Adaptive Leader-Follower Consensus Control of Multiple Flexible Manipulators With Actuator Failures and Parameter Uncertainties

In this paper,the leader-follower consensus problem for a multiple flexible manipulator network with actuator failures,parameter uncertainties,and unknown time-varying boundary disturbances is addressed.The purpose of this study is to develop distributed controllers utilizing local interactive protocols that not only suppress the vibration of each flexible manipulator but also achieve consensus on joint angle position between actual followers and the virtual leader.Following the accomplishment of the reconstruction of the fault terms and parameter uncertainties,the adaptive neural network method and parameter estimation technique are employed to compensate for unknown items and bounded disturbances.Furthermore,the Lyapunov stability theory is used to demonstrate that followers’angle consensus errors and vibration deflections in closed-loop systems are uniformly ultimately bounded.Finally,the numerical simulation results confirm the efficacy of the proposed controllers.

Solvability Condition for Robust Stabilization Problem of Control Systems with Parameter Uncertainties

Aim The solvability condition for robust stabilization problem associated with a plant family P(s,δ) having parameter uncertainty δ was considered. Methods Using Youla parameterization of the stabilizers this problem was transformed into a strong stabilization problem associated with a related plant family G (s, δ). Results A necessary solvability condition was established in terms of the parity interlacing property of each element in G(s,δ). Another apparently necessary solvability condition is that every element in P(s,δ) must be stabilizable. Conclusion The two conditions will be compared with each other and it will be shown that every element in G(s,δ) possesses parity interlacing property if P(s,δ) is stabilizable.

Robust model-reference control for descriptor linear systems subject to parameter uncertainties

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems： a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

Impacts of parameter uncertainties on deep chlorophyll maximum simulation revealed by the CNOP-P approach

Parameter uncertainty is a primary source of uncertainty in ocean ecosystem simulations.The deep chlorophyll maximum(DCM)is a ubiquitous ecological phenomenon in the ocean.Using a theoretical nutrients-phytoplankton model and the conditional nonlinear optimal perturbation approach related to parameters,we investigated the eff ects of parameter uncertainties on DCM simulations.First,the sensitivity of single parameter was analyzed.The sensitivity ranking of 10 parameters was obtained by analyzing the top four specifi cally.The most sensitive parameter(background turbidity)aff ects the light supply for DCM formation,whereas the other three parameters(nutrient content of phytoplankton,nutrient recycling coeffi cient,and vertical turbulent diff usivity)control nutrient supply.To explore the interactions among diff erent parameters,the sensitivity of multiple parameters was further studied by examining combinations of four parameters.The results show that background turbidity is replaced by the phytoplankton loss rate in the optimal parameter combination.In addition,we found that interactions among these parameters are responsible for such diff erences.Finally,we found that reducing the uncertainties of sensitive parameters could improve DCM simulations remarkably.Compared with the sensitive parameters identifi ed in the single parameter analysis,reducing parameter uncertainties in the optimal combination produced better model performance.This study shows the importance of nonlinear interactions among various parameters in identifying sensitive parameters.In the future,the conditional nonlinear optimal perturbation approach related to parameters,especially optimal parameter combinations,is expected to greatly improve DCM simulations in complex ecosystem models.

Modified robust finite-horizon filter for discrete-time systems with parameter uncertainties and missing measurements

A robust finite-horizon Kalman filter is designed for linear discrete-time systems subject to norm-bounded uncertainties in the modeling parameters and missing measurements.The missing measurements were described by a binary switching sequence satisfying a conditional probability distribution,the commonest cases in engineering,such that the expectation of the measurements could be utilized during the iteration process.To consider the uncertainties in the system model,an upperbound for the estimation error covariance was obtained since its real value was unaccessible.Our filter scheme is on the basis of minimizing the obtained upper bound where we refer to the deduction of a classic Kalman filter thus calculation of the derivatives are avoided.Simulations are presented to illustrate the effectiveness of the proposed approach.

Leader-Following Consensus for Discrete-Time Multi-Agent Systems with Parameter Uncertainties Based on the Event-Triggered Strategy

In this paper, the leader-following consensus for discrete-time nmlti-agent systems with parameter uncertainties is investigated based on the event-triggered strategy. And the parameter un- certainty is assmned to be norm-bounded. A consensus protocol is designed based on the event-triggered strategy to make the multi-agent systems achieve consensus without continuous communication among agents. Each agent only needs to observe its own state to determine its own triggering instants under the triggering function in this paper. In addition, a sufficient condition for the existence of the event- triggered consensus protocol is derived and presented in terms of the linear matrix inequality. Finally, a numerical example is given to illustrate to efficiency of the event-triggered consensus protocol proposed in this paper.

