Composite anti-disturbance control for uncertain Markovian jump systems with actuator saturation based disturbance observer and adaptive neural network

This paper studies the problem of composite control for a class of uncertain Markovian jump systems (MJSs) with partial known transition rates, multiple disturbances and actuator saturation. Compared with the existing results, a novel robust composite control scheme is put forward by virtue of adaptive neural network technique. For MJSs, the partial unknown information on transition rates and the actuator saturation influence the design of disturbance observer and the robust H_∞ controller. Firstly, without taking account of external disturbances, the network reconstruction error and saturation, a novel robust adaptive control strategy is established to ensure that all the signals of the closed-loop system are asymptotically bounded in mean square. Secondly, the solvability condition for ensuring the robust H_∞ performance is given by using a modified adaptive law, where the saturation is treated as a disturbance-like signal. Finally, the simulations for a numerical example and an application example are performed to validate the effectiveness of the proposed results.     

Resilient control based on disturbance observer for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters

In this paper, the composite anti-disturbance resilient control is considered for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters under multiple disturbances. Three kinds of disturbances are included in the studied system. One is generated by an external system and it enters the hybrid system from the channel of the control input. The other one is stochastic white noise. And the third one is the external unknown time-varying disturbance and it is supposed to be H₂ norm bounded. By combining the disturbance-observer-based-control scheme, H_∞ control technique and resilient control method, a composite anti-disturbance resilient controller is constructed to attenuate and eliminate the affection of these disturbances, and ensures the whole closed-loop system regular, impulse free and stochastically stable with the corresponding control performance. Then, some sufficient conditions and the gains of the controller and observer are obtained by using Lyapunov function method and the linear matrix inequalities (LMIs) technique. Finally, two numerical examples are given to show the effectiveness of presented method.     

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.     

Robust fault tolerant tracking controller design for a VTOL aircraft

This paper deals with the fault tolerant control (FTC) design for a Vertical Takeoff and Landing (VTOL) aircraft subject to external disturbances and actuator faults. The aim is to synthesize a fault tolerant controller ensuring trajectory tracking for the nonlinear uncertain system represented by a Takagi–Sugeno (T–S) model. In order to design the FTC law, a proportional integral observer (PIO) is adopted which estimate both of the faults and the faulty system states. Based on the Lyapunov theory and ?₂ optimization, the trajectory tracking performance and the stability of the closed loop system are analyzed. Sufficient conditions are obtained in terms of linear matrix inequalities (LMI). Simulation results show that the proposed controller is robust with respect to uncertainties on the mechanical parameters that characterize the model and secures global convergence.     

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.     

Fractional-order adaptive neuro-fuzzy sliding mode H∞ control for fuzzy singularly perturbed systems

This paper investigates the fractional-order (FO) adaptive neuro-fuzzy sliding mode control issue for a class of fuzzy singularly perturbed systems subject to the matched uncertainties and external disturbances. Firstly, a novel FO fuzzy sliding mode surface is presented. Secondly, by introducing an appropriate ε-dependent Lyapunov function, some H_∞ performance analysis criteria are given, which also ensure the robust stability of the sliding mode dynamics. Furthermore, a hybrid neuro-fuzzy network system (HNFNS) is introduced to estimate the matched uncertainty. Moreover, an FO adaptive fuzzy sliding mode controller is designed to drive the state trajectories of fuzzy singularly perturbed systems to the predefined FO sliding mode surface within a finite-time. Finally, two verification examples are presented to illustrate the validity of the proposed FO control scheme.     

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.     

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.     

Interval fuzzy robust non-fragile finite frequency control for active suspension of in-wheel motor driven electric vehicles with time delay

This paper proposes a fuzzy non-fragile finite frequency H_∞ control algorithm for the active suspension system (ASS) of the electric vehicles driven by in-wheel motors with an advanced dynamic vibration absorber (DVA). Firstly, an interval type-2 Takagi-Sugeno (T-S) fuzzy model is established to formulate the nonlinear time-delay ASS with the uncertainties of sprung mass, unsprung mass, suspension stiffness, and tire stiffness. Secondly, a differential evolution (DE) algorithm is adopted to optimize the parameters of vehicle suspension and DVA. Thirdly, a non-fragile finite frequency H_∞ control controller is developed under the consideration of controller perturbation and input delay to improve the comprehensive performance of the chassis under the finite frequency external disturbances. Finally, simulation tests are carried out to verify the effectiveness of the proposed controller.     

