Adaptive Fuzzy Dynamic Surface Control Research Articles

Anti-deadzone adaptive fuzzy dynamic surface control for planar space robot with elastic base and flexible links

In order to combat the impact of the dead zone and reduce vibration of the space robot's elastic base and flexible links, the trajectory tracking and vibration suppression of a multi-flexible-link free-floating space robot system are addressed. First, the elastic connection between the base and the link is considered as a linear spring. Then the assumed mode approach is used to derive the dynamic model of the flexible system. Secondly, a slow subsystem characterizing the rigid motion and a fast subsystem relating to vibration of the elastic base and multiple flexible links are generated utilizing two-time scale hypotheses of singular perturbation. For the slow subsystem with a dead zone in joint input torque, a dynamic surface control method with adaptive fuzzy approximator is designed. Dynamic surface control scheme is adopted to avoid calculation expansion and to simplify calculation. The fuzzy logic function is applied to approximate uncertain terms of the dynamic equation including the dead zone errors. For the fast subsystem, an optimal linear quadratic regulator controller is used to suppress the vibration of the multiple flexible links and elastic base, ensuring the stability and tracking accuracy of the system. Lastly, the simulation results verify the effectiveness of the proposed control strategy.

Control of state constrained nonlinear systems with unknown dead-zone nonlinearity: A unified fuzzy dynamic surface control approach

In this paper, we focus on the tracking control issue of state constrained nonlinear systems with unknown dead-zone nonlinearity. The systems also take into account unknown virtual control coefficients as well as external disturbances. The utilization of feasibility nonlinear transformed functions not only converts original constrained nonlinear systems into unconstrained systems, but also eliminates the difficulty of parameter selection of the barrier Lyapunov function. Under the premise of relaxing the limitation of systems, the property of the hyperbolic tangent function and adaptive estimated parameters are used to design controller to improve the robustness of control strategy. Through the combination of dynamic surface control and adaptive backstepping technology, an adaptive fuzzy dynamic surface control strategy is developed so that all signals of the closed-loop unconstrained system and original system are bounded, and states of the original system do not break predetermined constraints. Two examples are provided to illustrate that control strategy is effective.

Adaptive fuzzy dynamic surface control for nonstrict-feedback nonlinear state constrained systems with input dead-zone via event-triggered sampling

In this paper, a novel adaptive fuzzy dynamic surface control (DSC) via the event-triggered mechanism is developed for nonstrict-feedback nonlinear state constrained systems preceded by actuator dead-zone. The utilization of the dynamic surface technique avoids the issue of repeated differentiation of virtual control law and eliminates the drawback of the explosion of complexity with the backstepping technique. By utilizing the universal approximation property of fuzzy logic systems (FLSs), the unknown function is approximated successfully. By combining the DSC and event-triggered control (ETC) scheme, communication and computation strain are alleviated contemporaneously. An adaptive controller and an auxiliary system are cooperatively constructed to offset the effect of dead-zone nonlinear function. By employing the barrier Lyapunov functions (BLFs), all the states can remain within a prescribed interval. The tracking error can be restricted at the origin and all signals of closed-loop systems can be kept within the boundaries by the designed parameter adaptive laws and event-triggered controller. Finally, a numerical simulation result and a practical simulation result of the pendulum are proposed to guarantee the effectiveness of the presented control theory.

Observer-Based Event-Triggered Adaptive Fuzzy Control for Fractional-Order Time-Varying Delayed MIMO Systems Against Actuator Faults

This article presents the observer-based event-triggered adaptive hybrid fuzzy dynamic surface control strategy for a category of uncertain nonstrict-feedback fractional-order nonlinear multi-input multi-output systems, including unknown time-varying delays and actuator faults. First, an adaptive hybrid fuzzy state observer and a serial-parallel estimation system are constructed to estimate the unmeasured system states and incorporate them into the control design scheme, respectively, where some appropriate fuzzy logic systems are introduced to approximate the unknown nonlinear functions. According to the dynamic surface control technique, the designed adaptive fuzzy control approach can surmount the deficiency of “complexity explosion.” Then, an observer-based adaptive event-triggered control algorithm is developed by constructing the Lyapunov–Krasovskii functionals and estimating the compounded disturbances. Furthermore, it is proved that under the drive of the reference signals, all the signals in the closed-loop system are semiglobally uniformly ultimately bounded and Zeno behavior can be successfully excluded. Finally, an example with numerical simulations is utilized to exhibit the applicability of the obtained observer-based event-triggered adaptive fuzzy control approach.

