Time-varying Uncertainties Research Articles

Dissipativity analysis on switched uncertain nonlinear T–S fuzzy Systems with stochastic perturbation and time delay

The problem of dissipativity-based filtering for switched time-delayed Takagi–Sugeno (T–S) fuzzy nonlinear systems is investigated. Stochastic perturbation and state-dependent switching are taken into consideration simultaneously. Firstly, the characterized T–S fuzzy systems and designed fuzzy filtering error dynamic system should be mean-square exponential stability with a (ℵ, ℏ, ℓ)-δ-dissipative. This paper dedicates effort to stabilization analysis of continuous T–S fuzzy systems, diminishing the conservatism of stability conditions by means of constructing non-common Lyapunov–Krasovskii functional and employing linear matrix inequalities (LMIs). Secondly, the dissipative control problem for T–S fuzzy stochastic system with time-varying delay and uncertainties via state-dependent switching will be dealt with. Thirdly, Sufficient conditions are proposed to guarantee that the filter-based dynamical error system with time delays and uncertainties is mean-square exponentially stable through dissipativity analysis. Numerical simulation results demonstrate availability and effectiveness of the developed design scheme.

A Rectified Reiterative Sieved-Pollaczek Polynomials Neural Network Backstepping Control with Improved Fish School Search for Motor Drive System

As the six-phase squirrel cage copper rotor induction motor has some nonlinear characteristics, such as nonlinear friction, nonsymmetric torque, wind stray torque, external load torque, and time-varying uncertainties, better control performances cannot be achieved by utilizing general linear controllers. The snug backstepping control with sliding switching function for controlling the motion of a six-phase squirrel cage copper rotor induction motor drive system is proposed to reduce nonlinear uncertainty effects. However, the previously proposed control results in high chattering on nonlinear system effects and overtorque on matched uncertainties. So as to reduce the immense chattering situation, we then put forward the rectified reiterative sieved-Pollaczek polynomials neural network backstepping control with an improved fish school search method to estimate the external bundled torque uncertainties and to recoup the smallest reorganized error of the evaluated rule. In the light of Lyapunov stability, the online parametric training method of the rectified reiterative sieved-Pollaczek polynomials neural network can be derived by utilizing an adaptive rule. Moreover, to improve convergence and obtain beneficial learning manifestation, the improved fish school search algorithm is made use of to readjust two fickle learning rates of the weights in the rectified reiterative sieved-Pollaczek polynomials neural network. Lastly, the effectuality of the proposed control system is validated by examination results.

Adaptive Type-2 Fuzzy Neural-Network Control for Teleoperation Systems With Delay and Uncertainties

Interacting with human operators, remote environment, and communication networks, teleoperation systems are considerably suffering from complexities and uncertainties. Managing these is of paramount importance for safe and smooth performance of teleoperation systems. Among the countless solutions developed by researchers, type-2 fuzzy (T2F) algorithms have shown an outstanding performance in modeling complex systems and tackling uncertainties. Moreover, artificial neural networks (NNs) are well known for their adaptive learning potentials. This article proposes an adaptive interval type-2 fuzzy neural-network control scheme for teleoperation systems with time-varying delays and uncertainties. The T2F models are developed based on the experimental data collected from a teleoperation setup over a local computer network. However, the resulted controller is evaluated on an intercontinental communication network through the Internet between Australia and Scotland. Moreover, the slave robot and the remote workspace are completely different and unforeseen. Stability and performance of the proposed control is analyzed by Lyapunov–Krasovskii method. Comprehensive comparative studies demonstrate that the proposed controller outperforms traditional techniques in experimental evaluations.

A time-variant uncertainty propagation analysis method based on a new technique for simulating non-Gaussian stochastic processes

In this paper, the time-variant uncertainty propagation analysis is defined to solve the output stochastic process of a time-variant function with uncertainty. And a time-variant uncertainty propagation analysis method is constructed with the combination of an extended orthogonal series expansion method (extended OSE) and sparse grid numerical integration (SGNI). The SGNI serving as a classical uncertainty propagation method is utilized here to solve the moments and autocorrelation function at discrete time points of the time-variant performance function. And the extended OSE is proposed to simulate the output stochastic process based on the results from SGNI. By extended OSE, a non-Gaussian stochastic process is represented as the sumof orthogonal time functions with random coefficients, and these coefficients can be directly obtained by discretization of the target process. For these coefficients are correlated and non-Gaussian, the correlated polynomial chaos expansion method (c-PCE) is presented to represent them in terms of correlated standard Gaussian variables, and then the principal component analysis (PCA) is adopted to transform them into independent ones with dimension reduction. Finally we can obtain an explicit expression to represent the non-Gaussian process whatever it is stationary or non-stationary. Three illustrative examples are used to verify the performance of the extended OSE. In addition, two engineering problems are investigated to demonstrate the effectiveness of the time-variant uncertainty propagation method.

