Dynamic Surface Control Technique Research Articles

Distributed adaptive output consensus tracking for high-order nonlinear time-varying multi-agent systems with output constraints and actuator faults

This paper studies the problem of adaptive output consensus tracking for a class of high-order nonlinear time-varying multi-agent systems with output constraints, actuator faults and external disturbances. The upper bounds concerning the disturbances and the time-varying stuck faults, and the time-varying parameters are assumed to be unknown. Most importantly, the nonlinear state-dependent function (NSDF) is provided to solve the tracking problem with output constraints, and the dynamic surface control (DSC) technique is used to overcome the iterative derivative of virtual controllers caused by the backstepping design scheme. Next, by modeling the failure of the actuators for all nonlinear subsystems, the actuator faults of all nonlinear subsystems are properly handled. Furthermore, a distributed adaptive controller is proposed to guarantee that the tracking error converges to a small adjustable neighborhood of the origin, and the output constraints are not violated for any nonlinear subsystem. It is also shown that the signals of the closed-loop nonlinear subsystems are bounded. Finally, simulation results illustrate the effectiveness of the proposed control method.

Estimator-based MLP neuroadaptive dynamic surface containment control with prescribed performance for multiple quadrotors

This paper presents an estimator-based minimal learning parameter (EMLP) neuroadaptive dynamic surface containment control design capable of guaranteeing transient and steady-state behavior for multiple quadrotors with uncertainties, such that the followers can be driven into the convex hull constituted by multiple dynamic leaders with prescribed bounded errors. To facilitate the control design, the quadrotor dynamics is decomposed into translational and rotational subsystems. For each subsystem, in order to enable smooth and rapid learning of unknown system uncertainties and reduce the computational load in traditional neural network (NN), the estimation errors, instead of tracking errors, are used to regulate NN weights and only one NN learning parameter is required for adaptive neural approximation with the aid of MLP, which is more feasible for real-time implementation. Additionally, dynamic surface control (DSC) technique is introduced in control design to extract the time derivative of virtual control laws, and thus the issue of “explosion of complexity” can be circumvented. As an extension, prescribed performance function and error transformation technique are utilized to address the preselected containment synchronization error constraints problem. Finally, the stability analysis is established to prove that all error signals are uniformly ultimately bounded (UUB). Simulation results illustrate the effectiveness and superiority of the proposed control scheme.

Fault-Tolerant Neuro Adaptive Constrained Control of Wind Turbines for Power Regulation with Uncertain Wind Speed Variation

This paper presents a novel adaptive fault-tolerant neural-based control design for wind turbines with an unknown dynamic and unknown wind speed. By utilizing the barrier Lyapunov function in the analysis of the Lyapunov direct method, the constrained behavior of the system is provided in which the rotor speed, its variation, and generated power remain in the desired bounds. In addition, input saturation is also considered in terms of smooth pitch actuator bounding. Furthermore, by utilizing a Nussbaum-type function in designing the control algorithm, the unpredictable wind speed variation is captured without requiring accurate wind speed measurement, observation, or estimation. Moreover, with the proposed adaptive analytic algorithms, together with the use of radial basis function neural networks, a robust, adaptive, and fault-tolerant control scheme is developed without the need for precise information about the wind turbine model nor the pitch actuator faults. Additionally, the computational cost of the resultant control law is reduced by utilizing a dynamic surface control technique. The effectiveness of the developed design is verified using theoretical analysis tools and illustrated by numerical simulations on a high-fidelity wind turbine benchmark model with different fault scenarios. Comparison of the achieved results to the ones that can be obtained via an available industrial controller shows the advantages of the proposed scheme.

