Dynamic Surface Control Technique Research Articles

Fuzzy Robust Constrained Control for Nonlinear Systems With Input Saturation and External Disturbances

This article proposes a high-order disturbance observer (HODO) and dynamic surface control (DSC) technique-based adaptive fuzzy control scheme for nonlinear systems subjected to input saturation and external time-varying disturbances. First, based on a Sigmoid function, the saturation input is tackled by utilizing a well-defined nonlinear smooth function. Furthermore, HODO and fuzzy logic systems are used to estimate the external disturbances and to handle the lumped unknown functions, respectively. Then, by using the backstepping method and DSC technique, a HODO-based adaptive fuzzy tracking control scheme is proposed for nonlinear systems with saturation nonlinearity, uncertainties, and external disturbances. The Lyapunov analysis method is used to prove that all signals in the entire system are semiglobally uniformly ultimately bounded (SGUUB). In addition, the tracking error converges to a compact set with a tunable error bound determined by some design parameters. Finally, a numerical simulation of two-stage chemical reactor shows the effectiveness of the developed tracking control strategy.

On construction of the control that provides the desired trajectory of the movement of the single-link manipulator with elastic joint

The law of rotation of the electric motor, which ensures a global asymptotic direction of the trajectory of the model of a single-link manipulator with an elastic joint to a given program trajectory is obtained The elasticity of the joint is modeled by a torsion spring, the elastic force of which is considered to be nonlinearly dependent on the displacement. This fact makes it impossible to apply the usual approach and greatly complicates the task of control construction. The fact that some parameters of the model can be uncertain and, in some way, depend on some numerical parameter, the area of change of which is unknown in advance, also adds complexity. However, the use of DSC (Dynamic Surface Control) technique allows us to get the desired control. The development of the DSC technique, which consists in a specific choice of parameters and constants of filters, is proposed. It avoids the growth of the order of the auxiliary system, as well as a significant complication of the form of both the auxiliary system of differential equations and the control law, the so-called “explosion of terms”. It allows us to obtain explicitly the corresponding auxiliary function and to prove that the proposed control law solves the control problem. The robustness of such control is also proved, and the region of robustness in the system parameters space is defined. The obtained results are illustrated by the example of a mechanical model.

Unified adaptive event‐triggered control of uncertain multi‐input multi‐output nonlinear systems with dynamic and static constraints

AbstractIn this article, a unified adaptive neural event‐triggered control strategy is presented for uncertain multi‐input multi‐output (MIMO) nonlinear systems with dynamic and static constraints in the presence of unmodeled dynamics. By introducing an invertible nonlinear mapping based on hyperbolic tangent function, the constrained original system is transformed into an equivalent unconstrained MIMO pure‐feedback system. A dynamic signal is employed to dispose of the dynamical uncertainties in the novel system. Based on the transformed system, unified adaptive event‐triggered controller is formed by using modified dynamic surface control technique and the bounded characteristic of Gaussian function. Using the introduced compact set in stability analysis and Lyapunov function method, all signals in the closed‐loop system are proved to be the semiglobal uniform ultimate boundedness. Furthermore, all states and output signals can strictly comply with the defined constraint conditions. Simulations of two numerical examples including 2‐link rigid manipulator are provided to verify and clarify the theoretical results.

Distributed Finite-Time Containment Control for Nonlinear Multiagent Systems With Mismatched Disturbances.

This article proposes a finite-time adaptive containment control scheme for a class of uncertain nonlinear multiagent systems subject to mismatched disturbances and actuator failures. The dynamic surface control technique and adding a power integrator technique are modified to develop the distributed finite-time adaptive containment algorithm, which shows lower computational complexity. In order to overcome the difficulty from the mismatched uncertainties, the disturbance observers are constructed based on the backstepping technique. Moreover, the uncertain actuator faults, including loss of effectiveness model and lock-in-place model, are considered and compensated by the proposed adaptive control scheme in this article. According to the Lyapunov stability theory, it is demonstrated that the containment errors are practically finite-time stable in the presence of actuator faults. Finally, a simulation example is conducted to show the effectiveness of the proposed theoretical results.

