Uncertain Function Research Articles

An interval uncertain optimization method using back-propagation neural network differentiation

An interval uncertain optimization method is proposed for engineering uncertain optimization problems. The first-order derivative information may be unavailable in practical engineering systems. To overcome this drawback, the method to calculate the first-order partial derivatives with a back-propagation neural network is investigated, and a numerical example is presented to demonstrate its fine precision. In the optimization process, the back-propagation neural network and its first-order derivatives are introduced into the interval perturbation method and combined with the subinterval method, the extrema of the uncertain objective function and uncertain constraints can be approximated without much computational cost. Thus the most challenging problem in current interval optimization, namely low optimization efficiency caused by nested optimization can be solved to a certain extent. A two-bar structure system is adopted to validate its fine precision and high computational efficiency in interval bounds estimation. Based on the interval order relation and interval possibility degree model, an interval uncertain optimization model can be transformed into a deterministic optimization model, and be solved by some auxiliary optimization algorithm. A numerical example and an engineering application have indicated that this method is efficient for uncertain optimization problems.

EKF-Neural Network Observer Based Type-2 Fuzzy Control of Autonomous Vehicles

This paper proposes a novel robust path-following strategy for autonomous road vehicles based on type-2 fuzzy PID neural network (PIDT2FNN) method coupled to an Extended Kalman Filter-based Fuzzy Neural Network (EKFNN) observer. Uncertain Gaussian membership functions (MFs) are employed to self-adjust the universe of discourse for MFs using the adaptation mechanism derived from Lyapunov stability theory and Barbalat's lemma. External disturbances are significant in autonomous vehicles by changing the driving condition. Furthermore, parametric uncertainties related to the physical limits of tires and the change of the vehicle mass may significantly affect the desired performance of autonomous vehicles. The robustness of the proposed controller against the parametric uncertainties and external disturbances is compared with one active disturbance rejection control (ADRC) algorithm, and a linear-quadratic tracking (LQT) method. The obtained results in terms of the maximum error and root mean square error (RMSE), demonstrate the effectiveness of the proposed control algorithm to reach the minimized path-tracking error.

A class of multi-parametric quadratic program with an uncertain objective function

In this paper we analyze a class of multi-parametric quadratic program (mpQP) with parameters in the objective function. Except for parameters in coefficients associated with the linear term, the coefficient of the quadratic term, which is a positive definite matrix, is multiplied by a scalar parameter, while the quadratic coefficient of a standard mpQP is deterministic. We reveal the optimal solution is a linear fractional function in the parameters, and the critical regions remain polyhedral. The discussed mpQP can be reformulated as a standard mpQP via variable and parameter transformations. The proposed method is used to evaluate the economic operation of a residential energy system under time-and-level-of-use electricity pricing, highlighting the potential application in practical problems.

Making Functional Predictions Using Local Spatial Arrangements in the Haloacid Dehalogenase Superfamily

Beginning with the sequencing of the human genome in the 1990s, major efforts have been underway to expand significantly upon our current working knowledge of proteins. Between the years 2000–2015, the Protein Structure Initiative (PSI) solved 15,000+ protein structures, but most of them have unknown or uncertain biochemical function or have an incorrect assigned putative function. With all these structures, methodology must be developed to functionally annotate these proteins in order to identify potential applications, such as bioremediation and understanding cellular processes. Enzymes in the Haloacid Dehalogenase Superfamily (HADSF) possess a wide range of functions, including phosphatases important in cell membrane biosynthesis and dehalogenases that possesses the ability to detoxify and degrade halogenated compounds. The Ondrechen Research Group (ORG) at Northeastern University has successfully developed methodology that is being used to predict biochemical function for Structural Genomics (SG) proteins in the HADSF. These methods are Partial Order Optimum Likelihood (POOL) and Structurally Aligned Local Sites of Activity (SALSA). POOL is a machine learning method that uses the electrostatic features and metrics from THEoreticalMicroscope Anomalous TItration Curve Shapes (THEMATICS), ligand binding pocket and geometric features from ConCavity, and the evolutionary scores and phylogenetic trees from INformation‐theoretic TREe traversal for Protein functional site IDentification (INTREPID) to make the predictions about which residues are catalytically active or otherwise important for protein function. SALSA uses the functional residue predictions for SG proteins obtained from POOL and aligns them with consensus signatures from known enzyme subfamilies according to the local spatial arrangement of predicted residues at the active site. So far for the HAD superfamily, using SALSA we have made predictions for 20 SG proteins: one dehalogenase, eight sugar phosphatases, three NagD‐like phosphatases, four P‐Type ATPases, and four soluble epoxide hydrolases. These predictions will be experimentally validated by biochemical assays to establish the function of each protein and to verify our computational approach to protein function prediction. The ability to predict computationally the biochemical function of protein structures of unknown or uncertain function adds tremendous value to genomics data.Support or Funding InformationThis project is funded by NSF CHE‐1305655, CHE‐1905214, and CHE‐1757078.

