Observer-based sliding mode control for a class of discrete systems via delta operator approach

In this paper, an observer-based sliding mode control (SMC) problem is investigated for a class of uncertain delta operator systems with nonlinear exogenous disturbance. A novel robust stability condition is obtained for a sliding mode dynamics by using Lyapunov theory in delta domain. Based on a designed sliding mode observer, a sliding mode controller is synthesized by employing SMC theory combined with reaching law technique. The robust asymptotical stability problem is also discussed for the closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability of sliding surfaces is also investigated in state-estimate space and estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the developed method.     

Fixed-time leader-following consensus of multiple uncertain nonholonomic systems: An adaptive distributed observer approach

This paper discusses the fixed-time leader-following consensus problem for multiple uncertain nonholonomic systems, which are widely used in engineering models. According to our literature review, either the system is assumed to be known, or the uncertainty only contains state information, which does not meet the actual requirements. For this reason, this paper investigates more general nonholonomic systems with uncertainties driven by inputs and states. First, a fixed-time adaptive distributed observer is proposed to estimate the leader’s state and structural parameters, which ensures that the estimation errors converge to zero within a fixed time. Second, two regulator equations based on the idea of cooperative output regulation are constructed, and a novel observer-based distributed switching control law is proposed. This control law overcomes the nonholonomic constraints and appropriately relaxes the assumptions of uncertain functions in the existing references. Finally, the simulation results verify the effectiveness of the proposed control scheme.     

An adaptive fast super-twisting disturbance observer-based dual closed-loop attitude control with fixed-time convergence for UAV

In this paper, a fixed-time dual closed-loop attitude control method is investigated for a quadrotor unmanned aerial vehicle. Firstly, a fixed-time adaptive fast super-twisting disturbance observer is presented for estimating the unknown external disturbance. A modified adaptive law is employed based on an equivalent control method to obtain proper observer gains. Secondly, a fixed-time controller is designed by using a universal barrier Lyapunov function to satisfy asymmetric tracking error constraints. Then, a tracking differentiator is utilised to arrange the transition process. Finally, the implementation of the developed method in a quadrotor unmanned aerial vehicle is performed. Through stability analysis and simulation results, the effectiveness and superiority of the proposed fixed-time control method are validated.     

Disturbance observer-based robust missile autopilot design with full-state constraints via adaptive dynamic programming

This paper aims to develop a robust optimal control method for longitudinal dynamics of missile systems with full-state constraints suffering from mismatched disturbances by using adaptive dynamic programming (ADP) technique. First, the constrained states are mapped by smooth functions, thus, the considered systems become nonlinear systems without state constraints subject to unknown approximation error. In order to estimate the unknown disturbances, a nonlinear disturbance observer (NDO) is designed. Based on the output of disturbance observer, an integral sliding mode controller (ISMC) is derived to counteract the effects of disturbances and unknown approximation error, thus ensuring the stability of nonlinear systems. Subsequently, the ADP technique is utilized to learn an adaptive optimal controller for the nominal systems, in which a critic network is constructed with a novel weight update law. By utilizing the Lyapunov's method, the stability of the closed-loop system and the convergence of the estimation weight for critic network are guaranteed. Finally, the feasibility and effectiveness of the proposed controller are demonstrated by using longitudinal dynamics of a missile.     

A new on-line observer-based controller for leader-follower formation of multiple nonholonomic mobile robots

In this paper, a novel on-line observer-based trajectory tracking strategy for leader-follower formation of multiple nonholonomic mobile robots is developed. In the proposed strategy, a leader robot follows a certain trajectory whereas a number of followers track the leader as specified by a formation protocol. Unlike other techniques in the literature, a predefined trajectory is not required, and it can be changed on-line. Moreover, this strategy aims to have a fast transient response without showing undesired overshoots. To achieve this feature, a new observer is introduced. Based on the output of that observer, a control strategy with two components is derived. The first control component is responsible for tracking the desired trajectory, whereas the second control component is used to regulate the robot to its desired steady state position. The stability of the closed loop control system is investigated. Applications of the proposed observer-based controller to different case studies are presented to illustrate the effectiveness, robustness and applicability of the developed technique. To show the superiority of proposed controller, its performance in a trajectory tracking application is compared to that of a Lyapunov-based controller.     

