Robust Stability Design Research Articles

On robustification of digital event-based controllers for control-affine nonlinear systems

In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example.

On the robustification of digital event-based stabilizers for nonlinear time-delay systems

In this paper, the robust stabilization problem by means of quantized sampled-data event-based (QSE) controllers is investigated for nonlinear systems affected by state delays and unknown disturbances. In particular, a methodology for the design of robust QSE stabilizers is provided for control-affine nonlinear systems affected by unknown actuation disturbances and unknown measurement errors. Firstly, the notion of Steepest Descent Feedback (SDF), continuous or not, is suitably revised in order to deal with the robustification of event-based controllers. Then, Input-to-State Stability (ISS) redesign methodologies are used to provide the robustification term which is added to the SDF at hand in order to arbitrarily attenuate the effects of unknown external disturbances affecting the considered control scheme. A spline approximation approach is used in order to cope with the problem of the possible non-availability in the buffer of suitable past values of the system state required for the correct application of the proposed robust QSE controller. It is proved that there exist a suitably fast sampling and an accurate quantization of the input/output channels such that: the robust QSE implementation of SDFs, continuous or not, ensures the semi-global practical stability of the related closed-loop system, regardless of the above disturbances, provided that the observation errors affects marginally the new added control term. The stabilization in the sample-and-hold sense theory is used as a tool to prove the results. The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results.

Dynamic Responses of Electrical Hair Clippers with Fractional Damping and Its Robust Stabilization Design

Dynamic Responses of Electrical Hair Clippers with Fractional Damping and Its Robust Stabilization Design

Ellipsoidal Design of Robust Stabilization of Power Systems Exposed to a Cycle of Lightning Surges Modeled by Continuous-Time Markov Jumps

Power system stability is greatly affected by two types of stochastic or random disturbances: (1) topological and (2) parametric. The topological stochastic disturbances due to line faults caused by a series of lightning strikes (associated with circuit breaker, C.B., opening, and auto-reclosing) are modeled in this paper as continuous-time Markov jumps. Additionally, the stochastic parameter changes e.g., the line reactance, are influenced by the phase separation, which in turn depends on the stochastic wind speed. This is modeled as a stochastic disturbance. In this manuscript, the impact of the above stochastic disturbance on power system small-disturbance stability is studied based on stochastic differential equations (SDEs). The mean-square stabilization of such a system is conducted through a novel excitation control. The invariant ellipsoid and linear matrix inequality (LMI) optimization are used to construct the control system. The numerical simulations are presented on a multi-machine test system.

Ellipsoidal Design of Robust Stabilization for Markov Jump Power Systems under Normal and Contingency Conditions

The essential prerequisites for secure customer service are power system stability and reliability. This work shows how to construct a robust switching control for studying power system load changes using an invariant ellipsoid method. Furthermore, the suggested control ensures stability when the system is subjected to random stochastic external disturbances, and functions randomly in two conditions: normal and contingency. The extreme (least) reliability state is chosen as the most severe scenario (corresponding to a transmission line outage). As a two-state Markov random chain, the transition probabilities are utilized to simulate the switching between normal and contingency modes (or processes). To characterize the dynamics of the studied system, a stochastic mathematical model is developed. The effect of stochastic disturbances and random normal/contingency operations is taken into account during the design stage. For a stochastic power system, a novel excitation control is designed. The attractive ellipsoid approach and linear matrix inequalities (LMIs) optimization are used to build the best two-controller gains. Therefore, the proposed modeling/design technique can be employed for the power system under load changes, stochastic topological changes, and random disturbances. Finally, the system’s random dynamics simulation indicates the effectiveness of the designed control law.

Anti-disturbance observer-based control for fuzzy chaotic semi-Markov jump systems with multiple disturbances and mixed actuator failures

This article develops robust stabilization and anti-disturbance control design for fuzzy chaotic semi-Markov jump systems with randomly occurring uncertainties, nonlinear actuator faults, matched and mismatched disturbances. Primarily, the matched disturbances stimulated from the exogenous systems are dealt with by constructing a disturbance observer. At the same time, mismatched part is handled by the extended passivity performance. Additionally, the actuator fault model which encompasses both linear and nonlinear characteristics is put forward in the controller design. Thus, by taking advantage of the parallel distributed compensation methodology, a composite anti-disturbance control is framed by combining the fuzzy rule-based nonlinear fault-tolerant controller and estimation of the disturbance. Thereafter, by selecting relevant mode-dependent Lyapunov function candidate, adequate criteria are acquired in the context of linear matrix inequalities to ensure robust asymptotic stability along with the endorsed extended passivity performance level for the closed-loop system. In due course, by solving the developed inequalities under the aegis of MATLAB platform, the gain matrices of the devised controller and the framed disturbance observer are obtained. Last of all, to validate the effectiveness and applicability of the theoretical findings, simulation results of standard Chua’s circuit system, Lorenz system and Rössler system are exploited.

