Backstepping-based decentralized adaptive neural H∞ tracking control for a class of large-scale nonlinear interconnected systems

The decentralized tracking control methods for large-scale nonlinear systems are investigated in this paper. A backstepping-based robust decentralized adaptive neural H_∞ tracking control method is addressed for a class of large-scale strict feedback nonlinear systems with uncertain disturbances. Under the condition that the nonlinear interconnection functions in subsystems are unknown and mismatched, the decentralized adaptive neural network H_∞ tracking controllers are designed based on backstepping technology. Neural networks are used to approximate the packaged multinomial including the unknown interconnections and nonlinear functions in the subsystems as well as the derivatives of the virtual controls. The effect of external disturbances and approximation errors is attenuated by H_∞ tracking performance. Whether the external disturbances occur or not, the output tracking errors of the close-loop system are guaranteed to be bounded. A practical example is provided to show the effectiveness of the proposed control approach.     

Reliable H∞ output control of nonlinear systems with dynamic event-triggered scheme

This paper is concerned with the reliable event-triggered H_∞ output control of nonlinear systems with actuator faults. A dynamic triggering scheme depending on system outputs is implemented to reduce the amount of communication transmissions, which is different from existing constant triggering thresholds. The parameters of actuator faults are estimated via observer state. To compensate for the fault effects on systems, the reliable controller parameters are adjusted along with the obtained estimations. By using some technical lemmas, new sufficient conditions for the closed-loop system to be asymptotically stable with prescribed H_∞ performance are formed in linear matrix inequalities. Lastly, simulations are implemented to demonstrate the validity of the proposed method.     

H∞ output-feedback control for discrete-time switched linear systems via asynchronous switching

In this paper, we consider the H_∞ hybrid dynamical output-feedback control problem for discrete-time switched linear systems under asynchronous switching. A time-varying multiple Lyapunov-like-function (MLF) approach is applied to derive sufficient conditions that guarantee the stability and weighted l₂-gain performance of the closed-loop systems, where the established conditions explicitly depend on the upper and lower bounds of asynchronous switching delays. An alternative approach is proposed to decouple the bilinear problems of the control synthesis conditions. Convex optimization algorithms are also proposed based on the established conditions to determine the minimum l₂-gain performance. Two numerical examples are provided to illustrate the effectiveness of the proposed method, demonstrating significant improvement over the existing results.     

Mixed H∞ and passivity control for a class of stochastic nonlinear sampled-data systems

In this paper, we consider the problem of mixed H_∞ and passivity control for a class of stochastic nonlinear systems with aperiodic sampling. The system states are unavailable and the measurement is corrupted by noise. We introduce an impulsive observer-based controller, which makes the closed-loop system a stochastic hybrid system that consists of a stochastic nonlinear system and a stochastic impulsive differential system. A time-varying Lyapunov function approach is presented to determine the asymptotic stability of the corresponding closed-loop system in mean-square sense, and simultaneously guarantee a prescribed mixed H_∞ and passivity performance. Further, by using matrix transformation techniques, we show that the desired controller parameters can be obtained by solving a convex optimization problem involving linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the proposed method in practical systems are demonstrated by the simulation studies of a Chua’s circuit and a single-link flexible joint robot.     

Incremental H∞ performance for a class of stochastic switched nonlinear systems

In this paper, we investigate the incremental H_∞ performance problem for a class of stochastic switched nonlinear systems by using a state-dependent switching law and the maximum and minimum dwell time approach. By resorting to the state-dependent switching law, some sufficient conditions are provided to cope with the incremental H_∞ performance problem, which can be applied even if all subsystems are unstable. Then, based on the maximum and minimum dwell time scheme, the incremental H_∞ performance problem to be solvable is derived for two cases: one is all subsystems are incrementally globally asymptotically stable in the mean(IGASiM), another is both IGASiM subsystems and unstable subsystems coexist. When all subsystems are IGASiM, the stochastic switched nonlinear system is IGASiM and possesses a incremental L₂-gain under given conditions. When both IGASiM subsystems and unstable subsystems coexist, if the activation time ratio between IGASiM subsystems and unstable ones is not less than a specified constant, the sufficient conditions for the incremental H_∞ performance of the stochastic switched nonlinear system are given. Two numerical examples are given to illustrate the validity of methods proposed.     