Convergent upper bounds of peak response of LTI and polytopic LTV systems through LMIs

This paper addresses the problem of determining the response peak of dynamical systems, a classical problem in control systems. The paper starts by considering the impulse response of linear time-invariant (LTI) systems. A linear matrix inequality (LMI) condition for establishing upper bounds of the sought peak is proposed by embedding the trajectory onto the level set of a polynomial and by introducing a projection technique for evaluating the extension of this set. This condition is sufficient for any degree of the polynomial, which has to be chosen a priori, and is also necessary whenever this degree is large enough. Hence, the proposed methodology is extended to address the impulse response of polytopic linear time-varying (LTV) systems, in particular, linear systems affected linearly by structured time-varying uncertainty constrained into a polytope. Lastly, generalizations to various responses and specializations to some structures are also presented. As shown by several examples, which include randomly generated systems and physical systems, the proposed conditions may provide significantly less conservative results than the existing LMI methods.

A Fully Distributed Protocol for Flocking of Time-Varying Linear Systems With Dynamic Leader and External Disturbance

This article studies the flocking problem of multiagent systems (MASs) with a dynamic virtual leader (VL) for the linear systems subject to time-varying uncertainties and external disturbance problems. We assume that the agents follow a leader with a bounded acceleration, which information is sensed only by the informed agents. We assign an adaptive estimator to each uninformed agent to estimate the velocity of the leader. By deriving a lemma and using a standard adaptive law, we design a continuous adaptive controller for solving the problem under the mentioned challenges, which is also fully distributed. The designed flocking control ensures that the velocity of followers asymptotically is converged to that of the VL. Also, the agents’ network remains connected, and no collision occurs among agents. Finally, we present a simulation that illustrates the validity of the results.

Robust control for one‐sided Lipschitz non‐linear systems with time‐varying delays and uncertainties

For a class of one-sided Lipschitz systems with time-varying delays and parameter uncertainties, the robust control problem of the system based on state observer is elaborated in detail. By constructing Lyapunov–Krasovskii functional for closed-loop augmented system and combining one-sided Lipschitz condition and quadratically inner-bounded condition, the synthesis condition of observer design is derived, which makes the closed-loop augmented system asymptotically stable and satisfies the H ∞ performance index. Furthermore, bilinear matrix inequalities are transformed into a set of linear matrix inequalities by means of some special derivatives, which can be solved in one step. By using the mature Matlab LMI toolbox, the inequality is solved, thus the gain matrices of the controller and the observer are obtained at the same time. Finally, numerical examples are used to verify the correctness and superiority of the proposed theory.

Global robust super-twisting algorithm with adaptive switching gains for a hybrid robot

To improve the robustness performance of dynamic sliding mode control to the time-varying uncertainties without the upper bound information in a hybrid robot system, a global robust super-twisting algorithm with adaptive switching gains is proposed. The main contributions are as follows: (1) for the problem that the robustness of the sliding mode control system is not guaranteed in the reaching phase, a global robust sliding surface is designed to eliminate the reaching phase of the sliding mode control; (2) for the chattering problem existing in the sliding phase of the sliding mode control system due to the conservative selection of switching gains, based on a reconstructive super-twisting sliding mode control and the equivalent principle, a fast-adaptive law is designed to effectively reduce the chattering while the global robustness is ensured. The stability of the proposed algorithm is proved by Lyapunov stability theorem. The simulation and experiment on the hybrid robot prototype system are implemented to verify the effectiveness of the proposed control method.

