Dynamic Surface Control Approach Research Articles

Dynamic Surface Control Using Fuzzy Logic Systems for Uncertain, Strict‐feedback, Nonlinear Systems with Unknown Control Directions

This paper proposes an adaptive tracking control design procedure for a class of uncertain, strict‐feedback, nonlinear systems in the presence of unknown structure uncertainties, external disturbances, and unknown control directions. To stabilize the systems, fuzzy logic systems are utilized to approximate the unknown structure uncertainties, and the weight matrices and the upper bounds of approximation errors of fuzzy logic systems are not supposed to be known a priori. Then, to avoid the problem of ‘explosion of terms’, a dynamic surface control approach is employed by introducing a first‐order low‐pass filter. Furthermore, the issue of unknown control directions is solved by inserting the Nussbaum function. In addition, the projection operator is applied in the adaptation laws to guarantee the boundedness of the estimated parameters. Finally, simulation results are presented to show the validity of the proposed control strategy. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Three-dimensional integrated guidance and control for strap-down missiles considering seeker’s field-of-view angle constraint

This paper investigates a novel three-dimensional (3D) integrated guidance and control (IGC) method for skid-to-turn (STT) missiles with strap-down seeker. Firstly, a nonlinear IGC model considering seeker’s field-of-view (FOV) constraint is built by employing the strap-down decoupling model, based on which the strict feedback state equation with matched and unmatched uncertainties is derived. Secondly, to handle the FOV angle and the roll angle constraints, an IGC law is proposed by combining dynamic surface control (DSC) approach with integral barrier Lyapunov function (iBLF), by which an adaptive law is employed to estimate the square of the disturbance bound. Finally, the uniform ultimately boundedness of the closed-loop system is proved strictly based on the Lyapunov stability theory, and the effectiveness and robustness of the proposed IGC scheme are illustrated with numerical simulations.

Adaptive robust dynamic surface control for uncertain strict‐feedback nonlinear systems using fuzzy logic systems

AbstractIn this paper, an adaptive robust stabilization problem is dealt with for a class of uncertain strict‐feedback nonlinear systems in the presence of unknown structure uncertainties, external disturbances, and unknown time‐varying virtual control coefficients. It is not required to know the upper bounds of external disturbances, as well as the upper and lower bounds of unknown time‐varying virtual control coefficients. The controller is designed by adopting backstepping. In addition, to avoid suffering from the problem of ‘explosion of terms’, a dynamic surface control approach is employed by introducing the first‐order low‐pass filter. Furthermore, at every step of the backstepping design procedure, fuzzy logic systems are used to approximate the unknown structure uncertainties. In particular, the norms of weight matrices and the upper bounds of approximation errors of fuzzy logic systems are supposed to be unknown. It is also shown that the proposed controller can guarantee the uniform boundedness of uncertain strict‐feedback nonlinear systems. Finally, the simulation for a single‐link manipulator actuated by a brush DC motor is carried out to illustrate the validity of the proposed controller.

Adaptive neural output feedback tracking control for a class of nonlinear systems

In this paper, an adaptive neural output feedback control scheme based on backstepping technique and dynamic surface control (DSC) approach is developed to solve the tracking control problem for a class of nonlinear systems with unmeasurable states. Firstly, a nonlinear state observer is designed to estimate the unmeasurable states. Secondly, in the controller design process, radial basis function neural networks (RBFNNs) are utilised to approximate the unknown nonlinear functions, and then a novel adaptive neural output feedback tracking control scheme is developed via backstepping technique and DSC approach. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded and the tracking error converges to a small neighbourhood around the origin. Finally, two numerical examples and one realistic example are given to illustrate the effectiveness of the proposed design approach.

Adaptive Neural Network Dynamic Surface Control of the Post-capture Tethered Spacecraft

This paper presents an adaptive neural network dynamic surface control approach for the post-capture tethered spacecraft, where model uncertainties, input saturation, and state constraints exist. First, a dynamic model of the post-capture tethered spacecraft considering the three-dimensional attitude of the target satellite is derived by the Lagrange formalism. Then, the neural network is adopted to compensate the model uncertainties and the effects of input saturation, and a barrier Lyapunov function is employed to prevent the violation of the state constraints. The asymptotic stability of the closed-loop system is guaranteed by the Lyapunov stability theory. Finally, simulation results are given to illustrate the effectiveness of the proposed controller.

