Linear generalized synchronization of chaotic systems with uncertain parameters

A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.

Adaptive fault-tolerant control based on boundary estimation for space robot under joint actuator faults and uncertain parameters

Since the joint actuator of the space robot executes the control instructions frequently in the harsh space environment,it is prone to the partial loss of control effectiveness(PLCE)fault.An adaptive fault-tolerant control algorithm is designed for a space robot system with the uncertain parameters and the PLCE actuator faults.The mathematical model of the system is established based on the Lagrange method,and the PLCE actuator fault is described as an effectiveness factor.The lower bound of the effectiveness factors and the upper bound of the uncertain parameters are estimated by an adaptive strategy,and the estimated value is fed back to the control algorithm.Compared with the traditional fault-tolerant algorithms,the proposed algorithm does not need to predetermine the lower bound of the effectiveness factor,hence it is more in line with the actual engineering application.It is proved that the algorithm can guarantee the stability of the closed-loop system based on the Lyapunov function method.The numerical simulation results show that the proposed algorithm can not only compensate for the uncertain parameters,but also can tolerate the PLCE actuator faults effectively,which verifies the effectiveness and superiority of the control scheme.

Input torque sensitivity to uncertain parameters in biped robot

Input torque is the main power to maintain bipedal walking of robot, and can be calculated from trajectory planning and dynamic modeling on biped robot. During bipedal walking, the input torque is usually required to be adjusted due to some uncertain parameters arising from objective or subjective factors in the dynamical model to maintain the pre-planned stable trajectory. Here, a planar 5-link biped robot is used as an illustrating example to investigate the effects of uncertain parameters on the input torques. Kine-matic equations of the biped robot are firstly established by the third-order spline curves based on the trajectory planning method, and the dynamic modeling is accomplished by taking both the certain and uncertain parameters into account. Next, several evaluation indices on input torques are intro-duced to perform sensitivity analysis of the input torque with respect to the uncertain parameters. Finally, based on the Monte Carlo simulation, the values of evaluation indices on input torques are presented, from which all the robot param-eters are classified into three categories, i.e., strongly sensi-tive, sensitive and almost insensitive parameters.

Periodic synchronization of community networks with non-identical nodes uncertain parameters and adaptive coupling strength

In this paper, we propose a novel approach for simultaneously identifying unknown parameters and synchronizing time-delayed complex community networks with nonidentical nodes. Based on the LaSalle＇s invariance principle, a cri- teflon is established by constructing an effective control identification scheme and adjusting automatically the adaptive coupling strength. The proposed control law is applied to a complex community network which is periodically synchro- nized with different chaotic states. Numerical simulations are conducted to demonstrate the feasibility of the proposed method.

Robust output feedback cruise control for high-speed train movement with uncertain parameters

In this paper, the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated. The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible couplers, which is subject to rolling mechanical resistance, aerodynamic drag and wind gust. Based on Lyapunov＇s stability theory, the sufficient condition for the existence of the robust output feedback cruise control law is given in terms of linear matrix inequalities（LMIs）, under which the high-speed train tracks the desired speed, the relative spring displacement between the two neighboring cars is stable at the equilibrium state, and meanwhile a small prescribed H∞ disturbance attenuation level is guaranteed. One numerical example is given to illustrate the effectiveness of the proposed methods.

Complete synchronization of double-delayed Rssler systems with uncertain parameters

In this paper, we investigate complete synchronization of double-delayed RSssler systems with uncertain parameters as the master system is in chaotic synchronization. The uncertain parameters can be nonlinearly expressed in the system. The analysis and proof are given by means of the Lyapunov stability theorem. Based on theoretical analysis, some sufficient conditions of complete synchronization are proved. In order to validate the proposed scheme, numerical simulations are performed and the numerical results show that our scheme is very effective.

Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters

This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lu¨ and Chen systems are presented to validate the design and analysis.

Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework

This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM)” for the efficient and exact computation of 1st- and 2nd-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (i.e., model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2nd-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1st-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2nd-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (N2/2 + 3 N/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2nd-LASS requires very little additional effort beyond the construction of the 1st-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1st-LASS and 2nd-LASS requires the same computational solvers as needed for solving (i.e., “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1st-LASS and the 2nd-LASS. Since neither the 1st-LASS nor the 2nd-LASS involves any differentials of the operators underlying the original system, the 1st-LASS is designated as a “first-level” (as opposed to a “first-order”) adjoint sensitivity system, while the 2nd-LASS is designated as a “second-level” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2nd-LASS that involve the imprecisely known boundary parameters. Notably, the 2nd-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): II. Paradigm Application to a Bernoulli Model Comprising Uncertain Parameters

This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)” to a simplified Bernoulli model. The 5th-CASAM-N builds upon and incorporates all of the lower-order (i.e., the first-, second-, third-, and fourth-order) adjoint sensitivities analysis methodologies. The Bernoulli model comprises a nonlinear model response, uncertain model parameters, uncertain model domain boundaries and uncertain model boundary conditions, admitting closed-form explicit expressions for the response sensitivities of all orders. Illustrating the specific mechanisms and advantages of applying the 5th-CASAM-N for the computation of the response sensitivities with respect to the uncertain parameters and boundaries reveals that the 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

Performance evaluation of complex systems using evidential reasoning approach with uncertain parameters

The composition of the modern aerospace system becomes more and more complex.The performance degradation of any device in the system may cause it difficult for the whole system to keep normal working states.Therefore,it is essential to evaluate the performance of complex aerospace systems.In this paper,the performance evaluation of complex aerospace systems is regarded as a Multi-Attribute Decision Analysis(MADA)problem.Based on the structure and working principle of the system,a new Evidential Reasoning(ER)based approach with uncertain parameters is proposed to construct a nonlinear optimization model to evaluate the system performance.In the model,the interval form is used to express the uncertainty,such as error in testing data and inaccuracy in expert knowledge.In order to analyze the subsystems that have a great impact on the performance of the system,the sensitivity analysis of the evaluation result is carried out,and the corresponding maintenance strategy is proposed.For a type of Inertial Measurement Unit(IMU)used in a rocket,the proposed method is employed to evaluate its performance.Then,the parameter sensitivity of the evaluation result is analyzed,and the main factors affecting the performance of IMU are obtained.Finally,the comparative study shows the effectiveness of the proposed method.

Adaptive synchronization of Chen chaotic system with uncertain parameters

By the control method independent of system parameters, synchronization of two Chen chaotic systems with identical, but uncertain parameters is discussed in this article. Based on Lyapunov＇s theorem, an adaptive controller and the parameters estimate update law are derived to make the solution of the error dynamical equation converge at the point E（0, 0,0） with a quick speed, that is, the states of two Chen chaotic systems can be asymptotically synchronized. Numerical simulations verify the effectiveness and the adaptivity to the variation of Chen system parameters.

Research on the attribution evaluating methods of dynamic effects of various parameter uncertainties on the in-structure floor response spectra of nuclear power plant

： Consideration of the dynamic effects of the site and structural parameter uncertainty is required by the standards for nuclear power plants （NPPs） in most countries. The anti-seismic standards provide two basic methods to analyze parameter uncertainty. Directly manually dealing with the calculated floor response spectra （FRS） values of deterministic approaches is the first method. The second method is to perform probability statistical analysis of the FRS results on the basis of the Monte Carlo method. The two methods can only reflect the overall effects of the uncertain parameters, and the results cannot be screened for a certain parameter＇s influence and contribution. In this study, based on the dynamic analyses of the floor response spectra of NPPs, a comprehensive index of the assessed impact for various uncertain parameters is presented and recommended, including the correlation coefficient, the regression slope coefficient and Tornado swing. To compensate for the lack of guidance in the NPP seismic standards, the proposed method can effectively be used to evaluate the contributions of various parameters from the aspects ＆sensitivity, acuity and statistical swing correlations. Finally, examples are provided to verify the set of indicators from systematic and intuitive perspectives, such as the uncertainty of the impact of the structure parameters and the contribution to the FRS of NPPs. The index is sensitive to different types of parameters, which provides a new technique for evaluating the anti-seismic parameters required for NPPs.