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.     

Neural network-based sensor fault estimation and active fault-tolerant control for uncertain nonlinear systems

In this work, we developed a novel active fault-tolerant control (FTC) design scheme for a class of nonlinear dynamic systems subjected simultaneously to modelling imperfections, parametric uncertainties and sensor faults. Modelling imperfections and parametric uncertainties are dealt with using an adaptive radial basis function neural network (RBFNN) that estimates the uncertain part of the system dynamics. For sensor fault estimation (FE), a nonlinear observer based on the estimated dynamics is designed. A scheme to estimate sensor faults in real-time using the nonlinear observer and an additional RBFNN is developed. The convergence properties of the RBFNN, used in the fault FE part, are improved by using a sliding surface function. For FTC design, a sliding surface is designed that incorporates the real-time sensor FE. The resulting sliding mode control (SMC) technique-based FTC law uses the estimated dynamics and real-time sensor FE. A double power-reaching law is adopted to design the switching part of the control law to improve the convergence and mitigate the chattering associated with the SMC. The FTC works well in the presence and absence of sensor faults without the requirement for controller reconfiguration. The stability of the proposed active FTC law is proved using the Lyapunov method. The developed scheme is implemented on a nonlinear simulation of an unmanned aerial vehicle (UAV). The results show good performance of the proposed unified FE and the FTC framework.     

Observer based sliding mode controller for vehicles with roll dynamics

In this work, considering the roll dynamics and actuator dynamics, an observer-based control scheme for a vehicle is proposed. The proposal considers a nonlinear higher order sliding mode observer to estimate unmeasurable lateral velocity, roll angle and roll velocity. Using the observer information, a controller based on block control with sliding mode technique is designed for the reference trajectory tracking of the lateral and yaw velocities of the vehicle. The stability of the complete closed-loop system including zero dynamics is analyzed. The effectiveness of the proposed scheme is demonstrated through CarSim simulations.     

Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems

In this paper, the observer-based sliding mode control (SMC) problem is investigated for a class of uncertain nonlinear neutral delay systems. A new robust stability condition is proposed first for the sliding mode dynamics, then a sliding mode observer is designed, based on which an observer-based controller is synthesized by using the SMC theory combined with the reaching law technique. Then, a sufficient condition of the asymptotic stability is proposed in terms of linear matrix inequality (LMI) for the overall closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability problem is also discussed. It is shown that the proposed SMC scheme guarantees the reachability of the sliding surfaces defined in both the state estimate space and the state estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility of the proposed design scheme.     

Distributed observer-based consensus tracking for nonlinear MASs with nonuniform input delays and disturbances

In this paper, we investigate the consensus tracking problem of nonlinear MASs with nonuniform time-varying input delays and external disturbances. For each follower, the composited disturbance observer and the state observer are employed to estimate bounded composited disturbances and unmeasured states, and a distributed observer based on output-feedback is proposed to approximate the leader’s states approachably. Sequentially, the consensus tracking control is converted into a stability control problem for the nonlinear MASs with nonuniform time-varying input delays. Subsequently, a distributed controller based on the truncated prediction approach is presented, which only depends on the boundary value of time-varying input delays. The distributed controller can render each follower synchronically stable via the Lyapunov stability theory. Finally, a group of single-link manipulators is used as an example to verify the effectiveness of the theoretical results.     

Event-triggered fault estimation and sliding mode fault-tolerant control for a class of nonlinear networked control systems

This paper is concerned with integrated event-triggered fault estimation (FE) and sliding mode fault-tolerant control (FTC) for a class of discrete-time Lipschtiz nonlinear networked control systems (NCSs) subject to actuator fault and disturbance. First, an event-triggered fault/state observer is designed to estimate the system state and actuator fault simultaneously. And then, a discrete-time sliding surface is constructed in state-estimation space. By the use of a reformulated Lipschitz property and delay system analysis method, the sliding mode dynamics and state/fault error dynamics are converted into a unified linear parameter varying (LPV) networked system model by taking into account the event-triggered scheme, actuator fault, external disturbance and network-induced delay. Based on this model and with the aid of Lyapunov–Krasovskii functional method, a delay-dependent sufficient condition is derived to guarantee the stability of the resulting closed-loop system with prescribed H_∞ performance. Furthermore, an observed-based sliding mode FTC law is synthesized to make sure the reachability of the sliding surface. Finally, simulation results are conducted to verify the effectiveness of the proposed method.     