Adaptive Fuzzy Dynamic Surface Control of Nonlinear Constrained Systems With Unknown Virtual Control Coefficients

This paper studies the problem of adaptive fuzzy dynamic surface control (DSC) of nonstrict-feedback nonlinear systems subject to unknown virtual control coefficients, dead zone, and full state constraints. The Nussbaum gain technique is used to overcome the difficulty caused by the unknown virtual control coefficients. By utilizing the information of tan-type barrier Lyapunov function, the requirement of full state constraints is successfully achieved. In addition, to handle the problem of “explosion of complexity” resulted from backstepping itself, a DSC approach using the sliding mode differentiator is introduced. Then, based on backstepping control, we develop a new adaptive fuzzy DSC strategy, which ensures that all state constrains are not violated via designing parameters appropriately. Meanwhile, other signals existing in the closed-loop system are bounded. Finally, comparative results are provided to illustrate the effectiveness of the proposed approach.

Adaptive dynamic surface control using disturbance observer for nonlinear systems with input saturation and output constraints

ABSTRACTAn adaptive dynamic surface control (DSC) approach using fuzzy approximation and nonlinear disturbance observer (NDO) for uncertain nonlinear systems in the presence of input saturation, output constraint and unknown external disturbances is proposed in this paper. The issue of input saturation is addressed by introducing a lower bound assumption on the approximation function of saturation. The output constraint is handled by introducing an appropriate barried Lyapunov function. The nonlinear disturbance observer (NDO) is employed to estimate the unknown unmatched disturbances. It is manifested that the ultimately bounded convergence of all the variables in the closed-loop system is guaranteed and the tracking error can be made farely small by tuning the design parameters. Finally, two simulation examples illustrate the effectiveness and feasibility of the proposed approach.

An improved adaptive neural dynamic surface control for pure-feedback systems with full state constraints and disturbance

This paper discusses a neural dynamic surface control (DSC) problem for a class of nonlinear systems in the case of full-state constraints and unknown disturbances. Incorporating an improved DSC method and the neural networks (NNs) approximation with the minimization parameter method, an improved neural DSC approach is constructed for the studied system. By introducing a novel barrier Lyapunov function (BLF) in the design steps, the issue of full-state constraints existing in the system can be solved. The highlighting features of the proposed control method are that only one online estimation parameter should be updated, and the same stability property as the conventional backstepping method can be reserved. The transgressions of full state constraints never occur in the case of disturbances. By the Lyapunov stability analysis, all the signals of the closed-loop system are ultimately bounded. Finally, two simulation examples display the effectiveness of the proposed approach.

Robust fuzzy tracking control for flexible air-breathing hypersonic vehicles with measurement noises

Measurement noise is an obstacle to the performance improvement of a flexible air-breathing hypersonic vehicle. This paper explores a robust fuzzy tracking control scheme for the longitudinal dynamics of the hypersonic vehicle, which is constructed by utilizing type-2 fuzzy adaptive technique and dynamic surface control (DSC) approach. The control scheme is comprised of two parts: the state estimators and tracking controllers of velocity and altitude. The state estimators are designed by using the type-2 fuzzy logic system-based approximators, which guarantees the estimation of real states from measurement signals with noises. Furthermore, on the basis of the designed state estimators, the velocity and altitude tracking controllers are constructed by using the adaptive fuzzy DSC approach. On one hand, DSC approach can filter the virtual control law and avoid the amplification of the measurement noise. On the other hand, since the antecedent of the type-2 fuzzy logic system is based on the type-2 fuzzy sets and the consequent parameters are adjusted by an integral calculation in the adaptive law, the type-2 fuzzy adaptive technique in the adaptive fuzzy DSC tracking controller has the ability to further reduce the impact of the measurement noises. A Lyapunov-based stability analysis shows the tracking ability of the proposed control scheme. Nominal and comparison simulation considering the measurement noises are carried out for demonstrating the effectiveness of the proposed method.

Integrated guidance and control with partial state constraints and actuator faults

In this paper, a novel adaptive integrated guidance and control (IGC) scheme is proposed for skid-to-turn (STT) missile with partial state constraints and actuator faults. Considering the strict-feedback form of the IGC model, the dynamic surface control (DSC) approach is adopted to design the IGC scheme. To prevent the attack angle, sideslip angle and velocity deflection angle from violating the constraints, the barrier Lyapunov function (BLF) and modified saturation function are employed in the IGC design procedure. Moreover, an auxiliary system is constructed to remove the adverse effects that caused by the modified saturation function. The adaptive laws are constructed to estimate the actuation effectiveness of actuators and the upper bounds of lumped uncertainties in the IGC model. It is theoretically shown that all signals in the closed-loop system are bounded while the state constraints are not violated in presence of actuator faults and uncertainties. Numerical simulation results are presented to verify the effectiveness and robustness of the proposed IGC scheme.