Adaptive Pseudo Inverse Control for a Class of Nonlinear Asymmetric and Saturated Nonlinear Hysteretic Systems

This paper aims at eliminating the asymmetric and saturated hysteresis nonlinearities by designing hysteresis pseudo inverse compensator and robust adaptive dynamic surface control (DSC) scheme. The “pseudo inverse” means that an on-line calculation mechanism of approximate control signal is developed by applying a searching method to the designed temporary control signal where the true control signal is included. The main contributions are summarized as: 1) to our best knowledge, it is the first time to compensate the asymmetric and saturated hysteresis by using hysteresis pseudo inverse compensator because the construction of the true saturated-type hysteresis inverse model is very difficult; 2) by designing the saturated-type hysteresis pseudo inverse compensator, the construction of true explicit hysteresis inverse and the identifications of its corresponding unknown parameters are not required when dealing with the saturated-type hysteresis; 3) by combining DSC technique with the tracking error transformed function, the “explosion of complexity” problem in backstepping method is overcome and the prespecified tracking performance is achieved. Analysis of stability and experimental results on the hardware-in-loop platform illustrate the effectiveness of the proposed adaptive pseudo inverse control scheme.

Event-Triggered Fuzzy Adaptive Leader-Following Tracking Control of Nonaffine Multiagent Systems With Finite-Time Output Constraint and Input Saturation

This article considers the problem of distributed adaptive fuzzy event-based finite-time prescribed performance leader-following tracking control for heterogeneous nonlinear multiagent systems (NMASs) over a directed topology. Each agent is considered in a nonaffine nonstrict-feedback form under input saturation and output constraint which contains unknown dynamics and external disturbances. Fuzzy logic systems (FLSs) are exploited as an effective online approximation tool to tackle system uncertainties. By employing the unique property of FLS, the algebraic loop problem is overcome and by designing novel adaptive laws of the FLS weights, the computation burden is decreased significantly. The threshold of the event-triggered condition is improved compared to the conventional relative-threshold mechanism. A modified performance function called finite-time performance function is introduced to constrain the synchronization errors within the prescribed performance bounds in finite time. The dynamic surface control technique is then developed to avoid the issue of the “explosion of complexity.” Moreover, by developing a new decomposition for the controller gain function resulting from the mean-value theorem and introducing an auxiliary system, the input saturation nonlinearity that affects the nonaffine form stability is handled. Through the Lyapunov stability analyses, it is shown that the developed control algorithm ensures the closed-loop NMAS trajectory to be cooperatively semi-globally uniformly ultimately bounded. Additionally, the tracking errors are driven to a predefined region around zero in finite time. Finally, the efficiency of the established theoretical results is validated by the simulation studies.

Composite adaptive fuzzy decentralized tracking control for pure-feedback interconnected large-scale nonlinear systems

This paper focuses on a problem of composite adaptive fuzzy decentralized tracking control for a class of uncertain pure-feedback interconnected large-scale nonlinear systems with unmeasurable states. A fuzzy state observer is designed by using fuzzy logic systems; thus, the unmeasurable states of pure-feedback nonlinear systems are estimated based on the designed fuzzy state observer. A serial–parallel estimation model is designed by using the fuzzy state observer. To avoid the analytic computation, the command filters are employed to produce the command signals and their derivatives. The fuzzy adaptive laws are constructed by using prediction errors and compensating tracking errors. Finally, a controller is constructed by dynamic surface control technique. Through the proposed control method, all the signals in the closed-loop system are bounded, and the output of the system can track the given reference signal. The simulation studies verify the effectiveness of the proposed control method in this paper.