Finite-time fuzzy dynamic surface control for permanent magnet synchronous motor stochastic systems with input constraint and load disturbance

In this paper, a finite-time adaptive fuzzy dynamic surface control (DSC) method is proposed for the position tracking control of permanent magnet synchronous motors (PMSMs) stochastic nonlinear system with input constraint and load disturbance. First, the stochastic disturbance of PMSMs is considered in operation, and the fuzzy control method is applied to cope with the stochastic nonlinear function in the motor model. Second, the DSC technique is applied to avoid the “explosion of complexity” in the backstepping design. Moreover, the finite-time control is applied to the stochastic nonlinear system of PMSMs to improve the convergence speed of the system, tracking accuracy, and anti-interference ability. Conclusive, simulation results are given to verify the method that can achieve fast tracking of the desired signal.

Compound Adaptive Fuzzy Quantized Control for Quadrotor and Its Experimental Verification.

This article aims to realize a precise position and attitude tracking control for the quadrotor using a proposed fuzzy approximator-based compound adaptive fuzzy quantized control scheme. In the control scheme, a quantized output-feedback control for position tracking and a state-feedback quantized control for attitude trajectory tracking are combined to deal with the underactuated and strong coupling problems of the quadrotor. The main contributions are: 1) the adaptive fuzzy quantized control is realized, then the strong nonlinearities caused by the quantizer are effectively mitigated, which implies that the control precision can be improved when a low communication rate is required in the real-time control system of quadrotor; 2) by applying the adaptive fuzzy dynamic surface control (DSC) technique to the underactuated quadrotor control system, the "explosion of complexity" problem in the backstepping method is overcome and the L∞ tracking performance is achieved with the proposed initializing technique inspired by Zhang et al. This guarantees that the attitude signals promptly converge to the desired trajectories, then the underactuated problem of the quadrotor is overcome by solving the designed adaptive fuzzy-quantized control equations; and 3) the experiments on the platform of the Quanser Qball-X4 quadrotor are conducted and the effectiveness of the proposed control scheme is validated.

Adaptive Fuzzy Dynamic Surface Control for Nonlinear Systems with Time-Varying Input Delay and Sampled Data

This paper studies fuzzy adaptive dynamic surface control strategy for nonlinear system with sampled data and time-varying input delay. By utilizing the approximated property of fuzzy logic systems (FLSs), a fuzzy estimator (FE) model is designed to identify the states of the original system, which is mainly used to provide information of estimation states to replace the sampled data of the nonlinear controlled system. In the proposed strategy, with the help of sampled-data activity, an integral term is designed to compensate the problem of time-varying input delay. Moreover, by invoking the dynamic surface control (DSC) technique, the problem of ‘explosion of complexity’ has been overcame. And the developed control strategy demonstrates that all signals of the controlled system are semi-globally uniformly ultimately bounded (SGUUB). Ultimately, two numerical simulation examples are given to prove the feasibility of the developed control method and theory.

Tracking control of a class of nonlinear systems with output delay based on adaptive fuzzy dynamic surface control

ABSTRACTThis paper concerns with the tracking control problem of a class of unknown nonlinear time-delay systems in the presence of output delay and inaccessible states. To deal with the difficulties arising from unmeasurable states, a fuzzy logic observer based on delayed outputs is firstly employed. Then, based on the delayed output, observed states and filtered virtual control signals, proper change of coordinates is defined for the purpose of designing dynamic surface control. By introducing appropriate Lyapunov-Krasovskii functionals in the design procedures, a controller and adaptation laws are obtained for the control strategy of nonlinear systems subject to output delay. Moreover, by selecting design parameters and matrices based on the acquired stability criteria, it is proved that the proposed adaptive fuzzy dynamic surface output feedback control approach is able to guarantee the uniformly ultimately boundedness of all the signals in the closed loop unknown nonlinear output-delay systems. Finally, the theoretic achievements are applied to three well-known benchmark systems to illustrate the effectiveness and efficiency of the proposed approach.