Adaptive Backstepping Hybrid Fuzzy Sliding Mode Control for Uncertain Fractional-Order Nonlinear Systems Based on Finite-Time Scheme

A fractional-order integral fuzzy sliding mode control scheme is proposed for a class of uncertain fractional-order nonlinear systems subject to uncertainties and external disturbances. First, in each step, a neuro-fuzzy network system is developed to approximate the uncertain nonlinear function existing in fractional-subsystem and a fractional sliding mode surface is presented. Second, based on the fractional Lyapunov stability theory and the finite-time stability theory, a fractional adaptive backstepping neuro-fuzzy sliding mode controller is designed to drive the state trajectories of fractional-order systems to the prescribed sliding mode surface. Meanwhile, the finite-time stability of the fractional-order closed-loop system is proved. At last, three numerical examples are given to illustrate the effectiveness of the proposed control method.

P23 Adult onset Still’s disease as a novel autoimmune complication of alemtuzumab therapy: a case report and review of alemtuzumab associated autoimmune disease

Abstract Background Alemtuzumab is a monoclonal antibody targeted to CD52, an antigen of uncertain function on T and B lymphocytes. Alemtuzumab is an established treatment for active relapsing and remitting multiple sclerosis (MS). However, autoimmune disease (AID) is being increasingly recognised as a highly prevalent adverse effect of alemtuzumab treatment. Methods We describe a case of adult onset Still’s disease (AOSD) developing in a patient six months after alemtuzumab therapy, highlighting the need for awareness of the risk of AID in those who develop symptoms after alemtuzumab treatment, some of which can be potentially life-threatening. Results Our patient, a 37 year old female, was admitted to hospital with a three week history of fevers up to 39ºC, a flitting macular rash, sore throat and polyarthritis, neutrophils 35.2x109/L (2-7.5), ferritin 8349 ug/L (normal 15-150), ALP 151 U/L (25-105). She had a history of relapsing and remitting multiple sclerosis, that went into remission after treatment with alemtuzumab six months previously. Despite 72 hours of broad-spectrum intravenous antibiotics, fever and symptoms were unchanged. Immunology and microbiology tests were negative. CT scan of neck, chest abdomen and pelvis were unremarkable. A diagnosis of AOSD was made. She received prednisolone at 40mg daily and symptoms rapidly settled. By day three of prednisolone, ferritin had fallen to 3238, neutrophil count had halved, and ALP normalised. She continues on slow weaning of steroids and remains asymptomatic. Conclusion Alemtuzumab was approved in 2013 as a treatment for active relapsing and remitting MS. Treatment consists of two courses of ‘induction’ treatment 12 months apart, aiming to deplete T and B lymphocytes, with subsequent lymphocyte repopulation. Without requirement for continued ‘maintainance’ treatment, efficacy of alemtuzumab persists for years. The most common alemtuzumab associated AID are thyroid disease, nephropathies and immune thrombocytopenia. However, other AID has been reported, including sarcoidosis. To date, no reports exist describing AOSD post alemtuzumab therapy. Although lymphocyte reconstitution post alemtuzumab is thought to account for its therapeutic effects, this same reconstitution is postulated to contribute to AID. Baker et. al. postulated that rapid re-population of B lymphocytes and slower re-population of regulatory T lymphocytes may trigger B cell mediated AID. Further, rapid repopulation of immature B cells post alemtuzumab is associated with raised serum B cell activating factor (BAFF), which remains elevated for at least a year post treatment. BAFF has been recognised in multiple animal studies to be associated with antibody mediated AID. The hypothesis that B cells play a key role in alemtuzumab related AID may be supported by the success of rituximab in treating 2 cases of alemtuzumab associated AID. The possible critical role of B cells in the pathogenesis of alemtuzumab related AID could indicate a future treatment strategy for such AID. Disclosures N. Narayan None. G. Mazibrada None. N. Amft None.

