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.

Soft Sensor for Inputs and Parameters Using Nonlinear Singular State Observer in Chemical Processes

Chemical processes are usually nonlinear singular systems.In this study,a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes,which are augmented as state variables.Based on the observability of the singular system,this paper presents a simplified observability criterion under certain conditions for unknown inputs and uncertain model parameters.When the observability is satisfied,the unknown inputs and the uncertain model parameters are estimated online by the soft sensor using augmented nonlinear singular state observer.The riser reactor of fluid catalytic cracking unit is used as an example for analysis and simulation.With the catalyst circulation rate as the only unknown input without model error,one temperature sensor at the riser reactor outlet will ensure the correct estimation for the catalyst circulation rate.However,when uncertain model parameters also exist,additional temperature sensors must be used to ensure correct estimation for unknown inputs and uncertain model parameters of chemical processes.

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.

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.

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.

Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.

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.

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.

Adaptive Backstepping Slide Mode Control of Pneumatic Position Servo System

With the price decreasing of the pneumatic proportional valve and the high performance micro controller, the simple structure and high tracking performance pneumatic servo system demonstrates more application potential in many fields. However, most existing control methods with high tracking performance need to know the model information and to use pressure sensor. This limits the application of the pneumatic servo system. An adaptive backstepping slide mode control method is proposed for pneumatic position servo system. The proposed method designs adaptive slide mode controller using backstepping design technique. The controller parameter adaptive law is derived from Lyapunov analysis to guarantee the stability of the system. A theorem is testified to show that the state of closed-loop system is uniformly bounded, and the closed-loop system is stable. The advantages of the proposed method include that system dynamic model parameters are not required for the controller design, uncertain parameters bounds are not need, and the bulk and expensive pressure sensor is not needed as well. Experimental performance, as compared with some existing methods. results show that the designed controller can achieve better tracking

QoS multicast routing algorithm based on GA

The multicast routing problem with multiple QoS constraints in networks with uncertain parameters is discussed, and a network model that is suitable to research such QoS multicast routing problem is described. The QMRGA, a multicast routing policy for Internet, mobile network or other highperformance networks is mainly presented, which is based on the genetic algorithm(GA), and can provide QoSsensitive paths in a scalable and flexible way in the network environment with uncertain parameters. The QMRGA can also optimize the network resources such as bandwidth and delay, and can converge to the optimal or nearoptimal solution within few iterations, even for the network environment with uncertain parameters. The incremental rate of computational cost can be close to a polynomial and is less than exponential rate. The performance measures of the QMRGA are evaluated by using simulations. The results show that QMRGA provides an available approach to QoS multicast routing in network environment with uncertain parameters.

Interval Analysis Method on the Buckling of Composite Laminate

A method named interval analysis method, which solves the buckling load of composite laminate with uncertainties, is presented. Based on interval mathematics and Taylor series expansion, the interval analysis method is used to deal with uncertainties. Not necessarily knowing the probabilistic statistics characteristics of the uncertain variables, only little information on physical properties of material is needed in the interval analysis method, that is, the upper bound and lower bound of the uncertain variable. So the interval of response of the structure can be gotten through less computational efforts. The interval analysis method is efficient under the condition that probability approach cannot work well because of small samples and deficient statistics characteristics. For buckling load of a special cross-ply laminates and antisymmetric angle-ply laminates with all edges simply supported, calculations and comparisons between interval analysis method and probability method are performed.

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.

Validation of Flight Control Law Based on LFT and Structured Singular Value

The main goal of flight clearance is to use the structured singular value （ μ ） analysis of the flight control system when some parameters in the system vary in a certain range. As the p-analysis can only be done on a linear fractional transformation （LFT） model, the first step of flight clearance is to generate the LFT model of the flight control system. In this paper, based on the introduction of basic theory of LFT and μ-analysis, an X-fighter is chosen as an example to utilize the proposed methods. In order to realize the flight clearance process automatically, a novel soRware package based on MATLAB programming language is developed. The results of simulation experiments validate the feasibility and effectiveness of the novel methods proposed in this paper.

EXTENSION OF CONVEX MODELS AND ITS IMPROVEMENT ON THE APPROXIMATE SOLUTION

In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.