Additive-state-decomposition-based model predictive tracking control for PMSM servo system with multiple disturbances

This paper presents an additive-state-decomposition-based model predictive tracking control and disturbance rejection method for a permanent magnet synchronous motor (PMSM) servo system subject to unknown parameter perturbations, unmodeled dynamics, and time-varying load torque. The basic idea of this method is to equivalently decompose the original system into a primary system for handling the tracking control subproblem and a secondary system for dealing with the robust stabilization subproblem. A model predictive controller is designed for the primary system to achieve high-accuracy tracking of the reference speed. As for the secondary system, a novel high-order generalized extended state observer (HGESO) is constructed to estimate the multiple disturbances simultaneously, and a state feedback control law incorporating a disturbance compensator is developed to eliminate the adverse effect of the multiple disturbances on the system output. By combining the control inputs of the two subsystems together, the control objectives of the original system can be achieved. Both the stability criterion and design procedure of the closed-loop control system are developed. Finally, hardware-in-the-loop-based comparative experiments are conducted to demonstrate that the proposed method effectively suppresses the influence of the multiple disturbances on motor speed tracking accuracy and that the control system has both satisfactory dynamic performance and robustness.     

Distributed sensor fault diagnosis for a formation of multi-vehicle systems

In the paper, a distributed sensor fault detection and isolation scheme is presented for a network of second-order integrators. A new distributed control law is developed to achieve formation of the system. By using the integration information of distributed formation errors, the control law improves the robustness of the formation. A distributed observer is then designed in each vehicle based on the closed-loop dynamic model of the vehicle. Each vehicle updates the states of the distributed observer by employing the measurements of itself and the transmitted state estimations from its neighbors. Based on the distributed observer, a distributed fault detection observer and a distributed fault isolation observer are designed. The presented distributed fault detection observer in each vehicle is able to be sensitive to the faults of all vehicles in the system. By using the distributed fault isolation observers, each vehicle is able to be sensitive to the faults of itself, its neighbors and its neighbors’ neighbors and to be robust to the faults of other vehicles. Although the fault isolation of the proposed scheme is simple, computation loads of the scheme are lower than the current ones since only the model of the individual vehicle is used. Finally, the effectiveness of the control law and the fault diagnosis scheme is demonstrated by simulations and real-time experiments carried out based on a formation of three quadrotors.     

Neural network-based prescribed performance adaptive finite-time formation control of multiple underactuated surface vessels with collision avoidance

In this paper, a leader-follower formation control scheme of multiple underactuated surface vessels (USVs) is proposed for trajectory tracking, which not only solves the line of sight (LOS) and angle tracking errors within the prescribed performance, but also avoids collisions and maintains the communication connection distance. To achieve the prescribed performance and converge the tracking errors in finite time, a tan-type barrier Lyapunov function (TBLF) is introduced into the designed control strategy. In the process of formation control design, the measured values of the LOS range and angle are available, and the velocity of the leader is estimated using a high-gain observer. Next, a novel self-structuring neural network (SNN) is proposed to estimate the uncertain dynamics induced by the model uncertainties and environmental disturbances, and the computation amount is reduced by optimizing the number of neurons. Combining coordinate transformation and dynamic surface control (DSC), an adaptive NN controller with prescribed performance is proposed. The Lyapunov analysis shows that, although uncertain dynamics exist, the tracking errors can converge to a small region in finite time while achieving the prescribed performance, avoiding collisions, and maintaining the communication distance. In the closed-loop system, all signals are practical finite-time stable (PFS). Finally, the effectiveness of the proposed scheme is illustrated through a numerical simulation.     