Design of Robust Adaptive Fuzzy Controller for a Class of Single-Input Single-Output (SISO) Uncertain Nonlinear Systems

In order to solve the precision and stability control problems of nonlinear uncertain systems applied in machining systems, in this paper, a robust adaptive fuzzy control technique based on Dynamic Surface Control (DSC) method is proposed for the generalized single-input single-output (SISO) uncertain nonlinear system. A first-order low-pass filter is introduced in each step of the traditional robust control method to overcome the “calculation expansion” problem, and Takagi–Sugeno (T-S) fuzzy logic system is applied to approximate an uncertain nonlinear function of unknown structure in the system. The designed robust adaptive fuzzy controller is applied to the 3D elliptical vibration cutting (3D EVC) device system model, and the effectiveness of the controller design is verified by analysis of position tracking, speed tracking, and tracking error. The results of studies show that the robust adaptive fuzzy controller can effectively suppress the jitter problem of the three-dimensional elliptical vibration cutting device so that the control object can be stabilized quickly even if it has a little jitter at the beginning. It can be smoothed to move along the ideal displacement and velocity signals. It is verified that the designed controller has strong robust adaptability.

Neuroadaptive finite-time output feedback control for PMSM stochastic nonlinear systems with iron losses via dynamic surface technique

In this paper, an observer-based adaptive neural network finite-time dynamic surface control method is proposed for the position tracking control of PMSM stochastic nonlinear systems with iron losses. First, the finite-time technology is used to realize the fast and effective tracking of the desired signal and make the system have better robust performance. Then, the adaptive neural network (NN) technology and state observer are applied to approximating the uncertain nonlinear functions and estimating the immeasurable states, respectively. And, the dynamic surface control (DSC) technology is used to resolve the “explosion of complexity” problem. In addition, the influence of iron losses and stochastic disturbances in the system is considered, and a quartic stochastic Lyapunov function is established to analyze the stability of the system. Finally, the simulation results show the effectiveness of the proposed method.

Time-varying formation tracking control for high-order nonlinear multi-agent systems in fixed-time framework

In this paper, we investigate the time-varying formation tracking control (TVFTC) problem for high-order uncertain nonlinear multi-agent systems (MASs) with a dynamic leader. Both unknown disturbances and uncertain nonlinear functions are considered. A novel fixed-time TVFTC strategy is proposed with two steps, which can avoid the communication loop problem. Firstly, a distributed fixed-time observer (DFTO) for the directed graph is introduced, such that the leader’s information can be accurately obtained by each agent within a bounded time. Secondly, by using fixed-time technique, a Lyapunov-function-based design process has been schemed to avoid the singularity problem. The developed TVFTC protocols can ensure all the followers achieve the desired time-varying formation and track the leader simultaneously. Furthermore, according to practical requirements, the configuration of formation can be chosen as arbitrary shape and the corresponding convergence time is allowed to be pre-estimated or preset. Stability analysis and some simulation examples for the control strategy are given, which further verify the validity.

Adaptive control of electrically‐driven nonholonomic wheeled mobile robots: Taylor series‐based approach with guaranteed asymptotic stability

ABSTRACTTaking advantage of an adaptive Taylor series approximator, this research seeks to address a two‐loop robust controller for electrically‐driven differential drive wheeled mobile robots. A fictitious current signal is designed in the outer loop such that the good tracking performance as well as the asymptotic stability of system will be achieved. Also, the error of currents will be minimized by an actual control input in the inner loop. For both inner/outer loops, uncertain nonlinear functions can be approximated by adaptive Taylor series systems. To validate the proposed control algorithm, numerous simulations have been carried out with two different desired trajectories and multiple initial conditions. Also, the proposed controller is compared with a recent well‐designed robust adaptive fuzzy controller. In addition, to simplify the procedure of mathematical modelling of a wheeled mobile robot, the “Simscape Multibody” environment of “MATLAB” is used for 3D simulations.