Relationship between texture of polypropylene coatings and interface friction for sand at low stress levels

Pipelines in the offshore sector make common use of polypropylene (and other polymer) coating systems to protect the infrastructure and provide thermal insulation. High pressure high temperature pipelines are subject to large axial loads due to restraint by seafloor soils of thermal strains in the pipe wall. Friction between pipe coating material and seafloor soil plays a defining role in the build-up of axial stress and the formation of lateral buckling. Accurate quantification of pipe–soil interface friction is key to robust pipeline stability design and possibilities to enhance or manipulate the friction coefficient may be attractive to designers. An extensive campaign of soil and interface tests using a range of granular materials and polypropylene surface specimens engineered to achieve varying surface textures was carried out. The results show that interface friction primarily depends on stress level and the magnitude of the surface texture in relation to the particle size. Herein, a new relative texture parameter, Ta, is developed that, unlike alternative relative roughness parameters, can be obtained using conventional profilometry measurement techniques. An expression for estimating the friction coefficient in relation to texture and stress level is proposed that can serve as a useful predictor of pipe–soil interface friction.

Adaptive Robust Control for a Class of Uncertain Neutral Systems with Time Delays and Nonlinear Uncertainties

The problems of robust stabilization and adaptive robust controller design are considered for a class of uncertain neutral systems with time delays and nonlinear uncertainties. In this paper, Pade approximation is used to deal with input-delays, and the adaptation laws are proposed to estimate the norm of the unknown parameter uncertainties. Based on the improved Razumikhin-type theorem and the updated values, a class of delay-independent adaptive robust state feedback controllers is constructed to guarantee the uniform ultimate boundedness of uncertain neutral systems with input-delays and nonlinear uncertainties. Finally, the chemical two-stage dissolution tank is used to illustrate the effectiveness of the proposed method.

Robust Linear Parameter Varying Scalar Control Applied in High Performance Induction Motor Drives

This article presents a robust stabilizer designed to damp low-frequency electromechanical oscillations which occurs in induction machines controlled by scalar control when operating at low speed and light load. The robust stabilizer design is based on the linear parameter varying (LPV) approach. A discrete LPV model is identified to allow the design of the robust LPV controller. Experimental tests are performed on a 7.5-kW induction motor dynamometer using an industrial inverter driver. The results show satisfactory improvement of the motor performance with the damping controller activated.

Robust formation control under state constraints of multi-agent systems in clustered networks

This paper studies the formation control problem in clustered network systems composing of linear agents that are subjected to state constraints. In each cluster, there exists an agent called a leader who can communicate with other leaders outside of its cluster at some specific discrete instants. Moreover, the continuous-time communication structure in each cluster is represented by a fixed and undirected graph. A robust formation control protocol is proposed to deal with the hybrid communication described above and the constraints on states of agents. It is next shown that the hybrid robust formation control design for clustered multi-agent networks can be indirectly solved through the robust stabilization design of an equivalent system obtained by matrix theory and algebraic graph theory. Then, a robust controller is designed for the initial clustered network system in terms of linear matrix inequalities. Finally, a formation design for unmanned aerial vehicles is carried out and simulated to illustrate the effectiveness of the proposed hybrid formation control design method.

Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay

This work mainly studies the robust stability analysis and design of a controller for uncertain neutral stochastic nonlinear systems with time-delay. Using a modified Lyapunov–Krasovskii functional and the free-weighting matrices technique, we establish some new delay-dependent criteria in terms of linear matrix inequality (LMI). The innovative point of this work is that we generalize the robust stability analysis of nonlinear stochastic time-delay systems to the uncertain neutral stochastic systems. Due to the added derivative term of time-delay, the proposed scheme can be applied more widely. Finally, numerical examples are provided to validate the derived results.

Robust Consensus Analysis and Design Under Relative State Constraints or Uncertainties

This paper proposes a novel approach to analyze and design distributed robust consensus control algorithms for general linear leaderless multiagent systems (MASs) subjected to relative-state constraints or uncertainties represented by a locally or a globally sector-bounded condition. First, we show that the MAS robust consensus design under relative-state constraints or uncertainties is equivalent to the robust stability design under state constraints or uncertainties of a transformed MAS, which has lower dimensions. Next, the transformed MAS under state constraints or uncertainties is reformulated as a networked Lur’e system. By employing the S-procedure and Lyapunov theory, sufficient conditions for robust consensus and the designs of robust consensus controller gain are derived from solutions of distributed linear matrix inequality (LMI) convex problems. Finally, numerical examples are introduced to illustrate the effectiveness of the proposed theoretical approach.