Robust adaptive multistage anti-windup dynamic surface control for dynamic positioning ships with mismatched disturbance

In this paper, a novel robust adaptive multistage anti-windup control strategy is developed for dynamic positioning ships in presence of input constraint, mismatched disturbance and external disturbance. Based on dynamic surface control technique, a composite control law, where both mismatched and matched disturbances are compensated, is established to stabilize the system without the requirement of solving any partial differential equations. In particularly, the mismatched disturbance caused by the model transformation is analyzed firstly and the better steady performance is achieved. In addition, a novel multistage anti-windup control based on anticipatory activation compensation is constructed to handle the input constraint while the transient performance is improved significantly. Moreover, the stability of the closed-loop system is proven via Lyapunov technique rigorously, and the tracking error can be forced into an arbitrarily small neighborhood around zero. Finally, simulations with comparisons demonstrate the effectiveness of the proposed method.

Observer-based dynamic surface control for flexible-joint manipulator system with input saturation and unknown disturbance using type-2 fuzzy neural network

In this paper, the nonlinear disturbance observer (NDO) based dynamic surface control (DSC) with interval type-2 fuzzy neural network (IT2FNN) approximator is proposed for flexible-joint manipulator with the input saturation and unknown nonlinear disturbance. The DSC technique has tremendous advantages in eliminating the ’explosion of complexity’ problem. The IT2FNN approximator is used to deal with parameter uncertainties. The NDO is applied to estimate the unknown external disturbance and compensate the saturation constrain. From Lyapunov stability analysis, it is proved that with the proposed control scheme, all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Simulation results are carried out to demonstrate the effectiveness of the proposed scheme. Compared with the adaptive DSC with neural network (NN) approximator and type-1 fuzzy (T1F) approximator, the tracking error of the proposed control scheme converges to a sufficiently small value.

DSC-ESO Approach to Robust Sliding Model Control for Ship’s Curve Trajectory Tracking

In order to solve the problem of ship's curve trajectory-tracking control, the Norrbin nonlinear response model which can accurately describe the ship's motion state is selected in this paper. The hyperbolic tangent function is used to design the expected hemispheric angle equation, then the complex track control is transformed into a heading control problem. The fast terminal sliding mode (FTSM) is introduced together with the Backstepping control technique to reduce the system adjustment time, eliminate the chattering. Bying combined with extended states observer (ESO) and dynamic surface control (DSC) technique, the internal and external disturbances in real-time can be estimated and compensated, and the “explosion of complexity” caused by backstepping technique is solved. The state of the control system is bounded and stable, and the system error converges to zero. Matlab simulation proves that the controller can realize the trajectory-tracking control quickly and accurately, and has strong robustness to external disturbances.

Robust Composite Adaptive Control of Linearisable Systems With Improved Performance

Robust composite adaptive control designs for linearisable systems with known/unknown input gain functions are presented. They mainly consist of a standard adaptive linearizing controller and an immersion and invariance (I&I) based composite update algorithm, with the inclusion of a Lyapunov-based canceling term and a σ-modification term for ensuring the practical stability and preventing the parameter-drift phenomenon at the same time. Next, the adding an integrator and the dynamic surface control (DSC) techniques are incorporated for preventing the algebraic-loop problem in the latter case. In particular, the proposed designs ensure the convergence of prediction errors to an order of the exogenous disturbance without relying on persistent excitation (PE), which in turn improves the tracking performance significantly.

Adaptive synchronization of marine surface ships using disturbance rejection without leader velocity

This work realizes the adaptive neural disturbance rejection for the leader–follower cooperative synchronization of surface ships with model perturbations and ocean disturbances without leader velocity measurements. The virtual ship alleviates the requirements on leader ship’s velocities such that the information requirements are only position and heading on the leader ship. The adaptive neural networks approximate model perturbations. The robustifying term attenuates neural network approximation errors. The adaptive neural network-based disturbance observer achieves the disturbance rejection which is integrated with the dynamic surface control technique. The supply ship synchronization control system is ensured to be practical stable. The synchronization control realizes the ship’s cooperative synchronization navigation. Simulations with comparisons validate the synchronization scheme.