Experimental validation of a continuous-time MCSI algorithm with bounded adaptive gains

Model reference adaptive control algorithms with minimal controller synthesis have proven to be an effective solution to tame the behaviour of linear systems subject to unknown or time-varying parameters, unmodelled dynamics and disturbances. However, a major drawback of the technique is that the adaptive control gains might exhibit an unbounded behaviour when facing bounded disturbances. Recently, a minimal controller synthesis algorithm with an integral part and either parameter projection or σ-modification strategies was proposed to guarantee boundedness of the adaptive gains. In this article, these controllers are experimentally validated for the first time by using an electro-mechanical system subject to significant rapidly varying disturbances and parametric uncertainty. Experimental results confirm the effectiveness of the modified minimal controller synthesis methods to keep the adaptive control gains bounded while providing, at the same time, tracking performances similar to that of the original algorithm.     

Adaptive fractional order sliding mode controller with neural estimator

In this study, an adaptive fractional order sliding mode controller with a neural estimator is proposed for a class of systems with nonlinear disturbances. Compared with traditional sliding mode controller, the new proposed fractional order sliding mode controller contains a fractional order term in the sliding surface. The fractional order sliding surface is used in adaptive laws which are derived in the framework of Lyapunov stability theory. The bound of the disturbances is estimated by a radial basis function neural network to relax the requirement of disturbance bound. To investigate the effectiveness of the proposed adaptive neural fractional order sliding mode controller, the methodology is applied to a Z-axis Micro-Electro-Mechanical System (MEMS) gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed control system can improve tracking performance as well as parameter identification performance.     

Adaptive sliding mode trajectory tracking control of robotic airships with parametric uncertainty and wind disturbance

An adaptive sliding mode trajectory tracking controller is developed for fully-actuated robotic airships with parametric uncertainties and unknown wind disturbances. Based on the trajectory tracking model of robotic airships, an adaptive sliding mode control strategy is proposed to ensure the asymptotic convergence of trajectory tracking errors and adaptive estimations. The crucial thinking involves an adaptive scheme for the controller gains to avoid the off-line tuning. Specially, the uncertain physical parameters and unknown wind disturbances are rejected by variable structure control, and boundary layer technique is employed to avoid the undesired control chattering phenomenon. Computer experiments are performed to demonstrate the performance and advantage of the proposed control method.     

Design of a H∞ model reference tracking control for interconnected nonlinear systems by decentralized dynamic output-feedback

This study investigates the problem of robust tracking control for interconnected nonlinear systems affected by uncertainties and external disturbances. The designed H_∞ dynamic output-feedback model reference tracking controller is parameterized in terms of linear matrix inequalities (LMIs), which is formulated within a convex optimization problem readily implementable. The resolution of such a problem, guarantying not only the quadratic stability but also a prescribed performance level of the resulting closed-loop system, enables to calculate concurrently the robust decentralized control and observation gain matrices. The established LMI conditions are computed in a single-step resolution to obtain all the controller/observer parameters and therefore to overcome the problem of iterative algorithm based on a multi-stage resolution leading in most cases to conservative and suboptimal solutions. Numerical simulations on diverse applications ranging from a numerical academic example to coupled inverted double pendulums and a 3-strongly interconnected machine power system are provided to corroborate the merit of the proposed control scheme.     

L∞-gain analysis for positive singular time-delay systems

This paper is devoted to the characterization of L_∞-gain for positive singular systems with time-varying delays. First, we introduce an augmented system to replace the original system in order to analyze the positivity of singular systems with time-varying delays. By investigating the monotonicity of state trajectory, the L_∞-gain for singular system with constant delays is characterized. Then, by comparing the trajectories of time-varying delay system and constant delay case, we finally propose the L_∞-gain for singular system with time-varying delays. It is shown that the L_∞-gain of positive singular systems is independent of the magnitude of delays.     

