Time-varying Parameter Uncertainties Research Articles

New results on passivity of fractional-order uncertain neural networks

In this paper, robust passivity problem for a class of fractional-order uncertain neural networks (FUNNs) in the sense of Caputo’s fractional derivation is investigated. In particular, we consider two types of uncertainties (i.e. time-varying parameter uncertainty and interval uncertainty). With the help of linear matrix inequality (LMI) techniques and control theories of fractional system, some sufficient criteria are derived to ensure passivity of FUNNs, which enrich and improve the earlier integer-order and fractional-order publications. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.

Robust passivity and feedback passification of a class of uncertain fractional-order linear systems

ABSTRACTTheoretical results on robust passivity and feedback passification of a class of uncertain fractional-order (FO) linear systems are presented in the paper. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output matrices. Firstly, some suitable notions of passivity and dissipativity for FO systems are proposed, and the relationship between passivity and stability is obtained. Then, a sufficient condition in the form of linear matrix inequality (LMI) for such system to be robustly passive is given. Based on this condition, the design method of state feedback controller is proposed when the states are available. Moreover, by using matrix singular value decomposition and LMI techniques, the existing condition and method of designing a robust observer-based passive controller for such systems are derived. Numerical simulations demonstrate the effectiveness of the theoretical formulation.

Robust H∞ persistent dwell time control for switched discrete-time T–S fuzzy systems with uncertainty and time-varying delay

This paper is concerned with the controller synthesis for switched Takagi–Sugeno (T–S) fuzzy systems with time-varying delays, parameter uncertainties and process disturbances. A persistent dwell time (PDT) based control law is mainly proposed for the T–S fuzzy systems in presenting of high-frequency motion switches. Different with the most existing literatures, the dynamics of local subsystems are allowed to be unstable during fast switching time intervals as well as the jump time instants. In addition, the maximal period of persistence time is not limited. Under the influences of the time-varying delays, uncertainties and disturbances, the proposed method ensures the overall closed-loop system to be globally uniformly exponentially stable. Moreover, a pre-given H∞ performance can be simultaneously guaranteed. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

Adaptive iterative learning control for switched nonlinear continuous-time systems

ABSTRACTIn this paper, an adaptive iterative learning control (ILC) method is proposed for switched nonlinear continuous-time systems with time-varying parametric uncertainties. First, an iterative learning controller is constructed with a state feedback term in the time domain and an adaptive learning term in the iteration domain. Then a switched nonlinear continuous-discrete two-dimensional (2D) system is built to describe the adaptive ILC system. Multiple 2D Lyapunov functions-based analysis ensures that the 2D system is exponentially stable, and the tracking error will converge to zero in the iteration domain. The design method of the iterative learning controller is obtained by solving a linear matrix inequality. Finally, the efficacy of the proposed controller is demonstrated by the simulation results.

Interval type-2 fuzzy sampled-data control of time-delay systems

The problem of interval type-2 (IT2) fuzzy sampled-data stabilization is addressed for nonlinear continuous-time systems with time-varying delay and parameter uncertainties. The input-delay approach together with free-weighting and slack matrices is utilized to enforce the stability analysis, and a sufficient condition is formulated. Based on the condition, an IT2 fuzzy sampled-data controller is developed such that the closed-loop system is asymptotically stable. Illustrative examples are used to manifest the merits of this design.

Adaptive output-feedback synchronisation of electromechanical systems under time-varying communication delays

ABSTRACT This paper deals with the position synchronisation problem for a class of electromechanical systems, which can be represented by Euler–Lagrange equations, where velocities of agents are not measurable. The agents share their position errors and filter-output signals, instead of actual velocity errors, over a directed communication network, in the presence of time-varying delay. Besides, balanced communication topology is also not required. The proposed adaptive control mechanism ensures the position synchronisation among agents, as well as the tracking of each agent to given desired trajectory, under the effects of time-varying communication delay, parametric uncertainty and unknown external disturbance, simultaneously. By employing a classical Lyapunov approach and Lyapunov–Krasovskii functionals, it is concluded that the suggested control structure yields semi-global asymptotic convergence of all closed-loop errors, including synchronisation errors. The simulation results, on a six-marine vessel network system, are presented to validate the feasibility of the proposed control scheme.