Modal Parameter Identification Method of Jacket Platform Structure Based on AFDD and Optimized FBFFT

Offshore platforms are susceptible to structural damage due to prolonged exposure to random loads,such as wind,waves,and currents.This is particularly true for platforms that have been in service for an extended period.Identifying the modal parameters of offshore platforms is crucial for damage diagno sis,as it serves as a prerequisite and foundation for the process.Therefore,it holds great significance to prioritize the identification of these parameters.Aiming at the shortcomings of the traditional Fast Bayesian Fast Fourier Transform(FBFFT) method,this paper proposes a modal parameter identification method based on Automatic Frequency Domain Decomposition(AFDD) and optimized FBFFT.By introducing the AFDD method and Powell optimization algorithm,this method can automatically identify the initial value of natural frequency and solve the objective function efficiently and simply.In order to verify the feasibility and effectiveness of the proposed method,it is used to identify the modal parameters of the IASC-ASCE benchmark model and the j acket platform structure model,and the Most Probable Value(MPV) of the modal parameters and their respective posterior uncertainties are successfully identified.The identification results of the IASC-ASCE benc hmark model are compared with the identification re sults of the MODE-ID method,which verifies the effectivene ss and accuracy of the proposed method for identifying modal parameters.It provides a simple and feasible method for quantifying the influence of uncertain factors such as environmental parameters on the identification results,and also provide s a reference for modal parameter identification of other large structures.

Adaptive synchronization of uncertain Liu system via nonlinear input

This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with total parameters unknown. This method is simple and can be easily designed. What is more, it improves the existing conclusions in Ref [12]. Simulation results prove that the controller is effective and feasible in the end.

Robust Adaptive Path Following for Underactuated Surface Vessels with Uncertain Dynamics

A robust adaptive control strategy was developed to force an underactuated surface vessel to follow a reference path,despite the presence of uncertain parameters and unstructured uncertainties including exogenous disturbances and measurement noise.The reference path can be a curve or a straight line.The proposed controller was designed by using Lyapunov’s direct method and sliding mode control and backstepping techniques.Because the sway axis of the vessel was not directly actuated,two sliding surfaces were introduced,the first one in terms of the surge motion tracking errors and the second one for the yaw motion tracking errors.The adaptive control law guaranteed the uniform ultimate boundedness of the tracking errors.Numerical simulation results were provided to validate the effectiveness of the proposed controller for path following of underactuated surface vessels.

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchro-nization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master＇s and the slave＇s system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.

Verified Solution for a Statically Determinate Truss Structure with Uncertain Node Locations

We consider a statically determinate structural truss problem where all of the physical model parameters are uncertain： not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening （pruning） technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements.

Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control

The finite-time synchronization of fractional-order multi-weighted complex networks(FMCNs)with uncertain parameters and external disturbances is studied.Firstly,based on fractional calculus characteristics and Lyapunov stability theory,quantized controllers are designed to guarantee that FMCNs can achieve synchronization in a limited time with and without coupling delay,respectively.Then,appropriate parameter update laws are obtained to identify the uncertain parameters in FMCNs.Finally,numerical simulation examples are given to validate the correctness of the theoretical results.

Adaptive passive equivalence of uncertain Lfi system

An adaptive passive strategy for controlling uncertain Lu system is proposed. Since the uncertain Lü system is minimum phase and the uncertain parameters are from a bounded compact set, the essential conditions are studied by which uncertain Lu system could be equivalent to a passive system, and the adaptive control law is given. Using passive theory, the uncertain Lu system could be globally asymptotically stabilized at different equilibria by the smooth state feedback.