Mixed H∞ and passive control for a class of nonlinear switched systems with average dwell time via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for a class of nonlinear switched systems based on a hybrid control strategy. To solve this problem, firstly, using the Takagi–Sugeno (T–S) fuzzy model to approximate every nonlinear subsystem, the nonlinear switched systems are modeled as the switched T–S fuzzy systems. Secondly, the hybrid controllers are used to stabilize the switched T–S fuzzy systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. Thirdly, a new performance index is proposed for switched systems. This new performance index can be viewed as the mixed weighted H_∞ and passivity performance. Based on this new performance index, the weighted H_∞ control problem and the passive control problem for switched T–S fuzzy systems via the hybrid control strategy are solved in a unified framework. Together the multiple Lyapunov functions (MLFs) approach with the average dwell time (ADT) technique, new design conditions for the hybrid controllers are obtained. Under these conditions, the closed-loop switched T–S fuzzy systems are globally uniformly asymptotically stable with a prescribed mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the obtained results is illustrated by a numerical example.     

Event-triggered H∞ filtering control for a class of distributed parameter systems with Markovian switching topology

The H_∞ filtering problem for distributed parameter systems with stochastic switching topology is investigated in this paper based on event-triggered control scheme. The switching topology which subjects to a Markovian chain is considered in filter design because of the communication uncertainty of practical networks. An event-triggered mechanism as a sampling scheme is developed aiming at the benefit of reducing the computation load or saving the limited network resources. Based on some novel integral inequalities, the improved delayed method is proposed for the H_∞ filtering control problem with event-triggered scheme. Moreover, by employing stochastic stability theory, filters with Markovian jump parameters are designed to guarantee that the stochastically mean square stability and H_∞ performance of the underlying error system. Finally, in order to illustrate the applicability of the obtained results, numerical examples are presented.     

Robust H∞ control of an observer-based repetitive-control system

This paper concerns the problem of designing a robust observer-based modified repetitive-control system with a prescribed H_∞ disturbance rejection level for a class of strictly proper linear plants with unknown aperiodic disturbances and time-varying structural uncertainties. A correction to the amount of the delay in the repetitive controller is introduced that leads to a significant improvement in tracking performance. An integrated performance index is defined to quantify the overall effect of rejecting the aperiodic disturbances and tracking the periodic reference input. A Lyapunov functional with two tuning parameters is used to derive a linear-matrix-inequality based robust stability condition for the system with a prescribed disturbance-rejection bound. Combining the performance indices, an optimization algorithm that searches for the best combination of state-observer gain and the feedback control gains is developed. A numerical example illustrates the design procedure and demonstrates the effectiveness of the method.     

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

In this paper, a novel decentralized adaptive neural control approach based on the backstepping technique is proposed to design a decentralized H_∞ adaptive neural controller for a class of stochastic large-scale nonlinear systems with external disturbances and unknown nonlinear functions. RBF neural networks are utilized to approximate the packaged unknown nonlinearities. A novel concept with regard to bounded-H_∞ performance is proposed. It can be applied to solve an H_∞ control problem for a class of stochastic nonlinear systems. The constant terms appeared in stability analysis are dealt with by using Gronwall inequality, so that H_∞ performance criterion is satisfied. The assumption that the approximation errors of neural networks must be square-integrable in some literature can be eliminated. The design process for decentralized bounded-H_∞ controllers is given. The proposed control scheme guarantees that all the signals in the resulting closed-loop large-scale system are uniformly ultimately bounded in probability, and each subsystem possesses disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach.     

Simultaneous H∞ stabilization for large-scale systems within distributed wireless networked control framework over fading channels

In this paper, the simultaneous H_∞ stabilization problem is investigated for a physically interconnected large-scale system which works in multiple operation modes. A distributed wireless networked control framework is introduced, in which the distributed dynamic output feedback controllers not only use the local measurements, but also receive the neighboring controllers’ broadcasts via wireless networks. The channel fading in wireless communications is described as the Rice fading model. Our focus is on the design of the distributed controllers such that the large-scale system is mean-square stable in each operation mode and achieves a prescribed H_∞ disturbance attenuation level. By employing the Lyapunov functional method and related stochastic analysis techniques, a sufficient condition on the existence of desired controllers is presented, and the parameterization of the controller gains is derived. Finally, a numerical example is utilized to illustrate the feasibility of the proposed scheme.     