Adaptive fuzzy backstepping control for a two continuous stirred tank reactors process based on dynamic surface control approach

This work demonstrates an adaptive fuzzy backstepping control for a two cascaded continuous stirred tank reactors (CSTRs) system based on the dynamic surface control (DSC). The proposed controller is able to ensure the internal stabilization of the closed-loop system and render outputs track their reference signals asymptotically, although the CSTRs system is highly nonlinear and strong coupling. The effective and robust performance of the proposed controller in this research is certificated by the simulation analysis. Compared with previous researches, the on-line computation of controller is effectively reduced, which means that the proposed controller is easy to implement in engineering. The adaptive fuzzy dynamic surface control appears the potential for CSTRs process in mill operation.

Adaptive Fuzzy Dynamic Surface Control for Multi-Machine Power System Based on Composite Learning Method and Disturbance Observer

A composite learning dynamic surface control is proposed for a class of multi-machine power systems with uncertainties and external disturbances by using fuzzy logic systems (FLSs) and disturbance observer (DOB). The main characteristics of the proposed strategy are as follows: (1) The approximation ability of FLSs for nonlinear model of multi-machine power systems is enhanced considerably by using the composite learning method and providing additional correction information for the FLSs. These findings differ considerably from previous designs that focus directly on the system's tracking performance. (2) The filtering errors caused by the utilizations of the first-order low-pass filters in dynamic surface control (DSC) are compensated effectively by designing the compensating signals in the control law design process. (3) The compound disturbances including the FLSs' approximation error and external disturbances are estimated and mitigated by constructing DOB. Finally, the proposed control algorithm is verified on the StarSim Hardware-in-loop experimental platform, and the experimental results validate the effectiveness of the proposed control strategy in suppressing disturbances and enhancing the robustness of the controller.

Adaptive decentralized control for switched nonlinear large-scale systems with quantized input signal

This paper deals with the adaptive fuzzy dynamic surface control (DSC) of a class of switched nonlinear large-scale systems whose input is quantized by a class of sector-bounded quantizers and the quantization parameters are allowed to be unknown. A new control law with hyperbolic tangent function form is introduced to develop a compensation mechanism to remove the restriction of the global Lipschitz condition. By designing switched first-order filters and switched adaptive laws for different subsystems, the switched controllers can not only show the switched systems changes sufficiently but also deal with the problem of “explosion of complexity”. It is shown that the proposed control scheme can ensure that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of the origin regardless of arbitrary switching. The simulation results demonstrate the validity and applicability of the proposed control scheme.

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.

Robust adaptive steering control for unmanned surface vehicle with unknown control direction and input saturation

SummaryA robust adaptive steering control method is proposed to solve the control problem of the unmanned surface vehicle (USV) with uncertainties, unknown control direction, and input saturation. In the controller design process, the adaptive fuzzy system is incorporated into dynamic surface control (DSC) to approximate the uncertainty term induced by external environmental disturbances and model parameters. Then, the Nussbaum function is used to eliminate the requirement for a priori knowledge of the control direction. Besides, to handle the input saturation, the adaptive fuzzy DSC is extended by a second‐order nonlinear filter and antisaturation auxiliary function to compensate for the magnitude and rate saturation of the rudder. All signals of the closed‐loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov theorem and the Lemma of Nussbaum gain, and the course error can converge to a small neighborhood of zero through choosing design parameters appropriately. Finally, simulation results and comprehensive comparisons are shown for the USV course system, which is demonstrative of the proposed controller's effectiveness and robustness.

Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time‐varying delayed systems with unknown control directions and dead‐zone input