Causal relationships between inflation and inflation uncertainty

Abstract Since the publication of Friedman’s (1977) Nobel lecture, the relationships between the mean function of the inflation stochastic process and its uncertainty, and between inflation uncertainty (IU) and real output growth have been the subject of much research, with some studies justifying this causality and some reaching the opposite conclusion or finding an inverse correlation between mean inflation and inflation volatility with causation in either direction. We conduct a systematic econometric study of the relationships between the first two moments of the inflation stochastic process and between IU and output growth using state-of-the-art approaches and proposes a time-varying inflation uncertainty measure based on stochastic volatility to consider unpredictable shocks. Further, we extend the literature by providing a new econometric specification of this relationship using two semi-parametric approaches: the frequency evolutionary co-spectral approach and continuous wavelet methodology. We theoretically justify their use through an extension of Ball’s (1992) model. These frequency approaches have two advantages: they provide the analyses for different frequency horizons and do not impose restriction on the data. While the literature focused on the US data, our study explores these relationships for five major developed and emerging countries/regions (the US, the UK, the euro area, South Africa, and China) over the past five decades to investigate the robustness of our inferences and sources of inconsistencies among prior studies. This selection of countries permits investigation of the inflation versus inflation uncertainty relationship under different hypotheses, including explicit versus implicit inflation targets, conventional versus unconventional monetary policy, independent versus dependent central banks, and calm versus crisis periods. Our findings show a significant relationship between inflation and inflation uncertainty, which varies over time and frequency, and offer an improved comprehension of this ambiguous relationship. The relationship is positive in the short and medium terms during stable periods, confirming the Friedman–Ball theory, and negative during crisis periods. Additionally, our analysis identifies the phases of leading and lagging inflation uncertainty. Our general approach nests within it the earlier approaches, permitting explanation of the prior appearances of ambiguity in the relationship and identifies the conditions associated with the various outcomes.

Robust adaptive sliding mode control of a MEMS tunable capacitor based on dead-zone method

Uncertainty in parameters of a tunable Micro Electro Mechanical System (MEMS) capacitor, as the main component of AC Voltage Reference Source (VRS), is significant to obtain a precise output voltage unaffected by disturbance and noise. Although attempts are done to craft the capacitor with desired physical specification and improve accuracy of parameters, parametric uncertainties transpire in manufacturing due to micro-machining shortcomings. First off, this paper remarks design of a Robust Adaptive Sliding Mode Controller (RASMC) and its application for the MEMS AC VRS for the first time so that it can produce a stable precise regulated output at presence of uncertainties and disturbance. Secondly, it makes a comparison between the proposed novel controller and our previously designed ASMC. The comparison reassures one of robustness at exacerbating conditions in the tunable capacitor dynamics. The novelty is employment of the dead zone-based ASMC to manage parametric uncertainty and disturbance in the MEMS tunable capacitor. It also contributes to adaptive sliding mode control of the dynamics with stiffness and damping coefficients, which are non-slowly-varying time-dependent parameters, approaching dead-zone method. Uncertainty in the plate mass besides bounded time-variant uncertainty in stiffness and damping are considered. These restrictions were not deemed in the previous design.

Oil price uncertainty and U.S. employment growth

This paper studies the effects of oil price changes on U.S. aggregate and sectoral employment growth in the presence of time-varying oil price uncertainty. We estimate a bivariate GARCH-in-Mean VAR model using U.S. monthly data of oil prices and employment growth for the period 1974 m2:2018 m11. Based on the results, we show that an increase in oil prices reduces total employment growth and that in most private sectors, but the public sector is largely unaffected. The effects on employment growth in various ”hub” sectors are also different. Furthermore, employment growths at both aggregate and disaggregate levels respond asymmetrically to positive and negative oil price shocks, which could possibly be attributed to oil price uncertainty. This asymmetric impact is more evident when the model is estimated on the entire sample than on the 1970s sample, implying that the role of oil price uncertainty in accounting for variations in employment growth can differ over time. These findings underline the empirical relevance of oil price uncertainty for the U.S. labor market dynamics. • A theoretical model is developed to illustrate the relation between oil price uncertainty and employment. • A GARCH-in-mean-VAR model is estimated to empirically explore the effects of oil price changes on U.S. employment growth. • Oil price shocks have negative impact on employment growth in most sectors, but the public sector is largely unaffected. • Employment growth responds asymmetrically to oil price shocks, possibly attributed to oil price uncertainty.