H∞ tracking control for a class of asynchronous switched nonlinear systems with uncertain input delay

This paper studies the problems of stability and H∞ model reference tracking performance for a class of asynchronous switched nonlinear systems with uncertain input delay. First, it is assumed switched controller and corresponding piecewise Lyapunov function are unknown but the derivative of piecewise Lyapunov function has a condition; this condition implies that the nominal system (system without input delay and disturbance) is exponentially stable by any switched controller which satisfies this condition. With this assumption, a proper Lyapunov–Krasovskii functional is constructed. By employing this new functional and average dwell time technique, the delay-dependent input-to-state stability criteria are derived under a certain delay bound; in addition, a mechanism which finds the upper bound of input delay is proposed. Finally, a kind of state feedback control law which fulfils condition of aforesaid piecewise Lyapunov function is introduced to guarantee the input-to-state stability and H∞ model reference tracking performance. Simulation examples are presented to demonstrate the efficacy of results.     

H∞ finite time control for discrete time-varying system with interval time-varying delay

This paper discusses the problem of H_∞ finite time control for a discrete time-varying system with interval time-varying delay. By constructing a new augmented time-varying Lyapunov functional involving triple summation items and using discrete Wirtinger-type inequalities, delay-dependent conditions are derived, which guarantee that the closed-loop system is not only finite time bounded (FTB) but also satisfies an H_∞ performance. Furthermore, the time-varying feedback controller can be derived by solving a series of recursive linear matrix inequalities (RLMIs). Simulation results show the effectiveness and superiority of the proposed method.     

Finite-time H∞ control for a class of discrete-time nonlinear singular systems

This paper investigates the finite-time control problems for a class of discrete-time nonlinear singular systems via state undecomposed method. Firstly, the finite-time stabilization problem is discussed for the system under state feedback, and a finite-time stabilization controller is obtained. Then, based on which, the finite-time H_∞ boundedness problem is studied for the system with exogenous disturbances. Finally, an example of population distribution model is presented to illustrate the validity of the proposed controller. Because there is no any constraint for singular matrix E in the paper, controllers can be designed for more discrete-time nonlinear singular systems.     

Robust H∞ control for a class of uncertain nonlinear systems with mixed time-delays

This paper is concerned with the robust H_∞ control problem for a general class of uncertain nonlinear systems with mixed time-delays. The mixed time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is robustly stable for all admissible uncertainties with guaranteed H_∞ disturbance rejection attenuation level. By introducing a new Lyapunov–Krasovskii functional that reflects the mixed delays, sufficient conditions are established for the closed-loop system ensuring the robust stability as well as the H_∞ performance requirement. The controller design is facilitated in terms of the solvability of a Hamilton–Jacobi inequality. Two numerical examples are utilized to demonstrate the effectiveness of the proposed methods.     

A new delay-range-dependent H∞ filter design for T–S nonlinear systems

This paper focuses on the problem of _H∞$H_{\infty }$ filter design for continuous-time Takagi and Sugeno (T–S) fuzzy systems with time-varying delays. The partitioning time delay technique is used to construct the Lyapunov–Krasovskii functional, furthermore, a novel delay-dependent _H∞$H_{\infty }$ filter design approach is proposed based on the matrix decoupling approach, and the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). The numerical examples show that the proposed method is of less conservativeness than the existing methods.     

Robust H∞ dynamic output-feedback control for four-wheel independently actuated electric ground vehicles through integrated AFS/DYC

This paper simultaneously addresses the parameter/state uncertainties, external disturbances, input saturations, and actuator faults in the handling and stability control for four-wheel independently actuated (FWIA) electric ground vehicles (EGVs). Considering the high cost of the available sensors for vehicle lateral velocity measurement, a robust H_∞ dynamic output-feedback controller is designed to control the vehicle motion without using the lateral velocity information. The investigated parameter/state uncertainties include the tire cornering stiffness, vehicle mass, and vehicle longitudinal velocity. The unmodeled terms in the vehicle lateral dynamics model are dealt as the external disturbances. Faults of the active steering system and in-wheel motors can cause dangerous consequences for driving, and are considered in the control design. Input saturation issues for the tire forces can deteriorate the control effects, and are handled by the proposed strategy. Integrated control with active front steering (AFS) and direct yaw moment (DYC) is adopted to control the vehicle yaw rate and sideslip angle simultaneously. Simulation results based on a high-fidelity and full-car model via CarSim-Simulink show the effectiveness of the proposed control approach.     

