude. Access to the machine code implementing this simulation experiment is provided.

Philostrats ,Briefe‘ – Einheit in der Vielfalt, Vielfalt in der Einheit?

Abstract The complex manuscript tradition of Philostratus’ ‘Letters’ cause a row of problems and uncertainties: it is unclear, for example, which of the several surviving versions of the letter collection is the original one, which sequence of the letters is authorial, which version of some letters that have survived in different lengths is authentic, why some letters differ that much in form and content from others, and, last but not least, if the collection was written by Philostratus at all. These questions seem to pose insurmountable difficulties for the project of a new edition. Therefore, we still rely on editions from the nineteenth century for Philostratus’ ‘Letters’. The question is whether the problems of the formation of the epistolary corpus and the evaluation of its multiple versions can be explained by traditional textual criticism. I argue that a codicological, palaeographical, and historical examination of the individual textual witnesses could shed new light on the open research questions by focusing on the overall context, position, and function of Philostratus’ ‘Letters’ in each manuscript. At the same time, research on the still uncertain purpose and function of the ‘Letters’ could possibly contribute to understand the mechanisms of ( manuscript ) tradition of the corpus.

Driving mode analysis—How uncertain functional inputs propagate to an output

AbstractDriving mode analysis elucidates how correlated features of uncertain functional inputs jointly propagate to produce uncertainty in the output of a computation. Uncertain input functions are decomposed into three terms: the mean functions, a zero‐mean driving mode, and zero‐mean residual. The random driving mode varies along a single direction, having fixed functional shape and random scale. It is uncorrelated with the residual, and under linear error propagation, it produces an output variance equal to that of the full input uncertainty. Finally, the driving mode best represents how input uncertainties propagate to the output because it minimizes expected squared Mahalanobis distance amongst competitors. These characteristics recommend interpretation of the driving mode as the single‐degree‐of‐freedom component of input uncertainty that drives output uncertainty. We derive the functional driving mode, show its superiority to other seemingly sensible definitions, and demonstrate the utility of driving mode analysis in an application. The application is the simulation of neutron transport in criticality experiments. The uncertain input functions are nuclear data that describe how Pu reacts to bombardment by neutrons. Visualization of the driving mode helps scientists understand what aspects of correlated functional uncertainty have effects that either reinforce or cancel one another in propagating to the output of the simulation.