Adaptive dynamic surface control of nonaffine nonlinear system with time‐varying state constraints

SummaryThis paper investigates the problem of adaptive dynamic surface control for pure‐feedback time‐varying state constrained nonaffine nonlinear system. A continuous and semibounded condition is proposed of nonaffine function to ensure that the system can be controlled, and the invariant set is introduced for this mild condition. By employing the dynamic surface control technique, the “complexity explosion” problem caused by backstepping technique is averted in developed control method. Robust compensators are devised to weaken poor effect of disturbances and uncertainties. The time‐varying barrier Lyapunov functions are adopted to dispose the problem of time‐varying state constrains. Moreover, it is proved that the whole closed‐loop signals are bounded, the tracking error can converge to a small neighborhood of zero, and the system states are insured to maintain in the predefined compact sets. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed method.

Dynamic surface control for a class of nonlinearly parameterized systems with input time delay using neural network

By using the radial basis function neural network (RBF NN), this paper presents tracking control problem of the nonlinear systems with the input time delay, in which the unknown continuous functions may be nonlinearly parameterized. Different from the existing results which deal with the nonlinearly parameterized functions by using the separation principle, in this paper, the nonlinearly parameterized functions are lumped into the continuous functions, and then, the neural networks (NNs) are applied to approximate them. Moreover, through a state transformation the system can be easily transformed into a system without the input time delay. Finally, based on the minimal learning parameters (MLP) algorithm and the adaptive backstepping dynamic surface control (DSC) technique, a new adaptive NN backstepping control scheme is developed, and only two parameters need to be adjusted online in the controller design procedure. Thus, the proposed control method cannot only overcome the problem of “explosion of complexity” inherently existing in traditional backstepping design methods, but also reduce the computational burden greatly. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error can converge to a small neighborhood of the origin with an appropriate choice of design parameters. Finally, three examples are used to show the effectiveness of the proposed approach.

Neuroadaptive Control Design for Pure-Feedback Nonlinear Systems: A One-Step Design Approach.

In this article, we propose a one-step control design approach for pure-feedback nonlinear systems in the presence of unmatched and nonvanishing external disturbances. Different from the commonly utilized backstepping design, the proposed method, integrated with the dynamic surface control (DSC) technique, only involves one-step design with one single Lyapunov function in the whole control synthesis, which derives the actual control and the intermediate controls simultaneously in a collective way, avoiding the repetitive design procedures and multiple Lyapunov functions, yet circumventing the issue of "explosion of complexity." Furthermore, with this method, the increase in system order does not increase the design and analysis complexity. Numerical simulation examples confirm and validate the effectiveness of the proposed method.

Sliding mode based neural adaptive formation control of underactuated AUVs with leader-follower strategy

In this brief, the leader-follower formation control of underactuated autonomous underwater vehicles subject to uncertain dynamics and ocean disturbances is addressed. A robust sliding mode formation control strategy is presented by utilizing backstepping method, adaptive neural network and dynamic surface control technique. The stability of the formation control system is proved based on the Lyapunov's direct method where all the signals are guaranteed to be uniformly ultimately bounded. The main advantages of this control strategy are summarized as: (i) the presented controller only depends on the position measurements of the leader, which is more convenient to implement in practice. (ii) the proposed controller does not require any prior knowledge about the hydrodynamic damping and disturbances from the environment. (iii) a continuous PI function is designed to avoid the effect of inherent chattering in standard sliding mode control. (iv) the computational explosion of the standard backstepping method is avoided by the command filter based on the dynamic surface control technique. At last, the comparative simulations are provided to verify the effectiveness of the presented control strategy.

Observer-Based Fuzzy Adaptive Dynamic Surface Control of Uncertain Nonstrict Feedback Systems With Unknown Control Direction and Unknown Dead-Zone

In this paper, an observer-based fuzzy adaptive controller for a class of uncertain nonstrict nonlinear systems with unknown control direction and unknown dead-zone is presented. First, by using equivalence dead-zone inverse and a linear state transformation, the original system is converted to a new one. Then, by using fuzzy logic systems, the unknown nonlinearities are approximated based on an adaptive mechanism, and a nonlinear fuzzy state observer is designed to estimate immeasurable states. The dynamic surface control technique is employed to solve the problem of explosion of complexity in the traditional backstepping approach, and then, this method is combined with Nussbaum gain function to address the problem of unknown control direction. Besides, barrier Lyapunov function is employed to overcome the violation of system output. The proposed controller guarantees that the closed-loop system is stable; all the system states are bounded, and tracking errors converge to a neighborhood of the origin. A numerical simulation is provided to confirm the usefulness of the proposed control design.