Path following of a surface ship sailing in restricted waters under wind effect using robust H∞ guaranteed cost control

The path following problem of a ship sailing in restricted waters under wind effect is investigated based on Robust H∞ Guaranteed Cost Control (RHGCC). To design the controller, the ship maneuvering motion is modeled as a linear uncertain system with norm-bounded time-varying parametric uncertainty. To counteract the bank and wind effects, the integral of path error is augmented to the original system. Based on the extended linear uncertain system, sufficient conditions for existence of the RHGCC are given. To obtain an optimal robust H∞ guaranteed cost control law, a convex optimization problem with Linear Matrix Inequality (LMI) constraints is formulated, which minimizes the guaranteed cost of the close-loop system and mitigates the effect of external disturbance on the performance output. Numerical simulations have confirmed the effectiveness and robustness of the proposed control strategy for the path following goal of a ship sailing in restricted waters under wind effect.

Reliable asynchronous sampled-data filtering of T–S fuzzy uncertain delayed neural networks with stochastic switched topologies

This paper investigates the issue of the reliable asynchronous sampled-data filtering of Takagi–Sugeno (T–S) fuzzy delayed neural networks with stochastic intermittent faults, randomly occurring time-varying parameters uncertainties and controller gain fluctuation. The asynchronous phenomenon occurs between the system modes and controller modes. First, in order to reduce the utilization rate of communication bandwidth, a novel alterable sampled-data terminal method is considered via variable sampling rates. Second, based on the fuzzy-model-based control approach, improved reciprocally convex inequality and new parameter-time-dependent discontinuous Lyapunov approach, several relaxed conditions are derived and compared with the existing work. Third, the intermittent fault-tolerance scheme is also taken into fully account in designing a reliable asynchronous sampled-data controller, which ensures such that the resultant neural networks is asymptotically stable. Finally, two numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results.

New reliable nonuniform sampling control for uncertain chaotic neural networks under Markov switching topologies

This paper studies the stochastic exponential synchronization problem for uncertain chaotic neural networks (UCNNs) with probabilistic faults (PFs) and randomly occurring time-varying parameters uncertainties(ROTVPUs). To reflect more realistic control behaviors, a new stochastic reliable nonuniform sampling controller with Markov switching topologies is designed for the first time. First, by taking into full account more information on sawtooth structural sampling pattern, time delay and its variation, a novel loose-looped Lyapunov–Krasovskii functional (LLLKF) is developed via introducing matrices-refined-function and adjustable parameters. Second, with the aid of novel LLLKF and relaxed Wirtinger-based integral inequality (RWBII), new synchronization algorithms are established to guarantee that UCNNs are synchronous exponentially under probabilistic actuator and sensor faults. Third, based on the proposed optimization algorithm, the desired reliable sampled-data controller can be achieved under more larger exponential decay rate. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the designed algorithms.

New Criteria for Guaranteed Cost Control of Nonlinear Fractional-Order Delay Systems: a Razumikhin Approach

The Krasovskii–Lyapunov second method provides a powerful approach to stability analysis of nonlinear systems; however, it is not always effectively applied for fractional-order systems (FOSs) with delay. In this paper, we investigate the problem of guaranteed cost control of fractional-order delay systems subject to nonlinear perturbations and parametric time-varying uncertainties. By using fractional Razumikhin theorem, new sufficient conditions are derived for designing a guaranteed cost controller, which not only makes the closed-loop system asymptotically stable but also guarantees an adequate cost level of performance. Compared with the existing results on the integer-order control systems, our results are more effective and convenient for testing and application. The proposed approach allows us to derive stability criteria of linear uncertain FOSs with delay. Finally, numerical examples are given to show the effectiveness of the obtained results.

