Robust Control Theory Research Articles

Research of Mapping Element Space Method for Uncertain Lurie System Stability Diagnosis

A new diagnosis method of Lurie system stability by using Chaotic time series data was proposed in order to solve stability analysis of flight control system with fault and uncertain. Firstly, the reasons for the instability of the nonlinear system of Ruri leaf was analyzed by using the small gain theory and linear matrix inequalities in the robust control theory. And the stability conditions of Rui leaf system under the condition of uncertainty and failure were proved theoretically. In order to quantify the stability of nonlinear systems in complex Ruri leaves, based on the theory of phase space reconstruction, the nonlinear Ruri system with continuous discrete characteristics was converted into an approximate time discrete equation, mapping it to a low dimensional primitive space, by introducing Q Gauss function into Kernel function, the generalization ability of neural networks are enhanced, realizing the stability analysis method based on the characteristic of primitive migration, which is suitable for various fault and uncertainty conditions, and the relative quantized stability norm can be given. The simulation shows that the present method can effectively solve the stability analysis and determination of flight control system under various factors.

Unmanned Surface Vessel Steering L2 Gain Robust Control Based on Closed-Loop Shaping Filter

With the introduction of the closed-loop shaping filtering method into the L2 gain robust controller design strategy, a nonlinear robust steering controller for unmanned surface vessel is designed under the planning and control strategy in this paper. The rigorous mathematical analysis and synthesis characteristics of the L2 gain robust control theory and the Lyapunov design method are fully utilized in the controller design process. Furthermore, the concept of the closed-loop shaping filtering based on the classical closed-loop control theory is taken into the controller design strategy. Therefore, the time domain controller design methods integration with the frequency domain controller design strategy are merged togehter to complete the unmanned surface vessel steering controller design in the view of practical engineering and planning and control strategy. Finally, compared with several practical controller design methods in the multi-direction irregular waves, the simulation results show that the proposed steering controller design strategy has concise structure, distinctive physic meanings of the controller parameters and superior comprehensive control performance.

Robust Analysis for Premium-Reserve Models in a Stochastic Nonlinear Discrete-Time Varying Framework

The effective management of uncertainty and complexity in premium pricing and reserve accumulation processes provide new challenges to the decision- and policy- makers. In this regard, the implementation of complex mathematical tools and advanced statistical techniques is highly acquired. Over the last three decades, methodologies and applications of robust control theory to finance and economics have received strong attention among researchers and practitioners. However, relatively scant research has been carried out so far in relation to insurance. This paper proposes a stochastic, nonlinear time-varying premium-reserve (P-R) system with Lipschitz- type conditions in discrete-time to explore P-R system’s stability, stabilisation and Hoo-control properties. In our case, as an extension of the classical quadratic condition, the one-side Lipschitz conditions are also considered and a nonconvex feasibility problem is formulated and solved. In addition, both robust stochastic stability and a pre-specified disturbance attenuation level can be guaranteed. Finally, numerical examples are presented to illustrate the applicability of theoretical treatment.

Insulated-gate bipolar transistor junction temperature estimation based on ℋ∞ robust controller in wind energy applications

This article presents lifetime estimation using robust control based on thermal path degradation condition of insulated-gate bipolar transistor wind power modules. Online measurements of the on-state voltage [Formula: see text] are considered to be a promising method for obtaining a thermal-sensitive electrical parameter for wire-bond lift-off. This parameter demonstrates a good correlation with junction temperature. Due to the harsh environment, disturbances and uncertain parameters are founded within the compact set of wind energy generation systems. The uncertainty sacrifices some degree of accuracy of junction temperature measurements. Hence, robust control theory has been utilized to synthesize [Formula: see text] controller for the thermal impedance of high-power insulated-gate bipolar transistors. To study this reliability problem, an integrated model of wind energy generation system is built in MATLAB/Simulink for the closed-loop system. Simulation results show the benefit of the designed controller compared to the open-loop system in terms of thermal cycles of junction temperature and lifetime estimation.