Integrated design of trajectory tracking and inertia property identification for post-capture of non-cooperative target

This paper investigates the post-capture control problem associated with trajectory tracking and inertia property identification for a six degree-of-freedom (6DOF) combined spacecraft system subject to input saturation. Post-capture of non-cooperative target will cause a large shift in the dynamics of combined spacecraft mainly resulting from the change of inertia properties. An adaptive tracking control law for combined spacecraft is designed based on the terminal sliding mode and dynamic surface control techniques, and the inertia properties can be identified simultaneously. To estimate mass and inertia matrix, the expression of parameter estimation error is obtained by introducing a group of auxiliary filtered variables. A saturation compensator is employed to deal with the input saturation. Within the Lyapunov framework, the proposed controller is proved to guarantee the finite-time convergence of both trajectory tracking and inertia property identification driven by continuous control forces. Numerical simulations are finally performed to demonstrate the effectiveness of the designed control law.

Adaptive Fuzzy Tracking Control Design for a Class of Uncertain Nonstrict-Feedback Fractional-Order Nonlinear SISO Systems.

In this article, a class of uncertain nonstrict-feedback fractional-order nonlinear single-input-single-output (SISO) systems is investigated. Fuzzy-logic systems (FLSs) are employed to approximate the unknown nonlinear functions and model the uncertain fractional-order nonlinear systems. For the states measurable case, an adaptive fuzzy state-feedback control scheme is developed under the framework of the backstepping technique. For the states unmeasurable case, an observer-based output-feedback control design is proposed by introducing a serial-parallel estimation model and using the dynamic surface control (DSC) technique. Under the drive of the reference signals, the semiglobally uniformly ultimate boundedness for all signals and the tracking errors converging to a small neighborhood of the origin are proved based on the Lyapunov function theory by choosing appropriate design parameters. Two examples with numerical simulations are presented to illustrate the availability of the proposed control approaches.

Observed-based adaptive finite-time tracking control for a class of nonstrict-feedback nonlinear systems with input saturation

This paper concentrates upon the problem of adaptive neural finite-time tracking control for uncertain nonstrict-feedback nonlinear systems with input saturation. The design difficulty of non-smooth input saturation nonlinearity is solved by applying a smooth non-affine function to approximate the saturation signal. Neural networks, as a kind of specialized function estimators, are used to estimate the uncertain function. Meanwhile, a neural network-based observer is constructed to observe the unavailable states, and thus an observer-based adaptive finite-time tracking control strategy is developed by combining dynamic surface control (DSC) technique and backstepping approach. Furthermore, the stability of the considered system is analyzed via semi-global practical finite-time stability theory. Under the proposed control method, all the signals in the closed-loop system are bounded, and the system output can almost surely track the desired trajectory within a specified bounded error in a finite time. In the end, two examples are adopted to illustrate the validity of our results.

Pressure Observer Based Adaptive Dynamic Surface Control of Pneumatic Actuator with Long Transmission Lines

In this paper, the needle insertion motion control of a magnetic resonance imaging (MRI) compatible robot, which is actuated by a pneumatic cylinder with long transmission lines, is considered and a pressure observer based adaptive dynamic surface controller is proposed. The long transmission line is assumed to be an intermediate chamber connected between the control valve and the actuator in series, and a nonlinear first order system model is constructed to characterize the pressure losses and time delay brought by it. Due to the fact that MRI-compatible pressure sensors are not commercially available, a globally stable pressure observer is employed to estimate the chamber pressure. Based on the model of the long transmission line and the pressure observer, an adaptive dynamic surface controller is further designed by using the dynamic surface control technique. Compared to the traditional backstepping design method, the proposed controller can avoid the problem of “explosion of complexity” since the repeated differentiation of virtual controls is no longer required. The stability of the closed-loop system is analytically proven by employing the Lyapunov theory. Extensive experimental results are presented to demonstrate the effectiveness and the performance robustness of the proposed controller.