Efficient time-variant reliability analysis through approximating the most probable point trajectory

Time-variant reliability analysis (TRA) is widely utilized to assess the performance of engineering structures under various time-variant uncertainties. Recently, the time discretization-based TRA (TDTRA) methods have been developed, which can achieve satisfactory accuracy but need to excessively perform most probable point (MPP) searches at many equidistant time instants. To improve the efficiency of TDTRA, this paper proposes a TRA method based on approximating the MPP trajectory, referred to as AMPPT. First, this paper introduces a new concept of the MPP trajectory (MPPT), which is defined as the moving path of the MPP in the U-space when time changes. Then, a one-dimensional Kriging model is constructed to approximate the MPPT by the adaptive sampling method, which only performs MPP searches at several critical time instants. To further improve the computational efficiency, a warm-starting strategy is proposed to accelerate the MPP search. Then, the approximated MPPT is employed to transform the time-variant response into an equivalent Gaussian process. Finally, the spectral decomposition method and Monte Carlo simulation are used to compute the time-variant reliability. Comparative studies on four numerical examples and one practical engineering example of the solid rocket engine shell verify that the proposed AMPPT outperforms TDTRA in terms of both accuracy and efficiency. Test results also indicate that the efficiency gain of the proposed AMPPT comes from not only the reduction in the number of MPP searches but also the acceleration of the MPP search itself.

Quasi-time-dependent robust [formula omitted] static output feedback control for uncertain discrete-time switched systems with mode-dependent persistent dwell-time

This paper is concerned with the problem of robust H∞ static output feedback control for a class of uncertain discrete-time switched systems under mode-dependent persistent dwell-time (MPDT) switching scheme. The interested systems are described by the classical polytopic-type uncertain model with time-varying parametric uncertainties. The purpose of this paper is to design a static output feedback controller that ensures the resulting closed-loop system robustly globally uniformly asymptotically stable (GUAS) with a specified H∞ performance under MPDT switching. By using a quasi-time-dependent (QTD) and parameter-dependent switched Lyapunov-like function suitable to MPDT switching, the sufficient conditions for stability criterion and H∞ performance analysis are established. Furthermore, a set of QTD switched static output feedback controllers for the polytopic-type uncertain discrete-time switched system with MPDT are first designed. Finally, the effectiveness and potential of the proposed approaches is demonstrated by a water-quality control system.

Receptance-based robust stability criteria for second-order linear systems with time-varying delay and unstructured uncertainties

This paper presents new frequency domain criteria for the robust stability analysis of closed-loop second-order systems under time-varying internal delay. The proposed approach is derived from the small gain theorem for systems described by the versatile system receptance to guarantee robust stability despite time-varying delays and model uncertainties. Robust stability of systems with time-varying delays is challenging to cope because time-invariant paradigm does not hold, but the proposed approach is directly based on the frequency response analysis of the closed-loop system with unstructured uncertainty bound. The criteria can be applied to either single or multiple inputs systems, and no constraint is imposed on the delay derivative. A simple receptance-based Internal Model Control strategy is proposed to improve robust stability margins while nominal state-feedback design is preserved. Thus, a controller obtained from the delay-free nominal model can be used to ensure the robust stability of the uncertain second-order system with time-varying delay. Simulation case studies are used to illustrate the benefits of the proposed criteria.

High penetrated renewable energy sources‐based AOMPC for microgrid's frequency regulation during weather changes, time‐varying parameters and generation unit collapse

Using inverter-based topologies and lack of rotational masses can lead to a noticeable reduction in the inertia of modern systems and have detrimental effects on the resiliency, stability and strengths of microgrids. Effective frequency control ancillary services and modern adaptive control mechanisms can be proposed to resolve the mentioned challenges practically. From this perspective, several flexible and intelligent control approaches have been recently introduced to create a balance between generation and load demand during various operational conditions in low-inertia power systems. This study suggests a supportive collaboration between two distributed generations including virtual inertia of wind turbine generator and fast speed micro-turbine based on an adaptive optimal model predictive control (AOMPC). To demonstrate the effectiveness of the proposed framework, the results are compared with the previous controllers like optimal proportional–integral, optimal fractional order proportional–integral–derivative (PID), optimal fuzzy PID, the optimised membership function of fuzzy and adaptive MPC controller during multiple load variations, changes in the weather patterns, unwanted time-varying uncertainties and collapse of power generation units.