SummaryIn this paper, an adaptive prescribed performance control method is presented for a class of uncertain strict feedback nonaffine nonlinear systems with the coupling effect of time‐varying delays, dead‐zone input, and unknown control directions. Owing to the universal approximation property, fuzzy logic systems are used to approximate the uncertain terms in the system. Since there is no systematic approach to determine the required upper bounds of errors in control systems, the prior selection of control parameters to have a satisfactory performance is somehow impossible. Therefore, the prescribed performance technique as a solution is applied in this study to bring satisfactory performance indices to the system such as overshoot and steady state performance within a predetermined bound. Dynamic surface control strategy is also introduced to the proposed control scheme to address the “explosion of complexity” behavior existing in conventional backstepping methods. To ease the control design, the mean‐value theorem is utilized to transform the nonaffine system into the affine one. Moreover, with the help of this theorem, the unknown dead‐zone nonlinearity is separated into the linear and nonlinear disturbance‐like bounded term. The proposed method relaxes a prior knowledge of control direction by employing Nussbaum‐type functions, and the effect of time‐varying delays are compensated by constructing the proper Lyapunov‐Krasovskii functions. The proposed controller guarantees that all the closed‐loop signals are semiglobally uniformly ultimately bounded and the error evolves within the decaying prescribed bounds. In the end, in order to demonstrate the superiority of this method, simulation examples are given.

Nonlinear Systems With Uncertain Periodically Disturbed Control Gain Functions: Adaptive Fuzzy Control With Invariance Properties

This paper proposes a novel adaptive fuzzy dynamic surface control (DSC) method for an extended class of periodically disturbed strict-feedback nonlinear systems. The peculiarity of this extended class is that the control gain functions are not bounded a priori but simply taken to be continuous and with a known sign. In contrast with existing strategies, controllability must be guaranteed by constructing appropriate compact sets ensuring that all trajectories in the closed-loop system never leave these sets. We manage to do this by means of invariant set theory in combination with the Lyapunov theory. In other words, boundedness is achieved a posteriori as a result of stability analysis. The approximator composed of fuzzy logic systems and Fourier series expansion is constructed to deal with the unknown periodic disturbance terms.

Fuzzy Adaptive DSC Design for an Extended Class of MIMO Pure-Feedback Non-Affine Nonlinear Systems in the Presence of Input Constraints

A novel adaptive fuzzy dynamic surface control (DSC) scheme is for the first time constructed for a larger class of (multi-input multi-output) MIMO non-affine pure-feedback systems in the presence of input saturation nonlinearity. First of all, the restrictive differentiability assumption on non-affine functions has been canceled after using the piecewise functions to reconstruct the model for non-affine nonlinear functions. Then, a novel auxiliary system with bounded compensation term is firstly introduced to deal with input saturation, and the dynamic system employed in this work designs a bounded compensation term of tangent function. Thus, we successfully relax the strictly bounded assumption of the dynamic system. Additionally, the fuzzy logic systems (FLSs) are used to approximate unknown continuous systems functions, and the minimal learning parameter (MLP) technique is exploited to simplify control design and reduce the number of adaptive parameters. Finally, two simulation examples with input saturation are given to validate the effectiveness of the developed method.

Adaptive fuzzy dynamic surface control of flexible-joint robot systems with input saturation

In this paper, we propose an adaptive fuzzy dynamic surface control &#x0028 DSC &#x0029 scheme for single-link flexible-joint robotic systems with input saturation. A smooth function is utilized with the mean-value theorem to deal with the difficulties associated with input saturation. An adaptive DSC design with an auxiliary first-order filter is used to solve the &#x201C explosion of complexity &#x201D problem. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood around zero. The main advantage of the proposed method is that only one adaptation parameter needs to be updated, which reduces the computational burden significantly. Simulation results demonstrate the feasibility of the proposed scheme and the comparison results show that the improved DSC method can reduce the computational burden by almost two thirds in comparison with the standard DSC 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 dynamic surface control for uncertain nonlinear systems in pure-feedback form with input and state constraints using noisy measurements

ABSTRACTThis paper is concerned with the design of an adaptive fuzzy dynamic surface control for uncertain nonlinear pure-feedback systems with input and state constraints using a set of noisy measurements. The design approach is described as follows. The nonlinear uncertainties are approximated by using the fuzzy logic systems at the first stage, secondly the adaptive fuzzy dynamic surface control is introduced to remove the problem of the explosion of complexity for the derivation of the adaptive fuzzy backstepping control, thirdly a new saturation function for state constraints is proposed to design the controllers based on the Lyapunov function, fourthly the number of the adjustable parameters is reduced by using the simplified extended single input rule modules, and finally the weighted least squares estimator to take the estimates for the un-measurable states and the adjustable parameters is in a simplified structure designed. The proposed approach provides effective system performance in the simulation experiment.