Dynamic Control Allocation Algorithm for a Class of Distributed Control Systems

The control allocation algorithm is developed for a class of distributed control systems with hierarchical structure and similar models of the subsystems, to solve the real-time cooperative control taking the dynamics and possible variations of subsystems into consideration. The augmented state-space model of the subsystems is first established for the control allocation. Based on robust control theory, the constrained and convex optimization is then developed with LMIs form to design the gain matrix of the dynamic control allocation. Furthermore, the closed-loop stability of the distributed control system is analyzed on the basis of stable upper-level main control law. Finally, simulations on the four-corner leveling control system of an advanced hydraulic press demonstrate the effectiveness of the proposed control allocation algorithm.

Robust Forecasting-Aided State Estimation for Power System Against Uncertainties

Accurate forecasting-aided state estimation plays a vital role in reliable and secure operation of power systems. However, most of existing methods are unable to deal with the uncertainties that might be caused by uncertain model parameters or uncertain noise statistics. Therefore, the performance of these methods may be inevitably degraded significantly. To address these issues, based on the robust control theory, in this paper, by incorporating the modified innovation based Sage-Husa estimator of noise statistics and the proposed estimation error covariance matrix adaptive technique, a novel adaptive $H_{\infty }$ extended Kalman filter (AHEKF) is developed to realize robust forecasting-aided state estimation for power system with model uncertainties. Extensive simulations carried out on several different test systems demonstrate the efficiency and robustness of the proposed method.

Sliding Mode Control Laws Design by the ADAR Method with Subsequent Invariant Manifolds Aggregation

Sliding mode control (SMC) laws are commonly used in engineering to make a system robust to parameters change, external disturbances and control object unmodeled dynamics. State-of-the-art capabilities of the theory of adaptive and robust control, the theory of fuzzy systems, artificial neural networks, etc., which are combined with SMC, couldn’t resolve current issues of SMC design: vector design and stability analysis of a closed-loop system with SMC are involved with considerable complexity. Generally the classical problem of SMC design consists in solving subtasks for transit an object from an arbitrary initial position onto the sliding surface while providing conditions for existence of a sliding mode at any point of the sliding surface as well as ensuring stable movement to the desired state. As a general rule these subtasks are solved separately. This article presents a methodology for SMC design based on successive aggregation of invariant manifolds by the procedure of method of Analytical Design of Aggregated Regulators (ADAR) from the synergetic control theory. The methodology allows design of robust control laws and simultaneous solution of classical subtasks of SMC design for nonlinear objects. It also simplifies the procedure for closed-loop system stability analyze: the stability conditions are made up of stability criterions for ADAR method functional equations and the stability criterions for the final decomposed system which dimension is substantially less than dimension of the initial system. Despite our paper presents only the scalar SMC design procedure in details, the ideas are also valid for vector design procedure: the main difference is in the number of invariant manifolds introduced at the first and following stages of the design procedure. The methodology is illustrated with design procedure examples for nonlinear engineering systems demonstrating the achievement of control goals: hitting to target invariants, insensitivity to emerging parametric and external disturbances.

Finite-time robust control for transformerless H-bridge cascaded STATCOM with star configuration

This article presents a finite-time robust control (FTRC) of a transformerless STATCOM based on a cascaded multilevel H-bridge converter (CMHC) with star configuration. The FTRC is first proposed for the current loop control of a CMHC-based transformerless STATCOM by using the finite time robust control theory. Taking the parameters, perturbations and external disturbances into account and using coordinate transformation method, the nonlinear dynamic model of the CMHC-based transformerless STATCOM is transformed into a standard nonlinear port-controlled dissipative Hamiltonian (PCDH) structure. Based on the PCDH structure, an FTRC is designed for the CMHC-based transformerless STATCOM to improve the transient stability and oscillation damping of power system. Finally, the simulation results demonstrate that the FTRC has better dynamic performance and strong robustness in comparison with the passivity-based control of the CMHC-based transformerless STATCOM.

Fuzzy Control with Pole Assignment and Variance Constraints for Continuous-time Perturbed Takagi-Sugeno Fuzzy Models: Application to Ship Steering Systems

The stability analysis and controller design of stochastic systems have become much more important because the stochastic behaviors usually exist in practical nonlinear systems. In this paper, a robust fuzzy controller design approach is proposed with multiple constraints, including state variance constraints, output variance constraints, and pole placement constraints. At first, nonlinear systems are expressed as the Takagi-Sugeno fuzzy model, and the parallel distributed compensation method is applied to design the robust fuzzy controllers. Next, considering the stability analysis and the performance constraints of perturbed Takagi-Sugeno fuzzy models, Lyapunov conditions are developed based on covariance control theory, pole placement theory and robust control theory. By constructing the stability conditions with multiple constraints, the proposed fuzzy control problem can be effectively transferred into the linear matrix inequality problem. It can be solved by the convex optimal programming algorithm. At last, a nonlinear ship steering system is selected to verify the effectiveness and applicability of the proposed robust fuzzy controller design method.