Stabilization of a class of nonlinear uncertain ordinary differential equation by parabolic partial differential equation controller

SummaryThis article is concerned with stabilization for a class of uncertain nonlinear ordinary differential equation (ODE) with dynamic controller governed by linear 1−d heat partial differential equation (PDE). The control input acts at the one boundary of the heat's controller domain and the second boundary injects a Dirichlet term in ODE plant. The main contribution of this article is the use of the recent infinite‐dimensional backstepping design for state feedback stabilization design of coupled PDE‐ODE systems, to stabilize exponentially the nonlinear uncertain systems, under the restrictions that (a) the right‐hand side of the ODE equation has the classical particular form: linear controllable part with an additive nonlinear uncertain function satisfying lower triangular linear growth condition, and (b) the length of the PDE domain has to be restricted. We solve the stabilization problem despite the fact that all known backstepping transformation in the literature cannot decouple the PDE and the ODE subsystems. Such difficulty is due to the presence of a nonlinear uncertain term in the ODE system. This is done by introducing a new globally exponentially stable target system for which the PDE and ODE subsystems are strongly coupled. Finally, an example is given to illustrate the design procedure of the proposed method.

Approximation‐based adaptive fault compensation backstepping control of fractional‐order nonlinear systems: An output‐feedback scheme

SummaryAn observer‐based adaptive fuzzy backstepping approach is proposed for nonlinear systems with respect to fractional‐order differential equations, unmatched uncertainties, unmeasured states, and actuator faults. The approximation capability of fuzzy logic system and minimal learning parameter approaches are applied to identify uncertain functions in a simultaneous manner. For estimating the unavailable conditions, a fuzzy fractional‐order state‐observer is extended. Applying fault‐tolerant approach in a backstepping design methodology would provide a new fault‐tolerant adaptive fuzzy output‐feedback approach for fractional‐order strict‐feedback systems. This control structure would assure the considered system stability through selection of the appropriate Lyapunov candidate function. Two numerical simulations are run to exhibit the validity herein.

Towards Efficient Robust Optimization using Data based Optimal Segmentation of Uncertain Space

Performing multi-objective optimization under uncertainty is a common requirement in industries and academia. Robust optimization (RO) is considered as an efficient and tractable approach provided one has access to behavioral data for the uncertain parameters. However, solutions of RO may be far from the real solution and less reliable due to inability to map the uncertain space accurately, especially when the data appears discontinuous and scattered in the uncertain domain. Amalgamating machine learning algorithms with RO, this paper proposes a data-driven methodology, where a novel fuzzy clustering mechanism is implemented along-with boundary construction, to transcript the uncertain space such that the specific regions of uncertainty are identified. Subsequently, using intelligent Sobol sampling, samples are generated in the mapped uncertain regions. Results of two test cases are presented along with a comprehensive comparison study. Considered case-studies include highly nonlinear model for continuous casting process from steelmaking industries, where a multi-objective optimization problem under uncertainty is solved to balance the conflict between productivity and energy consumption. The Pareto-optimal solutions of the resulting RO problem are obtained through Non-Dominated Sorting Genetic Algorithm – II, and ~23–29% improvement is observed in the uncertain objective function. Further, the spread and diversity metrics are enhanced by ~10–95% as compared to those obtained using other standard uncertainty sets.

Adaptive Fuzzy Control for Nonstrict-Feedback Systems Under Asymmetric Time-Varying Full State Constraints Without Feasibility Condition

This article addresses an adaptive fuzzy control for the nonstrict-feedback nonlinear systems with asymmetric time-varying full state constraints. To prevent the state constraints being violated, the nonlinear state-dependent function (NSDF) is introduced instead of the tradition barrier lyapunov function (BLF). The constrained systems are transformed into a novel free-constrained systems based on the NSDF. A direct approach is given to cope with the state constraints. Fuzzy logic system is utilized to approximate the uncertain nonlinear system functions. The new affine variables are constructed for the transformed systems, and the prior knowledge of the control gains is not required necessarily. Under the designed control scheme, the boundedness of the signals in the closed-loop systems is guaranteed certainly, and the asymmetric time-varying constraints are maintained. This proposed method removes the feasibility condition on the virtual controller derived from the method of BLF. The effectiveness of the proposed control strategy is verified by two simulation examples.

A spatial oligopolistic electricity model under uncertain demands

This paper mainly investigates a single-period spatial oligopolistic model of electricity generators under uncertain demands. We maximize the beta -optimistic value of each generator’s uncertain profit function in this game. Emphasis is first put on computing the beta -optimistic value of the uncertain profit function through the inverse uncertainty distribution of the uncertain variable in the inverse demand function. We later focus on transforming the single-period spatial oligopolistic game, which is a generalized Nash equilibrium (short for GNE ) problem, into a variational inequality problem. Then the model is applied to simulate the transmission price of the electricity system of America, which reveals that our model is effective.