An Adaptive Output Feedback Proportional-Integral-Derivative Controller for n-Link Type (m,s) Electrically Driven Mobile Manipulators

The design of a trajectory tracking controller for a general class of n-link type (m,s) electrically driven wheeled mobile manipulators has been addressed in this paper. In order to achieve a high level of the tracking performance, an adaptive robust proportional-integral-derivative (PID) controller is proposed which only requires position measurements by designing a velocity observer. Integral actions are incorporated into the design of both controller and observer to reduce the steady-state error as much as possible. The dynamic surface control approach is also applied to reduce the design complexity at the actuator level. Lyapunov's direct method is used to guarantee that tracking and observation errors are semiglobally uniformly ultimately bounded. Simulation results are presented to illustrate the effectiveness of the proposed controller for a group of mobile manipulators.

Fuzzy State Observer‐Based Adaptive Dynamic Surface Control of Nonlinear Systems with Time‐Varying Output Constraints

In this paper, a new fuzzy dynamic surface control approach based on a state observer is proposed for uncertain nonlinear systems with time‐varying output constraints and external disturbances. An adaptive fuzzy state observer is used to estimate the states that cannot be measured in the systems. In our method, a time‐varying Barrier Lyapunov Function (BLF) is used to ensure that the output does not violate time‐varying constraints. In addition, dynamic surface control (DSC) technology is applied to overcome the problem of “explosion of complexity” in a backstepping control. Finally, the stability and signal boundedness of the system are confirmed by the Lyapunov method. The simulation results show the effectiveness and correctness of the proposed method.

A novel control for MDF continuous hot-pressing accurate tracking: adaptive fuzzy approach

In order to guarantee slab thickness precision of Medium Density Fibreboard (MDF), an adaptive fuzzy Dynamic Surface Control (DSC) was investigated. Firstly, a mathematical model for hydraulic servo system of the continuous hot-pressing machine with input saturation was proposed, and the auxiliary system was introduced to compensate the effect of input saturation. Due to the uncertain function in the model, a fuzzy logic system was introduced to approximate it. Subsequently, a slab thickness tracking controller with less complexity was developed with the help of the DSC approach. Simultaneously, an on-line adaptive law was applied to estimate the adjustable parameter vector in the fuzzy system. Finally, experimental results validated that the proposed method can ensure the MDF slab thickness precision in the hot-pressing process.

A novel control for MDF continuous hot-pressing accurate tracking: adaptive fuzzy approach

In order to guarantee slab thickness precision of Medium Density Fibreboard (MDF), an adaptive fuzzy Dynamic Surface Control (DSC) was investigated. Firstly, a mathematical model for hydraulic servo system of the continuous hot-pressing machine with input saturation was proposed, and the auxiliary system was introduced to compensate the effect of input saturation. Due to the uncertain function in the model, a fuzzy logic system was introduced to approximate it. Subsequently, a slab thickness tracking controller with less complexity was developed with the help of the DSC approach. Simultaneously, an on-line adaptive law was applied to estimate the adjustable parameter vector in the fuzzy system. Finally, experimental results validated that the proposed method can ensure the MDF slab thickness precision in the hot-pressing process.

Adaptive fuzzy backstepping control for a class of uncertain nonlinear strict-feedback systems based on dynamic surface control approach

In this paper, a singularity-free adaptive fuzzy backstepping control (AFBC) scheme is presented for uncertain nonlinear SISO systems with triangular structure by using dynamic surface control (DSC) design technique. As the intelligent approximator, fuzzy logic systems are employed to approximate the continuous nonlinear unknown functions in the uncertain systems. By utilizing DSC design technique into AFBC design framework, the proposed intelligent-based adaptive control system can overcome the problem of “explosion of complexity” inherent in the backstepping design method. Moreover, the further benefits of the proposed intelligent-based adaptive control method are that the control singularity problem is completely prevented and the upper bounds of the time differential of the gain functions are no longer needed during the control scheme design. Based on the backstepping technique, it can be proven that the closed-loop system is stable in the sense that all the variables are guaranteed to be bounded. The simulation examples demonstrate and validate the effectiveness of the proposed intelligent-based adaptive control method.