Observer-based iterative and repetitive learning control for a class of nonlinear systems

In this paper, both output-feedback iterative learning control &#x0028 ILC &#x0029 and repetitive learning control &#x0028 RLC &#x0029 schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.

Robust Nonlinear Disturbance Observer Based Adaptive Guidance Law Against Uncertainties in Missile Dynamics and Target Maneuver

The proposed robust nonlinear disturbance observer based adaptive guidance method considers the nonlinear coupled missile dynamics and rapidly maneuvering target. It also includes unavailable information such as high-order line-of-sight rates and target acceleration as time-varying parametric uncertainties and nonparametric disturbances. An integrated guidance and control model, a robust nonlinear disturbance observer, a nonlinear missile jerk observer, and a robust nonlinear guidance law are proposed, the validity of which is demonstrated by stability analysis and simulations.

Driver-Assistance Lateral Motion Control for In-Wheel-Motor-Driven Electric Ground Vehicles Subject to Small Torque Variation

Electric ground vehicles driven by in-wheel-motors (IWMs) have control flexibility of easily generating external yaw moment, which is effective for vehicle lateral motion control without interfering driver steering maneuvers. However, IWMs small torque variation may introduce undesired yaw moment that causes vehicle trajectory drifts and affects lateral motion. This paper proposes a driver-assistance lateral motion control method specifically considering IWMs small torque variation. In driving conditions where a driver steering maneuver is not expected, the controller compensates for small torque variation to reduce the driver workload. However, for driving conditions that require steering input from the driver, the controller assists the driver to maintain the path when there is a tendency of lane departure. A gain-scheduling robust controller is designed to deal with a time-varying parameter and system uncertainty. The weighted ${H_\infty }$ performance and eigenvalue placement technique are employed to derive a suitable feedback gain. CarSim simulations are conducted to illustrate the control effectiveness for compensating small torque variation and prevent lane departure. Furthermore, human-in-the-loop tests are conducted to verify the effectiveness of the designed controller for human drivers. Both simulation results and human driving simulator tests show that the proposed controller can assist drivers with vehicle lateral motion control under different driving conditions subject to IWMs small torque variation.

Reliable $$\mathcal {H}_{\infty }$$ H ∞ controller for uncertain networked control systems with additive time-varying delays and nonlinear actuator faults

In this paper, the problem of exponential stability for a class of networked control system is investigated. Proposed system consisting additive time-varying delays, parameter uncertainties, external disturbance, nonlinearities and actuator faults which makes more generalized system model. The inclusion of actuator fault matrix and nonlinear perturbation in the formulation of reliable controller gives more practical applications in networked control system. The main goal of this paper is to formulate a reliable $$\mathcal {H}_{\infty }$$ controller which assures the exponential stability of considered system. Based on the integral inequality technique, a new linear matrix inequality criteria has been obtained by formulating a suitable Lyapunov–Krasovskii functional for the exponential stability of the proposed networked control system. Finally, numerical example is provided to validate the effectiveness of the proposed method.

Finite-time H∞ adaptive attitude fault-tolerant control for reentry vehicle involving control delay

This paper proposes a finite-time adaptive fault tolerant control method for the attitude control of reentry vehicle, by combining the radial basis function (RBF) network technology with adaptive fault tolerant control method. We simultaneously considered actuator faults, control delay, input saturation, time-varying parameter uncertainties and external disturbances when designing the control method. The theoretical part of this paper includes the establishment of attitude dynamic model concerning actuator faults and the design of finite-time H∞ adaptive attitude fault-tolerant controller. We proved the stability of our proposed adaptive attitude fault-tolerant controller through the Lyapunov function and the linear matrix inequality (LMI) method. The simulation results show that our proposed method not only can effectively deal with actuator faults in the attitude control system, but also has very good robustness for control delay, input saturation, time-varying parameter uncertainties and external disturbances.