Neural observer-based path following control for underactuated unmanned surface vessels with input saturation and time-varying disturbance

In this study, a new neural observer-based dynamic surface control scheme is proposed for the path following of underactuated unmanned surface vessels in the presence of input saturation and time-varying external disturbance. The dynamic surface control technique is augmented by a robust adaptive radial basis function neural network and a nonlinear neural disturbance observer. Radial basis function neural network is employed to deal with system uncertainties, and the nonlinear neural disturbance observer is developed to compensate for the unknown compound disturbance that contains the input saturation approximation error and the external disturbance. Moreover, the stringent known boundary requirement of the unknown disturbance constraint is eliminated with the proposed nonlinear neural disturbance observer. Meanwhile, to deal with the non-smooth saturation nonlinearity, a new parametric hyperbolic tangent function approximation model with arbitrary prescribed precision is constructed, which results in the transient performance improvement for the path following control system. Stability analysis shows that all the signals in the closed-loop system are guaranteed to be ultimately bounded. Comparative simulation results further demonstrate the effectiveness of the proposed control scheme.

Observer-Based Adaptive Consensus for a Class of Nonlinear Multiagent Systems

This paper investigates an adaptive consensus problem of a class of nonlinear multiagent systems in which the states are unmeasurable and the dynamics of all agents are supposed to be in strict-feedback form with unknown time-varying control coefficients. Due to the presence of uncertain nonlinearities in agents’ dynamics, radial basis function neural networks are used to approximate the unknown nonlinear functions, and a neural-network-based observer is designed to estimate the unmeasured states. The adaptive observer-based protocols are based on the relative output information of neighbors, and are constructed by adopting the dynamic surface control technique. It is proved that practical consensus of the system can be achieved with the proposed protocols. A simulation example is given to show the effectiveness of the proposed method.

A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

SummaryThis paper investigates a composite neural dynamic surface control (DSC) method for a class of pure‐feedback nonlinear systems in the case of unknown control gain signs and full‐state constraints. Neural networks are utilized to approximate the compound unknown functions, and the approximation errors of neural networks are applied in the design of updated adaptation laws. Comparing the proposed composite approximation method with the conventional ones, a faster and better approximation performance result can be obtained. Combining the composite neural networks approximation with the DSC technique, an improved composite neural adaptive control approach is designed for the considered nonlinear system. Then, together with the Lyapunov stability theory, all the variables of the closed‐loop system are semiglobal uniformly ultimately bounded. The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances. Finally, two simulation examples show the effectiveness and feasibility of the proposed results.

Robust adaptive trajectory tracking control of underactuated autonomous underwater vehicles with prescribed performance

SummaryIn this paper, a novel robust adaptive trajectory tracking control scheme with prescribed performance is developed for underactuated autonomous underwater vehicles (AUVs) subject to unknown dynamic parameters and disturbances. A simple error mapping function is proposed in order to guarantee that the trajectory tracking error satisfies the prescribed performance. A novel additional control based on Nussbaum function is proposed to handle the underactuation of AUVs. The compounded uncertain item caused by the unknown dynamic parameters and disturbances is transformed into a linear parametric form with only single unknown parameter called virtual parameter. On the basis of the above, a novel robust adaptive trajectory tracking control law is developed using dynamic surface control technique, where the adaptive law online provides the estimation of the virtual parameter. Strict stability analysis indicates that the designed control law ensures uniform ultimate boundedness of the AUV trajectory tracking closed‐loop control system with prescribed tracking performance. Simulation results on an AUV in two different disturbance cases with dynamic parameter perturbation verify the effectiveness of our adaptive trajectory tracking control scheme.