Thruster fault-tolerant control for dynamic positioning of vessels

This paper proposes a fault-tolerant control (FTC) scheme for dynamic positioning (DP) of vessels under thruster faults. A fault state observer is constructed to estimate the unknown fault states. An integrated FTC design method based on the fault state observer is presented for the DP system using the dynamic surface control (DSC) approach. Furthermore, the FTC forces and moment computed from the designed FTC law are allocated to individual thrusters through applying the Lagrange multiplier method. By means of Lyapunov functions, it is proved that the FTC law can maintain the vessel position and heading at the desired values, while guaranteeing the uniform ultimate boundedness of all signals in the closed-loop DP FTC system of vessels under thruster faults. Finally, simulation studies on a 1:70 scale model of a supply vessel are carried out to demonstrate the effectiveness of the proposed FTC scheme.

Adaptive sensor fault-tolerant control for a class of multi-input multi-output nonlinear systems: Adaptive first-order filter-based dynamic surface control approach

This paper is concerned with the adaptive fault-tolerant control (FTC) problem for a class of multivariable nonlinear systems with external disturbances, modeling errors and time-varying sensor faults. The bias, drift, loss of accuracy and loss of effectiveness faults can be effectively accommodated by this scheme. The dynamic surface control (DSC) technique and adaptive first-order filters are brought together to design an adaptive FTC scheme which can reduce significantly the computational burden and improve further the control performance. The adaptation laws are constructed using novel low-pass filter based modification terms which enable under high learning or modification gains to achieve robust, fast and high-accuracy estimation without incurring undesired high-frequency oscillations. It is proved that all signals in the closed-loop system are uniformly ultimately bounded and the tracking-errors can be made arbitrary close to zero. Simulation results are provided to verify the effectiveness and superiority of the proposed FTC method.

Dead-Zone Model-Based Adaptive Fuzzy Wavelet Control for Nonlinear Systems Including Input Saturation and Dynamic Uncertainties

In this study, the problem of adaptive fuzzy wavelet network (FWN) control is investigated for nonlinear strict-feedback systems with unknown functions, unknown virtual control gains and unknown input saturation. An adaptive FWN as an adaptive nonlinear-in-parameter approximator is proposed to represent the model of the unknown functions. Saturation nonlinearity is described by the dead-zone operator-based model which does not require the bound of the saturated input to be known. Then, a novel control scheme is designed based on the adaptive FWN, the saturation model and the dynamic surface control approach. The proposed control scheme does not require any prior knowledge about input saturation, unknown dynamics and unknown virtual control gains. It simultaneously eliminates the “explosion of complexity” and “curse of dimensionality” problems; also, the design approach avoids the controller singularity problem completely without using projection algorithm. The stability analysis is studied using Lyapunov theorem; it shows that all signals of the resulting closed-loop system are uniformly ultimately bounded and the tracking error can be made small by proper selection of the design parameters. Comparing the simulation results of the proposed scheme with other control methods demonstrates the effectiveness and superior performance of the proposed scheme.

Anti-disturbance dynamic surface control scheme for a class of uncertain nonlinear systems with asymmetric dead-zone nonlinearity

This study proposes anti-disturbance dynamic surface control scheme for nonlinear strict-feedback systems subjected simultaneously to unknown asymmetric dead-zone nonlinearity, unmatched external disturbance and uncertain nonlinear dynamics. Radial basis function-neural network (RBF-NN) is invoked to approximate the uncertain dynamics of the system, and the dead-zone nonlinearity is represented as a time-varying system with a bounded disturbance. The nonlinear disturbance observer (NDO) is proposed to estimate the unmatched external disturbance which further will be used to compensate the effect of the disturbance. Then, by integrating RBF-NN, NDO and dynamic surface control (DSC) approaches, the proposed anti-disturbance control scheme is designed. Stability analysis of the closed-loop system shows that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error can be made arbitrarily small by proper selection of the design parameters. In comparison with the existing methods, the proposed scheme deals with the unmatched external disturbance, uncertain dynamics and unknown asymmetric dead-zone nonlinearity, simultaneously; it avoids the "explosion of complexity" problem and develops the simple control law without singularity concern. Furthermore, some imposed assumptions to the dead-zone input and disturbances are relaxed. Simulation and comparison results verify the effectiveness of the proposed approach.

Adaptive neural network synchronization for uncertain strick-feedback chaotic systems subject to dead-zone input

In this paper, an adaptive neural network (NN) synchronization controller is designed for two identical strict-feedback chaotic systems (SFCSs) subject to dead-zone input. The dead-zone models together with the system uncertainties are approximated by NNs. The dynamic surface control (DSC) approach is applied in the synchronization controller design, and the traditional problem of “explosion of complexity” that usually occurs in the backstepping design can be avoided. The proposed synchronization method guarantees the synchronization errors tend to an arbitrarily small region. Finally, this paper presents two simulation examples to confirm the effectiveness and the robustness of the proposed control method.