Design of a stabilizing controller for discrete-time switched delay systems with affine parametric uncertainties

This paper studies the stabilization problem of discrete-time switched systems in the presence of a time-varying delay and parametric uncertainties. The main goal is to provide a state feedback controller to guarantee the stability of the closed-loop system with an evaluated average dwell time. In this regard, an appropriate Lyapunov–Krasovskii functional is constructed and the sufficient conditions for stability of the closed-loop system are developed in terms of feasibility testing of proposed linear matrix inequalities. These conditions only depend on the upper bounds of the time delay and uncertain parameters. Additionally, a numerical example is provided to verify the theoretical results.

Robust normalisation and P–D state feedback control for uncertain singular Markovian jump systems with time‐varying delays

This study is concerned with the problem of robust normalisation and stabilisation of singular Markovian jump systems (SMJSs) with time-varying delays and parameter uncertainties. The main aim is to design a proportional and derivative state feedback controller to realise the normalisation and stabilisation of the delayed SMJSs. Based on the constructed Lyapunov–Krasovskii functional, sufficient conditions are presented in terms of linear matrix inequalities via utilising the free-weighting matrix method. Illustrative examples including an resistor inductor capacitor (RLC) circuit network are employed to demonstrate the effectiveness and usefulness of the obtained results.

Generalized Proportional Integral Observer-Based Robust Finite Control Set Predictive Current Control for Induction Motor Systems with Time-Varying Disturbances

During the past few years, finite control set predictive current control (PCC) method has attracted more and more attention in research and industry applications. However, PCC method could be improved by considering two points. First, the current reference used in the cost function of PCC control scheme is usually produced by a proportional and integration speed controller. Confront with load torque and time-varying system parameters, it is a better solution to design a disturbance estimation based feed-forward compensated controller. In this way, the current reference could be generated faster and more accurate. Second, the PCC method is model-based method which means the accuracy of the model parameters are essential. In real system, time-varying parameters existed almost always. This paper investigates a generalized proportional integral observer based PCC approach for dealing with load torque disturbance, time-varying parameter uncertainties. The effectiveness of the proposed method has also been confirmed by simulation and a lab-constructed experimental prototype.

Non-Fragile Control for Variable Sampling Period Network Control System with Actuator Failure

The guaranteed cost control problem is studied in this paper for a class of nonlinear discrete-time systems with both time-varying parametric uncertainty and actuator failures. At present, the researches on related fields of networked control systems are relatively mature, and many achievements have been made. But at the same time, most of the researches are focused on linear networked control systems, and the research on nonlinear networked control systems is relatively less. The goal is to design a non-fragile state feedback control law so that the closed-loop system is asymptotically stable and the closed-loop cost function value is no more than a specified upper bound for all admissible uncertainties. Firstly, the system model is established by using the method of variable sampling period. Secondly, the sufficient conditions for the asymptotic stability of the closed-loop system are given by using Lyapunov stability theory. Thirdly, based on the above researches, a non-fragile state feedback controller is designed by using linear matrix inequality (LMI). In the end, through the study of this paper, the cost function of the system under the designed non-fragile guaranteed cost controller does not exceed the given upper bound. This paper considers the actuator failure, and gives the design method of the non-fragile guaranteed cost controller of the nonlinear network control system, and makes a contribution to the field of network control system.

Robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach

The problem of robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach is investigated. The time-varying delay and parameter uncertainties are assumed to be of an internal-like type and a structured linear fractional form, respectively. Based on a Lyapunov–Krasovskii functional in delta domain, robust ℋ∞ filter scheme is proposed. Then, a sufficient condition is established for the existence of the desired filter in terms of linear-matrix inequalities. A numerical example is provided to illustrate the design procedure of the present method.