Robust distributed consensus tracking control for high‐order uncertain nonlinear MASs with directed topologies

AbstractThis paper addresses the robust distributed consensus tracking problem for leader‐follower multi‐agent systems (MASs) with nonlinear dynamics and external disturbances under directed graph topologies. The nonlinear uncertainties are not required to be continuous or meet the matching conditions. The backstepping design method combined with signal compensation approach is proposed to design robust controllers in order to guarantee the consensus tracking property between the followers and the one leader. Moreover, the dynamic surface control technique is used to deal with the 'explosion of complexity' problem. It is proven that the robust distributed consensus tracking property of the MASs can be guaranteed. Furthermore, the consensus tracking errors can be designed as small as required and the convergence speed can be chosen arbitrarily. Finally, two examples are presented to show the validity of the proposed consensus tracking control protocols.

Fuzzy Adaptive Finite Time Fault-tolerant Control for Multi-input and Multi-output Nonlinear Systems with Actuator Faults

This paper investigates the problem of fuzzy adaptive finite-time fault tolerant control (FTC) for a class of multi-input and multi-output (MIMO) nonlinear systems with actuator failure. In control design, the fuzzy logic systems (FLSs) are adopted to identify the unknown nonlinear functions and a state observer is constructed to estimate the unmeasurable states. By combining dynamic surface control (DSC) technique with backstepping design, a novel finite-time fuzzy adaptive FTC strategy is proposed based on fault-tolerant control technique to overcomes the “explosion of complexity” problem. The presented control method demonstrates that all signals of the closed-loop system are semi-global practical finite-time stability (SGPFS), and the tracking errors converge to a small neighborhood of zero in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the presented control method.

Distributed fixed‐time consensus tracking for high‐order uncertain non‐linear multi‐agent systems with switching topologies

This study investigates the distributed fixed-time consensus tracking for high-order uncertain non-linear multi-agent systems with switching topologies. Each follower is assumed to be in strict-feedback form with both unknown parameters and mismatched disturbances. Different from traditional centralised tracking control problem, only a subset of the agents can acquire the desired trajectory information. By adopting backstepping method and dynamic surface control technique, the distributed fixed-time consensus protocol and appropriate adaptive laws are designed without requiring knowledge of the upper bounds of disturbances. Moreover, the problem of `explosion of complexity' in standard backstepping design is avoided. Under the proposed control protocol, it is shown from the Lyapunov-based analysis that the tracking errors between all followers and the leader can converge to a small neighbourhood of the origin within a fixed time, even though the communication structures among agents dynamically change over time. Finally, a numerical example is carried out to illustrate the effectiveness of the proposed method.

Tracking control of MIMO nonlinear systems under full state constraints: A Single-parameter adaptation approach free from feasibility conditions

This paper investigates the tracking control problem of a class of multi-input multi-output (MIMO) nonlinear systems under asymmetric full-state constraints. By integrating a nonlinear transformed function (NTF) with the upper bound estimation technique, we develop a robust adaptive dynamic surface control (DSC) method that exhibits several attractive features: 1) both symmetric and asymmetric state constraints are directly addressed without the need for converting the state constraints into new constraints on tracking errors (as used in the Barrier Lyapunov Function (BLF) in most existing works). Such control scheme (with its structure unchanged) is also applicable to the systems free from state constraints; 2) the undesirable feasibility conditions on virtual control laws commonly involved in most existing works are completely eliminated; and 3) the utilization of NTF-based DSC and upper bound estimation technique not only avoids the explosion of complexity problem in traditional backstepping design, but also allows a structurally simple and computationally inexpensive control scheme to be developed, in which only one single parameter updating is needed, significantly reducing the design complexity and online computation. The effectiveness of the proposed scheme is verified via simulation.