Global asymptotic stability of a class of nonlinear systems with parametric uncertainty

Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems are deduced. The simulation shows the effectiveness of the method.

Exponential synchronization of stochastic impulsive perturbed chaotic Lur'e systems with time-varying delay and parametric uncertainty

This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur＇e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur＇e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities （LMIs）, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi-perturbation chaotic Lur＇e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Composite anti-disturbance position and attitude control for spacecrafts with parametric uncertainty and flexible vibration

The rendezvous and proximity operations with respect to a tumbling non-cooperative target pose high requirement for the position and attitude control accuracy of servicing spacecraft.However,multiple disturbances including parametric uncertainties,flexible vibration,and unknown nonlinear dynamics degrade the control performance significantly.In order to enhance the system anti-disturbance ability,this paper proposes a composite anti-disturbance control law for the spacecraft position and attitude tracking.Firstly,the relative position and attitude dynamic models with multiple disturbances are established,where the refined descriptions of multiple disturbances are accomplished based on their characteristics.Then,by combining a dual Disturbance ObserverBased Control(DOBC)and a sliding mode control,a composite controller with hierarchical architecture is proposed,where the dual DOBC in the feedforward channel is used to reject the flexible vibration,environment disturbance,and complicated nonlinear dynamics,while the parametric uncertainties are attenuated by the sliding mode control in the feedback channel.Stability analysis is carried out for the closed-loop system by unifying the sliding mode dynamics and observer dynamics.Finally,the effectiveness of the proposed controller is verified via numerical simulation and hardware-in-the-loop test.

Robust decentralized H_∞ control of multi-channel systems with norm-bounded parametric uncertainties

A robust decentralized H∞ control problem for uncertain multi-channel systems is considered. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. The dynamic output feedback is mainly dealt with. A necessary and sufficient condition for the uncertain multi-channel system to be stabilized robustly with a specified disturbance attenuation level is derived based on the bounded real lemma, which is reduced to a feasibility problem of a nonlinear matrix inequality （NMI）. A two-stage homotopy method is used to solve the NMI iteratively. First, a decentralized controller for the nominal system with no uncertainty is computed by imposing structural constraints on the coefficient matrices of the controller gradually. Then the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, a variable is fixed alternately at the iterations to reduce the NMI to a linear matrix inequality （LMI）. A given example shows the efficiency of this method.

Decentralized robust stabilization of discrete-time fuzzy large-scale systems with parametric uncertainties: a LMI method

Decentralized robust stabilization problem of discrete-time fuzzy large-scale systems with parametric uncertainties is considered. This uncertain fuzzy large-scale system consists of N interconnected T-S fuzzy subsystems, and the parametric uncertainties are unknown but norm-bounded. Based on Lyapunov stability theory and decentralized control theory of large-scale system, the design schema of decentralized parallel distributed compensation （DPDC） fuzzy controllers to ensure the asymptotic stability of the whole fuzzy large-scale system is proposed. The existence conditions for these controllers take the forms of LMIs. Finally a numerical simulation example is given to show the utility of the method proposed.

Adaptive Backstepping Tracking Control of a 6-DOF Unmanned Helicopter

This paper presents an adaptive backstepping control design for a class of unmanned helicopters with parametric uncertainties. The control objective is to let the helicopter track some pre-defined position and yaw trajectories. In order to facilitate the control design, we divide the helicopter s dynamic model into three subsystems. The proposed controller combines the backstepping method with online parameter update laws to achieve the control objective. The global asymptotical stability(GAS) of the closed-loop system is proved by a Lyapunov based stability analysis. Numerical simulations demonstrate that the controller can achieve good tracking performance in the presence of parametric uncertainties.

A practical approach to robust impulsive lag synchronization between different chaotic systems

In this paper, a practical impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. By virtue of the new definition of synchronization and the theory of impulsive differential equations, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level. The idea and approach developed in this paper can provide a more practical framework for the synchronization between identical and different chaotic systems in parameter perturbation circumstances. Simulation results finally demonstrate the effectiveness of the method.