An Adaptive Neural Network Controller for Active Suspension Systems With Hydraulic Actuator

In this paper, an adaptive neural network (NN) controller is proposed for a class of nonlinear active suspension systems (ASSs) with hydraulic actuator. To eliminate the problem of “explosion of complexity” inherently in the traditional backstepping design for the hydraulic actuator, a dynamic surface control technique is developed to stabilize the attitude of the vehicle by introducing a first-order filter. Meanwhile, the presented scheme improves the ride comfort even when the uncertain parameter exists. Due to the existence of uncertain terms, the NNs are used to approximate unknown functions in the ASSs. Finally, a simulation for a servo system with hydraulic actuator is shown to verify the effectiveness and reliability of the proposed approach.

Adaptive fuzzy output regulation of uncertain pure‐feedback non‐linear systems with prescribed performance

The output regulation problem for pure-feedback non-linear systems with prescribed performance (PP) driven by an external linear system with unknown parameter are investigated. First, an observer with a disturbance signal is designed to observe unmeasured system states. Secondly, fuzzy logic systems (FLS) are used to approximate unknown non-linear non-affine functions. Thirdly, a fuzzy internal model is obtained to reject disturbance, and an adaptive fuzzy output feedback algorithm is proposed based on dynamic surface control (DSC) technique and backstepping method. Simultaneously, an L function is constructed so that the overall property (steady-state property and dynamic property) of the tracking error are constrained by PP functions. The results explain that the proposed control algorithm can make sure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SUUB), and the tracking error is semi-globally PP uniformly ultimately bounded (SPPUUB). Finally, two examples are given to show the validity of the results.

Output Constrained Adaptive Controller Design for Nonlinear Saturation Systems

This paper considers the adaptive neuro-fuzzy control scheme to solve the output tracking problem for a class of strict-feedback nonlinear systems. Both asymmetric output constraints and input saturation are considered. An asymmetric barrier Lyapunov function with time-varying prescribed performance is presented to tackle the output-tracking error constraints. A high-gain observer is employed to relax the requirement of the Lipschitz continuity about the nonlinear dynamics. To avoid the “explosion of complexity”, the dynamic surface control (DSC) technique is employed to filter the virtual control signal of each subsystem. To deal with the actuator saturation, an additional auxiliary dynamical system is designed. It is theoretically investigated that the parameter estimation and output tracking error are semi-global uniformly ultimately bounded. Two simulation examples are conducted to verify the presented adaptive fuzzy controller design.

Distributed Adaptive Output Feedback Leader-Following Consensus Control for Nonlinear Multiagent Systems

This paper investigates the problem of the distributed adaptive output feedback leader-following consensus control for a class of high-order nonlinear multiagent systems with unknown parameters and nonlinear terms. First, the reduced order dynamic gain k-filters are built to estimate the unmeasured state variables. The bounds of the unknown parameters are estimated in order to avoid the over-estimation problem. Then, the dynamic surface control technique is used to design the distributed controller, and the computation load of the system is greatly reduced. Finally, a numerical example is shown to verify the effectiveness of the designed controller.

Adaptive Fuzzy Leader–Follower Synchronization of Constrained Heterogeneous Multiagent Systems

This article considers the distributed adaptive neuro-fuzzy output feedback control protocol design to solve the output synchronization problem for heterogeneous multiagent systems with nonlinear strict-feedback agent dynamics. The output constraints and actuator saturation are considered simultaneously. First, a distributed high-gain observer is employed to estimate the unmeasured agent state and relax the requirement of the Lipschitz continuity of nonlinear follower dynamics. Second, an asymmetric barrier Lyapunov function with time-varying constraint is presented to deal with both the transient and the steady-state constraints on the output synchronization error. To avoid the “explosion of complexity,” the dynamic surface control technique is employed to filter the virtual control signal for each follower. To deal with the actuator saturation, a distributed auxiliary dynamical system is designed for each follower. The fuzzy logic system is employed to compensate for the uncertain follower dynamics with guaranteed semiglobal uniformly ultimately boundedness of all closed-loop signals. Finally, a simulation example is conducted to verify the efficacy of the presented adaptive neuro-fuzzy controller design.