Global control for a class of feedforward nonlinear systems with uncertain measurement functions

Based on the nested-saturation technique, this paper investigates the global stabilization problem for a class of upper-triangular nonlinear systems with uncertain measurement functions. By imposing certain assumptions on the uncertain powers, a state-feedback controller, only involving the known parameters, is designed to locally stabilize the nonlinear system. Then, a saturated controller is constructed by combining the nested function and the local stabilizer. With appropriate saturation level, it can be proved that the saturated controller is able to make the closed-loop system globally asymptotically stable. Finally, a simulation example is presented to demonstrate the effectiveness and robustness of the proposed control scheme.

Fuzzy Adaptive Backstepping Control of Nonlinear Uncertain Systems With Unmeasured States and Input Saturation

Considering the uncertainties caused by multiple concurrent complex environments, we investigate the robust adaptive control of multi-source uncertain systems under unmeasurable states and input saturation. For the unmeasurable states caused by sensor faults, a state observer is proposed to provide state estimation values for the controller; for the compound uncertain functions composed of nonlinear uncertain parameters and environmental disturbances, an optimal fuzzy approximation strategy is designed to reproduce these uncertain functions. Finally, the state observer with optimal approximation errors is proved to be stable. Subsequently, the low-pass filter, dynamic surface, and backstepping joint control scheme ensures the robust stability of the uncertain systems, while avoiding the differential explosion caused by disturbances. A series of hierarchical adaptive laws enable the controller to adjust parameters to achieve an optimal tracking of the entire process of time-varying reference output. The compensation algorithm designed with a Nussbaum function solves the problem of input saturation caused by actuator faults. Finally, the nonlinear uncertain systems based on fuzzy adaptive backstepping achieve robust tracking control of time-varying signals. The stability is proved by Lyapunov functions, and the effectiveness of the method simulation is verified using hypersonic vehicle model as an example.

Adaptive Discontinuous Control for Homogeneous Systems Approximated by Neural Networks

This study is devoted to the design of an adaptive discontinuous control based on differential neural networks (DNNs) for a class of uncertain homogeneous systems. The control is based on the universal approximation properties of artificial neural networks (ANNs) applied on a certain class of homogeneous nonlinear functions. The adaptation laws for the DNNs parameters are obtained with the application of the Lyapunov stability theory and the homogeneity properties of the approximated nonlinear system. The stability analysis of the closed loop system with the proposed controller is presented. The estimation error in the approximation of the uncertain homogeneous functions is considered in the stability analysis. The performance of the controller is illustrated by means of a numerical simulation of a homogeneous model.

The salivary protein BPIFA2 differentially regulates sodium preference and blood pressure in male and female mice

AbstractBPIFA2 (PSP, SPLUNC2, C20orf70) is a major salivary protein of uncertain physiological function. BPIFA2 is downregulated in salivary glands of spontaneously hypertensive rats, pointing to a role in blood pressure regulation. This study used a novel Bpifa2 knockout mouse model to test the role of BPIFA2 in sodium preference and blood pressure. Blood pressure did not differ between wild-type male and female mice but was significantly lower in male knockout mice compared to male wild-type mice. In contrast, blood pressure was increased in female knockout mice compared to female wild-type mice. Female wild-type mice showed a significant preference for 0.9% saline compared to male mice. This difference was reduced in the knockout mice. BPIFA2 is an LPS-binding protein but it remains to be determined if the reported effects are mediated by the LPS-binding activity of BPIFA2.

Adaptive Output Feedback Tracking of Nonlinear Time-Delay Systems Subject to Nonsymmetric Dead-Zone Input

In this paper, an output feedback control scheme was proposed to achieve global adaptive output tracking by prescribing arbitrarily small error for a class of dead-zone nonlinear systems including time-delay and uncertain nonlinear functions with unknown output-polynomial growth rate. Two dynamic gains based respectively on identification and non-identification mechanism were introduced in the observer and controller. Picking the appropriate Lyapunov-Krasovskii functional, the constructive proof was given by combining high-gain scaling technique and one-step backstepping method. Finally, two simulation examples showed the effectiveness of the control scheme.