Robust lag synchronization between two different chaotic systems via dual-stage impulsive control

In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme （the so-called dual-stage impulsive control）, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.

Anticontrol of chaos for discrete-time fuzzy hyperbolic model with uncertain parameters

This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto theorem, it is proven that the chaos generated by this controller satisfies the Li-Yorke definition. An example is presented to demonstrate the effectiveness of the approach.

STABILITY MARGIN OF SYSTEMS WITH MIXED UNCERTAINTIES UNDER THE IQC DESCRIPTIONS

Stability perturbation bounds problem for systems with mixed uncertainties is discussed. It is supposed that the linear part in the forward loop is of parametric uncertainties described by interval perturbation mode, and that the nonlinear part in the feedback loop is characterized by an integral quadratic constraint (IQC). The definition of stability margin under the interval perturbation mode is given by using the Minkowski functional. The infinite stability checking problem of the mixed uncertain system can be converted to finite or one dimensional stability checking for different structures of the IQC multipliers based on the concepts of biconvex and convex-concave junctions and their properties. The result is illustrated to be efficient through an example.

An improved impulsive control approach to robust lag synchronization between two different chaotic systems

In this paper, a novel robust impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the theory of impulsive functional differential equations and a new differential inequality, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined region. Finally, some numerical simulations for the Lorenz system and Chen system are given to demonstrate the effectiveness and feasibility of the proposed method. Compared with the existing results based on so-called dual-stage impulsive control, the derived results reduce the complexity of impulsive controller, moreover, a larger stable region can be obtained under the same parameters, which can be shown in the numerical simulations finally.

FREQUENCY DOMAIN CRITERIA FOR ROBUST D-STABILITY OF MIMO SYSTEMS BASED ON LMI METHOD

The problem of checking robust D-stability of multi-in and multi-out （MIMO） systems was studied. Three system models were introduced, i.e. multilinear polynomial matrix, polytopic polynomial matrix and feedback system model. Furthermore, the convex property of each model with respect to the parametric uncertainties was estabilished respectively. Based on this, sufficient conditions for D-stability were expressed in terms of linear matrix inequalities （LMIs） involving only the convex vertices. Therefore, the robust D-stability was tested by solving an LMI optimal problem.

Robust Control Strategy for Inductive Parametric Uncertainties of DC/DC Converters in Islanded DC Microgrid

Direct current(DC) microgrid consists of many parallel power converters that share load currents through the inductance of DC/DC converters. Usually, the inductance parameters are dependent on the physical implementation of the system, and their values may not match their nameplates. Such disparities could lead to unequal response characteristics of the system, which can potentially reduce the performances of the DC microgrid operation. This paper proposes a robust control strategy for inductive parametric uncertainties of DC/DC converters using an optimal control method with integral action. To achieve such a goal, the system model parameters with nominal values are transformed into parametric unmatched uncertainties to form a robust control problem, which is then transformed into a linear quadratic regulator problem. The inductance uncertainties are stabilized with the uncertainty dynamic algebraic Riccati equation(UDARE) using state feedback gain under linear quadratic regulator. The closed-loop control with integral action is adopted to achieve a steady-state error of zero on the DC-link voltage at any uncertainty of the inductive parameter, which subsequently ensures the equal load current sharing. Off-line simulations and real-time validations based on OpalRT have been conducted to demonstrate the effectiveness and robustness of the proposed robust control strategy.

Observer-based passive control for uncertain linear systems with delay in state and control input

This paper deals with the robust passivity synthesis problem for a class of uncertain linear systems with timevarying delay in state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all matrices of the model. The problem aims at designing an observer-based dynamic output-feedback controller that robustly stabilizes the uncertain systems and achieves the strict passivity of closed-loop systems for all admissible uncertainties. By converting the problem at hand into a class of strictly passive control problem for a parameterized system, the explicit solution is established and expressed in terms of a linear matrix inequality. A numerical example is provided to demonstrate the validity of the proposed approach.