Fuzzy Static Output Feedback H_∞ Control for Nonlinear Systems Subject to Parameter Uncertainties

This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertainties. An interval type-2 fuzzy static output feedback controller is designed to synthesize the interval type-2 T-S fuzzy systems. The membership-function-dependent stability conditions are derived by utilizing the information of upper and lower membership functions. The proposed stability conditions are presented in the form of linear matrix inequalities（LMIs）. LMI-based stability conditions for interval type-2 fuzzy static output feedback H_∞ control synthesis are also developed.Several simulation examples are given to show the superiority of the proposed approach.

Global asymptotic tracking of asymmetrical underactuated surface vessels with parameter uncertainties

In this work, we investigate the tracking control problem of asymmetrical underactuated surface vessels with parameter uncertainties. The tracking error model is first derived via appropriate coordinate transformations, and is considered as a cascade structure composed of two subsystems. The Lyapunov redesign approach is employed to construct the control laws separately to stabilize the two subsystems with unknown model parameters. The cascade system theory is applied to prove the global uniform asymptotic convergence of the state trajectory to the reference one provided the desired yaw velocity is not vanishing. The effectiveness of the proposed control laws is verified by simulation examples.

Impulsive control of permanent magnet synchronous motors with parameters uncertainties

The permanent magnet synchronous motors （PMSMs） may have chaotic behaviours for the uncertain values of parameters or under certain working conditions, which threatens the secure and stable operation of motor-driven. It is important to study methods of controlling or suppressing chaos in PMSMs. In this paper, robust stabilities of PMSM with parameter uncertainties are investigated. After the uncertain matrices which represent the variable system parameters are formulated through matrix analysis, a novel asymptotical stability criterion is established. Some illustrated examples are also given to show the effectiveness of the obtained results.

Robust Cooperative Control of Multiple Autonomous Vehicles for Platoon Formation Considering Parameter Uncertainties

This paper proposes a robust cooperative control strategy for multiple autonomous vehicles to achieve safe and efficient platoon formation,and it analyzes the effects of vehicle stability boundaries and parameter uncertainties.The cooperative vehicle control framework is composed of the upper planning level and lower tracking control level.In the planning level,the trajectory of each vehicle is generated by using the multi-objective flocking algorithm to form the platoon.The parameters of the flocking algorithm are optimized to prevent the vehicle speed and yaw rate from going beyond their limits.In the lower level,to realize the stable platoon formation,a lumped disturbance observer is designed to gain the stable-state reference,and a distributed robust model predictive controller is proposed to achieve the offset-free trajectory tracking while downsizing the effects of parameter uncertainties.The simulation results show the proposed cooperative control strategy can achieve safe and efficient platoon formation.

Robust H_∞ control for aseismic structures with uncertainties in model parameters

This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LM1 toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H∞ strategy, a six-story building was subjected both to the 1940 E1 Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.

A Stable Fuzzy-Based Computational Model and Control for Inductions Motors

In this paper,a stable and adaptive sliding mode control(SMC)method for induction motors is introduced.Determining the parameters of this system has been one of the existing challenges.To solve this challenge,a new self-tuning type-2 fuzzy neural network calculates and updates the control system parameters with a fast mechanism.According to the dynamic changes of the system,in addition to the parameters of the SMC,the parameters of the type-2 fuzzy neural network are also updated online.The conditions for guaranteeing the convergence and stability of the control system are provided.In the simulation part,in order to test the proposed method,several uncertain models and load torque have been applied.Also,the results have been compared to the SMC based on the type-1 fuzzy system,the traditional SMC,and the PI controller.The average RMSE in different scenarios,for type-2 fuzzy SMC,is 0.0311,for type-1 fuzzy SMC is 0.0497,for traditional SMC is 0.0778,and finally for PI controller is 0.0997.

Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters

A dynamics-based adaptive control approach is proposed for a planar dual-arm space robot in the presence of closed-loop constraints and uncertain inertial parameters of the payload. The controller is capable of controlling the po- sition and attitude of both the satellite base and the payload grasped by the manipulator end effectors. The equations of motion in reduced-order form for the constrained system are derived by incorporating the constraint equations in terms of accelerations into Kane＇s equations of the unconstrained system. Model analysis shows that the resulting equations perfectly meet the requirement of adaptive controller design. Consequently, by using an indirect approach, an adaptive control scheme is proposed to accomplish position/attitude trajectory tracking control with the uncertain parameters be- ing estimated on-line. The actuator redundancy due to the closed-loop constraints is utilized to minimize a weighted norm of the joint torques. Global asymptotic stability is proven by using Lyapunov＇s method, and simulation results are also presented to demonstrate the effectiveness of the proposed approach.

Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters

Random dynamic responses caused by the uncertainty of structural parameters of the coupled train-ballasted track-subgrade system under train loading can pose safety concerns to the train operation.This paper introduced a computational model for analyzing probabilistic dynamic responses of three-dimensional(3D)coupled train-ballasted track-subgrade system(TBTSS),where the coupling effects of uncertain rail irregularities,stiffness and damping properties of ballast and subgrade layers were simultaneously considered.The number theoretical method(NTM)was employed to design discrete points for the multi-dimensional stochastic parameters.The time-histories of stochastic dynamic vibrations of the TBSS with systematically uncertain structural parameters were calculated accurately and efficiently by employing the probability density evolution method(PDEM).The model-predicted results were consistent with those by the Monte Carlo simulation method.A sensitivity study was performed to assess the relative importance of those uncertain structural parameters,based on which a case study was presented to explore the stochastic probability evolution mechanism of such train-ballasted track-subgrade system.

Distributed fuzzy fault-tolerant consensus of leader-follower multi-agent systems with mismatched uncertainties

In this paper,the distributed fuzzy fault-tolerant tracking consensus problem of leader-follower multi-agent systems(MASs)is studied.The objective system includes actuator faults,mismatched parameter uncertainties,nonlinear functions,and exogenous disturbances under switching communication topologies.To solve this problem,a distributed fuzzy fault-tolerant controller is proposed for each follower by adaptive mechanisms to track the state of the leader.Furthermore,the fuzzy logic system is utilized to approximate the unknown nonlinear dynamics.An error estimator is introduced between the mismatched parameter matrix and the input matrix.Then,a selective adaptive law with relative state information is adopted and applied.When calculating the Lyapunov function’s derivative,the coupling terms related to consensus error and mismatched parameter uncertainties can be eliminated.Finally,a numerical simulation is given to validate the effectiveness of the proposed protocol.

Nash Model Parameter Uncertainty Analysis by AM-MCMC Based on BFS and Probabilistic Flood Forecasting

A hydrologic model consists of several parameters which are usually calibrated based on observed hy-drologic processes. Due to the uncertainty of the hydrologic processes, model parameters are also uncertain, which further leads to the uncertainty of forecast results of a hydrologic model. Working with the Bayesian Forecasting System (BFS), Markov Chain Monte Carlo simulation based Adaptive Metropolis method (AM-MCMC) was used to study parameter uncertainty of Nash model, while the probabilistic flood forecasting was made with the simu-lated samples of parameters of Nash model. The results of a case study shows that the AM-MCMC based on BFS proposed in this paper is suitable to obtain the posterior distribution of the parameters of Nash model according to the known information of the parameters. The use of Nash model and AM-MCMC based on BFS was able to make the probabilistic flood forecast as well as to find the mean and variance of flood discharge, which may be useful to estimate the risk of flood control decision.

Robust sliding mode control for fractional-order chaotic economical system with parameter uncertainty and external disturbance

This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method.

Parameter uncertainty modeling of safety instrumented systems

In this study,a novel safety integrity level(SIL)determination methodology of safety instrumented systems(SISs)with parameter uncertainty is proposed by combining multistage dynamic Bayesian networks(DBNs)and Monte Carlo simulation.A multistage DBN model for SIL determination with multiple redundant cells is established.The models of function inspection test interval and function inspection test stages are alternately connected to form the multistage DBNs.The redundant cells can have different M out of N voting system architectures.An automatic modeling of conditional probability between nodes is developed.The SIL determination of SISs with parameter uncertainty is constructed by using the multistage DBNs and Monte Carlo simulation.A high-pressure SIS in the export of oil wellplatform is adopted to demonstrate the application of the proposed approach.The SIL and availability of the SIS and its subsystems are obtained.The influence of single subsystem on the SIL and availability of the SIS is studied.The influence of single redundant element on the SIL and availability of the subsystem is analyzed.A user-friendly SIL determination software with parameter uncertainty is developed on MATLAB graphical user interface.

Portfolio Choice under the Mean-Variance Model with Parameter Uncertainty

Assuming the investor is uncertainty-aversion,the multiprior approach is applied to studying the problem of portfolio choice under the uncertainty about the expected return of risky asset based on the mean-variance model. By introducing a set of constraint constants to measure uncertainty degree of the estimated expected return,it built the max-min model of multi-prior portfolio,and utilized the Lagrange method to obtain the closed-form solution of the model,which was compared with the mean-variance model and the minimum-variance model; then,an empirical study was done based on the monthly returns over the period June 2011 to May 2014 of eight kinds of stocks in Shanghai Exchange 50 Index. Results showed,the weight of multi-prior portfolio was a weighted average of the weight of mean-variance portfolio and that of minimumvariance portfolio; the steady of multi-prior portfolio was strengthened compared with the mean-variance portfolio; the performance of multi-prior portfolio was greater than that of minimum-variance portfolio. The study demonstrates that the investor can improve the steady of multi-prior portfolio as well as its performance for some appropriate constraint constants.