Robust nonlinear state estimation for a class of infinite-dimensional systems using reduced-order models

A methodology for designing robust, low-order observers for a class of spectral infinite-dimensional nonlinear systems is presented. This approach uses the low-dimensional subspace explicitly in the observer design. Then, robustness to bounded model uncertainties is incorporated using the Lyapunov reconstruction method from robust control theory. Furthermore, the proposed design includes a data-driven learning algorithm that auto-tunes the observer gains to optimise the performance of the state estimation. A numerical study using a model from fluid dynamics -Burgers equation- demonstrates the effectiveness of the proposed observer.

Synchronization of Uncertain Complex Dynamical Networks

The synchronization problem of a kind of complex dynamical networks with uncertain links and external disturbances is studied in this paper. The adaptive and impulsive controller is designed after a series of researches on nonlinearity of joints, time variability and uncertainty of system parameters as well as uncertainty of coupling relationship among joints. The stability criteria of the uncertain complex dynamical networks are obtained based on the robust control theory and Lyapunov function theory, thus the synchronization for this kind of complex networks can be realized. The simulation results verify the effectiveness of the method in this paper.

Robust collaborative object transportation using multiple MAVs

Collaborative object transportation using multiple MAV with limited communication is a challenging problem. In this paper, we address the problem of multiple MAV mechanically coupled to a bulky object for transportation purposes without explicit communication between agents. The apparent physical properties of each agent are reshaped to achieve robustly stable transportation. Parametric uncertainties and unmodeled dynamics of each agent are quantified and techniques from robust control theory are employed to choose the physical parameters of each agent to guarantee stability. Extensive simulation analysis and experimental results show that the proposed method guarantees stability in worst-case scenarios.

Discrete-Time Sliding Mode Control for Deployment of Tethered Space Robot With Only Length and Angle Measurement

This paper proposes a nonlinear discrete-time sliding mode based tension control for deployment of tethered space robot with only length and angle measurements. The discrete-time dynamics of deployment is uncovered based on discretization of Hamilton's principle. Taking into account the underactuated dynamics, the proposed discrete-time sliding surface can generate a specified reduced-order system, which can be regarded as an uncertain discrete-time system with multiple time delays, which is caused by a considerable sample interval, and the stability of a reduced-order system is well analyzed by combining a linear matrix inequation technique based on robust control theory and nonlinear discrete-time Lyapunov method. A novel input structure with the auxiliary variable sequence is presented to deal with the tension saturation, and the states can converge to the specified reduced-order system although the input saturation occurs. The proposed discrete-time method makes no appeal to velocity terms. It is cost-effective to use the proposed method for the information of length and angle are easily measured rather than that of velocity, and it conduces to low requirements for the measurement ability of sensors. Simulation results verify the stability analyses, and are coincident with the stability analyses.

A Theoretical Framework of Robust H-Infinity Unscented Kalman Filter and Its Application to Power System Dynamic State Estimation

This paper presents a new theoretical framework that, by integrating robust statistics and robust control theory, allows us to develop a robust dynamic state estimator of a cyber-physical system. This state estimator combines the generalized maximum-likelihood-type (GM) estimator, the unscented Kalman filter (UKF), and the H -infinity filter into a robust H -infinity UKF filter in the Krein space, which is able to handle large system uncertainties as well as suppress outliers while achieving a good statistical efficiency under Gaussian and non-Gaussian process and observation noises. Specifically, we first use the statistical linearization approach to build a linearlike regression model in the Krein space. Then, we show that the H -infinity UKF is just the Krein space Kalman filter that exhibits a bounded estimation error in presence of system uncertainties while minimizing the least squares criterion; consequently, it suffers from a lack of robustness to outliers and non-Gaussian noise. Because the GM estimator is able to handle outliers, but it may yield large estimation errors in the presence of system uncertainties, we propose to combine it with the H -infinity UKF in a robust H -infinity UKF. We carry out a theoretical analysis to demonstrate the connections that our filter has with the H -infinity UKF and the GM-UKF. The good performance of the new filter is demonstrated via extensive simulation performed on the IEEE 39-bus power system.