A parameter estimation based adaptive actuator failure compensation control scheme

An adaptive actuator failure compensation control scheme is developed using an indirect adaptive control method,by calculating the controller parameters from adaptive estimates of system parameters and actuator failure parameters.A key technical issue is how to deal with the actuator failure uncertainties such as failure pattern,time and values.A complete parametrization covering all possible failures is used to solve this issue for adaptive parameter estimation.A simultaneous mapping from the estimated system/failure parameters to the controller parameters is employed to make the control system capable of ensuring the desired system performance under failures,which is verified by simulation results.

Design of an Attitude and Disturbance Rejection Controller for Spacecraft

According to the Rodrigues parameter and the internal model principle,an adaptive state feedback control law is proposed for a rigid spacecraft with inertia uncertainty and exotic disturbances generated by an unknown nonlinear exosystem.The uncertainty of parameters is treated by an adaptive control law.And a new internal model is proposed to estimate the exotic disturbances.By using the Lyapunov analysis method,the control law is designed to ensure that the system's state variables asymptotically converge to stable,and the disturbances can be completely rejected.Finally,numerical simulations are included to demonstrate the performance of the presented controller.

Integral Performance Criteria Based Analysis of Load Frequency Control in Bilateral Based Market

Performance index based analysis is made to examine and highlight the effective application of Particle Swarm Optimization (PSO) to optimize the Proportional Integral gains for Load Frequency Control (LFC) in a restructured power system that operates under Bilateral based policy scheme. Various Integral Performance Criteria measures are taken as fitness function in PSO and are compared using overshoot, settling time and frequency and tie-line power deviation following a step load perturbation (SLP). The motivation for using different fitness technique in PSO is to show the behavior of the controller for a wide range of system parameters and load changes. Error based analysis with parametric uncertainties and load changes are tested on a two-area restructured power system. The results of the proposed PSO based controller show the better performance compared to the classical Ziegler-Nichols (Z-N) tuned PI and Fuzzy Rule based PI controller.

Epistemic uncertainty quantification in flutter analysis using evidence theory

Aimed at evaluating the structural stability and flutter risk of the system, this paper manages to quantify epistemic uncertainty in flutter analysis using evidence theory, including both parametric uncertainty and method selection uncertainty, on the basis of information from limited experimental data of uncertain parameters. Two uncertain variables of the actuator coupling system with unknown probability distributions, that is bending and torsional stiffness, which are both described with multiple intervals and the basic belief assignment（BBA） extricated from the modal test of actuator coupling systems, are taken into account. Considering the difference in dealing with experimental data by different persons and the reliability of various information sources, a new combination rule of evidence––the generalized lower triangular matrices method is formed to acquire the combined BBA. Finally the parametric uncertainty and the epistemic uncertainty of flutter analysis method selection are considered in the same system to realize quantification. A typical rudder of missile is selected to examine the present method, and the dangerous range of velocity as well as relevant belief and plausibility functions is obtained. The results suggest that the present method is effective in obtaining the lower and upper bounds of flutter probability and assessing flutter risk of structures with limited experimental data of uncertain parameters and the belief of different methods.

Ultra-narrow parametric magnetic resonances in a miniature vapor cell

Multi-photon parametric magnetic resonance in a miniature vapor cell is demonstrated. Much more multi-photon magnetic resonance can be observed when the radio frequency field becomes stronger. The linewidth of the n photons magnetic resonance equals that of the first-order resonance divided by n, which means that the uncertainty of the magnetic sublevel is reduced by the factor n. The signal-to-noise ratio can be improved when the low-frequency multi-photon resonance takes place, which finds a possible application in precision magnetic field measurement.

Robust state estimation for uncertain linear discrete systems with d-step measurement delay and deterministic input signals

In this study,the state estimation problems for linear discrete systems with uncertain parameters,deterministic input signals and d-step measurement delay are investigated.A robust state estimator with a similar iterative form and comparable computational complexity to the Kalman filter is derived based on the state augmentation method and the sensitivity penalisation of the innovation process.It is discussed that the steady-state properties such as boundedness and convergence of the robust state estimator under the assumptions that the system parameters are time invariant.Numerical simulation results show that compared with the Kalman filter,the obtained state estimator is more robust to modelling errors and has nice estimation accuracy.