A novel grey decision-DE optimized internal model controller for vibration control of nonlinear uncertain aeroelastic blade system

In this paper, a novel grey decision-differential evolution (GD-DE) optimized internal model controller is proposed for the control of nonlinear aeroelastic blade system (ABS) under time-varying uncertainties and control saturations. Two-port internal model control structure is presented for saturation compensation. The filter parameter of the controller is optimally tuned by proposed GD-DE algorithm, which is designed based on the grey decision incidence theory and differential evolution algorithm. The superiority of GD-DE optimized tuning technique is verified, compared to conventional IMC tuning method and other evolutionary algorithm based techniques. The robustness is analysed by comprehensive simulations from time-invariant uncertainties to large periodic or random time-varying uncertainties. The realistic condition with input/output disturbances is also involved. Simulation results show that the proposed controller outperforms existing adaptive IMC controller and other advanced controllers with greatly improved dynamic performance, stronger robustness and better saturation compensation on various conditions.

Adaptive compensation for time-varying uncertainties in model-based control of lower-limb exoskeleton systems

Adaptive compensation for time-varying uncertainties in model-based control of lower-limb exoskeleton systems

NESO-Based Path Following Control for Underactuated Hovercrafts with Unknown Nonlinear Uncertainties and a Safety Limit Constraint

In this brief, the path following control problem of underactuated hovercrafts subject to nonlinear time-varying uncertainties and a safety limit constraint (SLC) is addressed. A novel homogenous nonlinear extended state observer (NESO)-based safe motion controller for a path following control scenario of underactuated hovercrafts is proposed. First, a NESO is constructed to estimate and compensate the nonlinear time-varying uncertainties for the underactuated hovercraft. Then, a NESO-based backstepping sliding mode control (BSMC) law with a turning SLC is proposed to achieve the yaw control for underactuated hovercrafts, which improves both safety and maneuverability of the underactuated hovercraft during the path following control scenario. The nonlinear time-varying turning SLC is first directly taken into the control system design, which is achieved by introducing an auxiliary dynamic system to limit the virtual input control during the backstepping design process. A NESO-based backstepping surge control law is also designed to achieve the surge control for underactuated hovercrafts. Furthermore, all error signals of the proposed closed-loop control system are proven to be bounded. Finally, an application case is tested on an underactuated hovercraft to illustrate the effectiveness and superiority of the designed control scheme.

Robust H∞ Pinning Synchronization for Complex Networks With Event-Triggered Communication Scheme

This paper investigates the issue of global robust ${H_\infty }$ pinning synchronization for a class of complex networks with sampled-data-based event-triggered communication via a pinning control approach. The complex network is subject to network-induced time-varying delays, parametric uncertainties and external disturbances. A directed and weighted communication topology is taken into account, and the phenomenon of uncertainties is reflected in both modelling and inner coupling matrices. In order to save communication resources, a new and practical event-triggered communication mechanism with an asynchronous sampling manner is developed, with which the Zeno behaviour can be absolutely avoided. Then, based on the presented event-triggered strategy, a pinning control protocol is proposed to reduce the frequency of controller updates and the computational burden. The problems on the minimal number and which of the nodes should be chosen are addressed. By Lyapunov stability theory, sufficient conditions are deduced to ensure the underlying network achieves global robust ${H_\infty }$ pinning synchronization. Finally, numerical examples are provided to verify the effectiveness of the new design techniques.

Adaptive robust control for tank stability: A constraint-following approach

This article addresses a control problem for tank stability based on constraint following. The objective is to design a control to drive the tank stability control system to follow a pre-specified stability constraint approximately: with the consideration of (possibly) time-varying uncertainty (including system modeling error and road excitation), if the barrel deviates from the target angle, drive it to be arbitrarily close to the target angle; and if the barrel points to the target angle, drive it to stay there. This is formulated as a problem of approximate constraint-following control. First, as the model-based control design object, the dynamic equation of the tank stability control system with the system modeling error and the road excitation is obtained. Second, as the control objective, the stability constraint is formulated. Third, as the control strategy, an adaptive robust control is proposed for approximate constraint following. Fourth, as the control object, a virtual prototype model of tank driving on bumpy road is established with multi-body dynamics software RecurDyn. Finally, real-time servo control and target observation of the tank stability system are performed by co-simulation. It shows that the constraint-following error converges quickly to [Formula: see text] in 1.5 s. By this, the tank stability control system can be always stable even if the tank is driving and disturbed with frequent road excitation.