An adaptive iterative learning algorithm for boundary control of a coupled ODE–PDE two-link rigid–flexible manipulator

To perform repetitive tasks, this paper proposes an adaptive boundary iterative learning control (ILC) scheme for a two-link rigid–flexible manipulator with parametric uncertainties. Using Hamilton?s principle, the coupled ordinary differential equation and partial differential equation (ODE–PDE) dynamic model of the system is established. In order to drive the joints to follow desired trajectory and eliminate deformation of flexible beam simultaneously, boundary control strategy is added based on the conventional joints torque control. The adaptive iterative learning algorithm for boundary control scheme includes a proportional-derivative (PD) feedback structure and an iterative term. This novel controller is designed to deal with the unmodeled dynamics and other unknown external disturbances. Numerical simulations are provided to verify the performance of proposed controller in MATLAB.     

Nonlinear and adaptive control of NO/NO2 ratio for improving selective catalytic reduction system performance

Reducing the NO_x emissions from Diesel engines remains as a challenging issue as the emission standards for Diesel engine powered vehicles have become more stringent than ever before. Urea-based selective catalytic reduction (SCR) systems have emerged as a promising technique in addressing this issue. However, the SCR performance in terms of NO_x reduction and ammonia slip continues as an ongoing challenge due to the engine exhaust gas temperature variations, Diesel emission characteristics (especially high NO/NO₂ ratio), and immature SCR controls. The purpose of this study is to improve the SCR performance by feeding the SCR system with exhaust gas having the desired NO/NO₂ ratio. The proposed complete active NO/NO₂ ratio control consists of a low-level adaptive NO/NO₂ ratio controller and a high-level nonlinear soot mass controller. The low-level controller utilizes the pre-SCR catalysts such as Diesel oxidation catalyst (DOC) to convert part of NO into NO₂, while the high-level controller was designed and coordinated with the low-level controller to avoid NO₂ reduction through the Diesel particulate filter (DPF). Simulation and experimental results show that the proposed active NO/NO₂ ratio control has the potentials of regulating the NO/NO₂ ratio to the desired value and thus considerably improving the SCR performance. Simulation results also illustrate that the active NO/NO₂ ratio control can enable the SCR system size reduction by a half without a significant sacrifice on the overall tailpipe emission control performance. Such an integrated aftertreatment system control can be instrumental in reducing the cost and improving the performance of SCR systems, especially in low-temperature operations.     

Adaptive fuzzy-based composite anti-disturbance control for a class of switched nonlinear systems with unknown backlash-like hysteresis

For a class of switched nonlinear systems with unmatched external disturbances and unknown backlash-like hysteresis, an adaptive fuzzy-based control strategy is proposed to handle the anti-disturbance issue. The unmatched external disturbances come from a switched exosystem. Our aim is to achieve the output tracking performance and the disturbance attenuation by using the adaptive fuzzy-based composite anti-disturbance control technique. First, based on the fuzzy logics, we design a switching adaptive fuzzy disturbance observer to estimate unmatched external disturbances. Second, a composite switching adaptive anti-disturbance controller is constructed. By means of the backstepping technique, disturbance estimations are added in each virtual control to offset the unmatched disturbances, which results in the different coordinate transformations. At last, the availability of the proposed approach is illustrated by a mass-spring-damper system.     

Disturbance-observer-based formation-containment control for UAVs via distributed adaptive event -triggered mechanisms

In this paper, the adaptive event-triggered formation-containment control for unmanned aerial vehicles (UAVs) is investigated in the presence of multiple leaders and external disturbances. By utilizing the leader-following model, the reference leader provides the desired flight trajectory for multiple formation leaders while the followers are driven into the convex hull spanned by the formation leaders. Initially, some effective disturbance observers are designed to obtain the estimations for eliminating the negative effects of external disturbances. Secondly, in order to alleviate the network burden, a dynamic triggering law is designed for the adaptive event-triggered mechanism (AETM) and the triggering frequency is heavily related to the triggering errors. Then, by exploiting Kronecker product technique and Lyapunov stability theory, two sufficient conditions on the stability of closed-loop system are established, which can help achieve the desired formation control target. Furthermore, the controller gains and observer ones can be determined by calculating the derived linear matrix inequalities (LMIs). Finally, a simulation example is given to illustrate the feasibility of the designed control protocol.     

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.