On the complexity of detecting convexity over a box

It has recently been shown that the problem of testing global convexity of polynomials of degree four is strongly NP-hard, answering an open question of N.Z. Shor. This result is minimal in the degree of the polynomial when global convexity is of concern. In a number of applications however, one is interested in testing convexity only over a compact region, most commonly a box (i.e., a hyper-rectangle). In this paper, we show that this problem is also strongly NP-hard, in fact for polynomials of degree as low as three. This result is minimal in the degree of the polynomial and in some sense justifies why convexity detection in nonlinear optimization solvers is limited to quadratic functions or functions with special structure. As a byproduct, our proof shows that the problem of testing whether all matrices in an interval family are positive semidefinite is strongly NP-hard. This problem, which was previously shown to be (weakly) NP-hard by Nemirovski, is of independent interest in the theory of robust control.

Event‐based distributed robust synchronization control for multiple Euler‐Lagrange systems without relative velocity measurements

SummaryThis paper focuses on the event‐based distributed robust leaderless synchronization control for multiple Euler‐Lagrange systems with directed communication topology that contains a directed spanning tree. Update frequency of the system is reduced by taking advantages of the event‐triggered approach, which can help extend the service life of the controller. Robust control theory is employed to guarantee the synchronization stability of the networked Euler‐Lagrange systems when unmodeled dynamics occur. The cost on the distributed synchronization protocol design can be saved due to the relaxation of the requirement on relative velocity measurements. Furthermore, our results are more practical because unknown disturbance is taken into consideration. In addition, it can be rigorously analyzed that each agent can exclude the undesired Zeno behavior. Some simulation examples are provided in the end to demonstrate the effectiveness of the proposed event‐based distributed robust control algorithm.

Novelty of Frequency Domain Data in Smart Structures using ?-Analysis

This paper deals with the advantages of robust control in smart structures. First we present the implementations of H infinity control in the frequency domain. A dynamic model for smart structure under wind excitations is considered. Then robust control theory is used a model to synthesize controllers achieving stabilization with guaranteed performance for smart structures. We use ?-analysis to express the control problem as a mathematical optimization problem and then find the controller that solves the optimization problem in the frequency domain.

Novelty of Frequency Domain Data in Smart Structures using μ-Analysis

This paper deals with the advantages of robust control in smart structures. First we present the implementations of H infinity control in the frequency domain. A dynamic model for smart structure under wind excitations is considered. Then robust control theory is used a model to synthesize controllers achieving stabilization with guaranteed performance for smart structures. We use μ-analysis to express the control problem as a mathematical optimization problem and then find the controller that solves the optimization problem in the frequency domain.

A Distributed Architecture for Robust and Optimal Control of DC Microgrids

This paper presents a distributed, robust, and optimal control architecture for a network of multiple dc–dc converters. The network of converters considered form a dc microgrid in order to regulate a desired dc bus voltage and meet prescribed time-varying power sharing criteria among different energy sources. Such coordinated microgrids provide an important framework for leveraging the benefits of distributed power generation and consumption. The proposed control design seamlessly accommodates communication architectures that range from the centralized to decentralized scenarios with graceful degradation of the performance with lessened communication ability. Moreover, the methods developed are applicable to the case where the desired proportion in which the sources provide the power varies with time. A distinguishing feature of the control design approach is that it regards the net load current as a disturbance signal, lending itself to tractable analysis with tools from the robust and optimal control theory. A quantifiable analysis of the closed-loop stability and the performance of the network of converters is performed; the analysis simplifies to studying the closed-loop performance of an equivalent single-converter system. The control approach is demonstrated through simulations and experiments.

A unified modeling of muti-sources cyber-attacks with uncertainties for CPS security control

In this paper, the issue of CPS security is investigated. By analyzing the process of multi-sources cyber-attacks of denial-of-service (DoS), information disclosure, stealthy attack and replay attack, a unified system model with uncertainties is formulated. Under this system model framework, robust control theory is applied to design the control scenarios for cyber-attack prevention. Furthermore, a double closed-loop NCS framework combined with information integration technology is proposed, necessary conditions for security guarantee are derived. Finally, a DC motor speed moderating example is given to demonstrate the problem.