Finite-Time Tracking Control for a Class of Uncertain Strict-Feedback Nonlinear Systems With State Constraints: A Smooth Control Approach.

This article is concerned with the finite-time tracking control problem for a class of strict-feedback nonlinear systems involving state constraints, unknown nonlinearities, and nonvanishing disturbances. Unlike the literature that mainly focuses on a C0 finite-time controller, in this article, a novel C1 smooth finite-time adaptive neural network (NN) controller is proposed by employing a smooth switch between the fractional and cubic form state feedback. The proposed controller not only avoids the singularity but also makes it possible to implement the dynamic surface control (DSC) technique. By applying the adaptive NN control technique, together with barrier Lyapunov functions (BLFs) and a generalized first-order filter including both linear and fractional terms, the desired fast finite-time control performance of the closed-loop nonlinear systems can be guaranteed, and meanwhile, the state constraints are never violated. Under the proposed control scheme, the tracking control problems of nonlinear systems with output constraint and full-state constraints are, respectively, discussed. It is explicitly shown that all the internal error signals are driven to converge into small regions in a finite time. Finally, the effectiveness of the control scheme is also confirmed by the applications to the control of a second-order nonlinear system and an uncertain ship autopilot.

Anti-disturbance dynamic surface trajectory stabilization for the towed aerial recovery drogue under unknown airflow disturbances

This paper focuses on the anti-disturbance trajectory stabilization problem of the flexible cable towed aerial recovery drogue under multiple unknown airflow disturbances. Firstly, the 6 degrees of freedom (DOF) dynamics of the towed drogue are established in affine nonlinear form for nonlinear control design. Then, several finite-time convergent high order sliding mode observers (HOSMO) are designed to accurately estimate these lumped disturbances which include the effects of the unmeasurable tensions and airflow disturbance in each subsystem of the drogue’s dynamics. With the feed-forward compensations of these estimated disturbances, a HOSMO based anti-disturbance back-stepping controller is proposed to stabilize aerial recovery drogue subjecting to the unmeasurable cable tensions and airflow disturbances. The dynamic surface control (DSC) technique is used to avoid the “explosion of complexity” problem in the standard back-stepping. Also, the closed-loop stability is analyzed to show all the signals are ultimately bounded. Therewith, the proposed method’s performance and effectiveness for the aerial recovery drogue are compared with the case without any active stabilizer.

Neural-Network-Based Adaptive DSC Design for Switched Fractional-Order Nonlinear Systems.

Due to the particularity of the fractional-order derivative definition, the fractional-order control design is more complicated and difficult than the integer-order control design, and it has more practical significance. Therefore, in this article, a novel adaptive switching dynamic surface control (DSC) strategy is first presented for fractional-order nonlinear systems in the nonstrict feedback form with unknown dead zones and arbitrary switchings. In order to avoid the problem of computational complexity and to continuously obtain fractional derivatives for virtual control, the fractional-order DSC technique is applied. The virtual control law, dead-zone input, and the fractional-order adaptive laws are designed based on the fractional-order Lyapunov stability criterion. By combining the universal approximation of neural networks (NNs) and the compensation technique of unknown dead-zones, and stability theory of common Lyapunov function, an adaptive switching DSC controller is developed to ensure the stability of switched fractional-order systems in the presence of unknown dead-zone and arbitrary switchings. Finally, the validity and superiority of the proposed control method are tested by applying chaos suppression of fractional power systems and a numerical example.