Dynamic predictor-based adaptive cruise control

We study the stabilization problem of a platoon of Adaptive Cruise Control (ACC) vehicles in the presence of input-delay. We use a dynamic predictor for input-delay compensation, a filtered version of the standard finite spectrum assignment method that overcomes robustness issues, in particular those raised by the approximation of distributed time-delay terms. Each vehicle must achieve the velocity of the preceding vehicle while ensuring a safe inter-vehicular distance established by a time headway-based spacing policy. To this end, a proportional-integral type controller combined with a dynamic predictor is added to each vehicle in the platoon that guarantees stability and zero steady-state error. String stability property of the closed-loop system, i.e., the platoon’s ability to attenuate fluctuations arising in the motion of the leading vehicle, is analyzed using a frequency domain framework. The effectiveness of the proposed control scheme is illustrated with simulation results of a platoon of five vehicles.     

Model predictive tracking control with disturbance compensation for wheeled mobile robots in an environment with obstacles

This paper explores the trajectory tracking control problem for a wheeled mobile robot (WMR) in an environment with obstacles and unknown disturbances. A fixed-time extended state observer is presented, which is utilized to estimate unknown disturbances and improve the convergence speed of estimation errors. By introducing the obstacle avoidance cost, a model predictive controller with disturbance compensation is proposed to guarantee desired tracking performance in the presence of obstacles. The proposed method is analyzed for recursive feasibility and closed-loop system stability subject to unknown disturbances and obstacles. Finally, both simulation and experiment are conducted to express the satisfactory tracking effect of the developed approach.     

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.     

Robust finite-time cooperative formation control of UGV-UAV with model uncertainties and actuator faults

This paper investigates the finite-time cooperative formation control problem for a heterogeneous system consisting of an unmanned ground vehicle (UGV) - the leader and an unmanned aerial vehicle (UAV) - the follower. The UAV system under consideration is subject to modeling uncertainties, external disturbance as well as actuator faults simultaneously, which is associated with aerodynamic and gyroscopic effects, payload mass, and other external forces. First, a backstepping controller is developed to stabilize the leader system to track the desired trajectory. Second, a robust nonsingular fast terminal sliding mode surface is designed for UAV and finite-time position control is achieved using terminal sliding mode technique, which ensures the formation error converges to zero in finite time in the presence of actuator faults and other uncertainties. Furthermore, by combining the radial basis function neural networks (NNs) with adaptive virtual parameter technology, a novel NN-based adaptive nonsingular fast terminal sliding formation controller (NN-ANFTSMFC) is developed. By means of the proposed adaptive control strategy, both uncertainties and actuator faults can be compensated without the prior knowledges of the uncertainty bounds and fault information. By using the proposed control schemes, larger actuator faults can be tolerated while eliminating control chattering. In order to realize fast coordinated formation, the expected position trajectory of UAV is composed of the leader position information and the desired relative distance with UGV, based on local distributed theory, in the three-dimensional space. The tracking and formation controllers are proved to be stable by the Lyapunov theory and the simulation results demonstrate the effectiveness of proposed algorithms.     

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.     

Leader-follower synchronization controller design for a network of boundary-controlled wave PDEs with structured time-varying perturbations and general disturbances

A feedback controller based on an infinite dimensional observer is proposed to solve the synchronous control problem of network wave equations with time-varying and general perturbations at the boundary. An agent in the network as a virtual leader, and all remaining agents need to incrementally track the status of the virtual leader and each agent is controlled by the Neumann-type drive through the boundary. In this paper, by adopting the idea of the active disturbance rejection control (ADRC) technology, the design of the synchronous controller is divided into three parts and has various functions in this paper. Firstly, it compensates the total disturbance asymptotically. Secondly, it ensures the asymptotic convergence between the network state and the virtual leader state to track the virtual leader. Finally, it ensures that the paired states are synchronized. The convergence of infinite dimensional systems and the suitability of closed-loop systems are analyzed and proved. Three network wave equations with disturbance observer feedback control are simulated numerically, and the simulation results show the effectiveness of the proposed method.