Application of Information Gap Decision Theory to the Design of Robust Wide-Area Power System Stabilizers Considering Uncertainties of Wind Power

This paper proposes the application of information gap decision theory (IGDT) to the design of robust wide-area power system stabilizers (WPSSs) with consideration of wind farm (WF) power outputs variations and transmission line outages. According to IGDT, an optimization problem is constructed to tune WPSS parameters. Then, the derived optimal WPSSs can achieve explicit and favorable robustness to ensure the required damping control effects on the interarea oscillations over a maximum variation range of WF steady-state power outputs in normal and emergent operating conditions. Moreover, with the intent of using the excellent global searching capability of particle swarm optimization (PSO), a customized PSO algorithm is proposed to efficiently solve the resulting highly nonlinear programming problem. Finally, simulations are carried out on a modified New England (10-machine 39-bus) system to validate the efficiency of the IGDT-based design method. The derived WPSSs exhibit expected robustness with respect to the wind power variations and transmission line outages.

Optimal robust stabilizer design based on UPFC for interconnected power systems considering time delay

AbstractA robust auxiliary wide area damping controller is proposed for a unified power flow controller (UPFC). The mixedH2/H∞problem with regional pole placement, resolved by linear matrix inequality (LMI), is applied for controller design. Based on modal analysis, the optimal wide area input signals for the controller are selected. The time delay of input signals, due to electrical distance from the UPFC location is taken into account in the design procedure. The proposed controller is applied to a multi-machine interconnected power system from the IRAN power grid. It is shown that the both transient and dynamic stability are significantly improved despite different disturbances and loading conditions.

Stabilization of Non‐Linear Fractional‐Order Uncertain Systems

AbstractIn this paper, we present a stabilization method on the non‐linear fractional‐order uncertain systems. Firstly, a sufficient condition for the robust asymptotic stabilization of the non‐linear fractional‐order uncertain system is presented based on direct Lyapunov approach. Secondly, utilising the matrix's singular value decomposition (SVD) method, the systematic robust stabilization design algorithm is then proposed. Finally, two numerical examples are provided to illustrate the efficiency and advantage of the proposed algorithm.

Stability Feelerによるロバスト安定解析・設計

Stability Feelerによるロバスト安定解析・設計

Observer‐Based Robust Controller Design for Nonlinear Fractional‐Order Uncertain Systems via LMI

We discuss the observer‐based robust controller design problem for a class of nonlinear fractional‐order uncertain systems with admissible time‐variant uncertainty in the case of the fractional‐order satisfying 0 < α < 1. Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer‐based nonlinear fractional‐order uncertain systems is presented. Employing Finsler’s Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations.

Iterative LMI approach to design robust state-feedback controllers for Lur’e systems with time-invariant delays

In this paper, we present a design of robust state-feedback stabilization and a design of robust state-feedback H∞ control for Lur’e systems with time-invariant delays and norm-bounded uncertainties. The criteria of state-feedback stabilization and state-feedback H∞ control are developed using Lyapunov-Krasovskii Theorem with a delay-partitioning Lyapunov-Krasovskii functional and an integral of sector-bounded nonlinearities. The design criteria are given in terms of bilinear matrix inequality, which is non-convex optimization. We develop algorithms based on coordinate optimization, which alternate between two LMI optimization problems, to solve for the robust state-feedback controllers. The proposed iterative LMI algorithm for H∞ control design is a local optimization procedure, but it can return satisfactory state-feedback controllers depending on the initialization. Numerical examples show that the proposed LMI algorithms can provide robust state-feedback stabilization to guarantee the closed-loop stability of LSTD and yield robust state-feedback control to guarantee the worstcase H∞ performance of the closed-loop LSTD.

Frontier technologies of trust computing and network security

The increasing complexity of computer systems and communication networks induces tremendous requirements for trust and security. This special issue includes topics on trusted computing, risk and reputation management, network security and survivable computer systems/networks. These issues have evolved into an active and important area of research and development. The past decade has witnessed a proliferation of concurrency and computation systems for practice of highly trust, security and privacy, which has become a key subject in determining future research and development activities in many academic and industrial branches. This special issue aims to present and discuss advances of current research and development in all aspects of trusted computing and network security. In addition, this special issue provides snapshots of contemporary academia work in the field of network trusted computing. We prepared and organized this special issue to record state-of-the-art research, novel development and trends for future insight in this domain. In this special issue, 14 papers have been accepted for publication, which demonstrate novel and original work in this field. A detailed overview of the selected works is given below.

Disturbance rejection control for non-minimum phase systems with optimal disturbance observer

This paper investigates the disturbance rejection control for stable non-minimum phase (NMP) systems with time delay. A robust disturbance observer (DOB) based control structure is proposed. Specifically, the robust DOB is employed to compensate the uncertain plant into a nominal one, based on which a prefilter is adopted to acquire desired performance. Then, a novel DOB configuration strategy for stable NMP systems is proposed. This strategy synthesizes the internal and robust stability, relative order and mixed sensitivity design requirements together to establish the optimization function. The optimal solution is obtained by standard H∞ theory under the condition of guarantying the presented requirements. We also investigate how the DOB can compensate the uncertain plant into a nominal one. The specifical design procedure is presented for an uncertain plant with both unstable zeros and time delay.