Reliable H∞ control on saturated linear Markov jump system with uncertain transition rates and asynchronous jumped actuator failure

This paper is concerned with reliable H_∞?control for saturated linear Markov jump systems with uncertain transition rates and asynchronous jumped actuator failure. The actuator failures are assumed to occur randomly under the Markov process with a different jumping mode from the system jumping mode. In considering the mixed-mode-dependent state feedback controller, both H_∞ stochastic stability analysis for closed-loop system with completely accessible transition rates and uncertain transition rates are investigated. Moreover, based on the obtained stability conditions, the H_∞?control problems are investigated, and the controller gains can be obtained by solving a convex optimization problem with minimizing H_∞ performance as objective and linear matrix inequalities (LMIs) as constraints. The problem of designing state feedback controllers such that the estimate of the domain of attraction is enlarged is also formulated and solved as an optimization problem with LMI constraints. Simulation results are presented to illustrate the effectiveness of the proposed results.     

Immersion and invariance adaptive control with σ-modification for uncertain nonlinear systems

A novel adaptive control with σ-modification for uncertain nonlinear systems is proposed in the paper. The application of conventional adaptive control is severely limited by the problems of construction of Lyapunov function and parameter drift because of non-parametric uncertainties. The proposed adaptive control that is on the basis of the immersion and invariance theory and σ-modification can be used to deal with these problems to some extent. It turns out to be a structured design method without requiring a Lyapunov function in the design level and robust to non-parametric uncertainties. Moreover, constrained command filter backstepping is adopted to meet the amplitude and rate constraints on the states and actuators. The uniformly ultimately bounded stability of the closed-loop system has been analyzed by Lyapunov theory with parametric and non-parametric uncertainties of the controlled model. To demonstrate the design flexibility, the method is applied to the position tracking control system design of a mass-damper-spring system and the flight control system design of a scramjet-powered air-breathing hypersonic vehicle. Finally, the effectiveness of the proposed adaptive control method is illustrated by numerical simulations.     

Sum-of-squares-based robust H∞ controller design for discrete-time polynomial fuzzy systems

This paper investigates a robust H_∞ controller design for discrete-time polynomial fuzzy systems based on the sum-of-squares (SOS) approach when model uncertainties and external disturbances are simultaneously considered. At the beginning of the controller design procedure, a general discrete-time polynomial fuzzy control system proposed in this paper is used to represent a nonlinear system containing model uncertainties and external disturbances. Subsequently, through use of a nonquadratic Lyapunov function and the H_∞ performance index, the novel SOS-based robust H_∞ stability conditions are derived to guarantee the stability of the entire control system. By solving those stability conditions, control gains of the robust H_∞ polynomial fuzzy controller are obtained. Because the model uncertainties and external disturbances are considered simultaneously in the controller design procedure, the closed-loop control system achieves greater robustness and H_∞ performance against model uncertainties and external disturbances. Moreover, the novel operating-domain-based robust H_∞ stability conditions are derived by considering the operating domain constraint to relax the conservativeness of solving the stability conditions. Finally, simulation results demonstrated the availability and effectiveness of the proposed stability conditions, which are more general than those used in existing approaches.     

Robust mixed H2/H∞ model predictive control for Markov jump systems with partially uncertain transition probabilities

This paper addresses the control problem for a class of discrete-time Markov jump linear systems with partially unknown transition probabilities using model predictive controller subject to external disturbances and input constraints. Our focus is on the design of a model predictive controller to stabilize the system with a given mixed H₂/H_∞ performance index. Sufficient conditions are derived in terms of a set of linear matrix inequalities. Examples are presented to demonstrate the effectiveness of the proposed controller design method.