Adaptive fuzzy-based composite anti-disturbance control for a class of switched nonlinear systems with unknown backlash-like hysteresis

For a class of switched nonlinear systems with unmatched external disturbances and unknown backlash-like hysteresis, an adaptive fuzzy-based control strategy is proposed to handle the anti-disturbance issue. The unmatched external disturbances come from a switched exosystem. Our aim is to achieve the output tracking performance and the disturbance attenuation by using the adaptive fuzzy-based composite anti-disturbance control technique. First, based on the fuzzy logics, we design a switching adaptive fuzzy disturbance observer to estimate unmatched external disturbances. Second, a composite switching adaptive anti-disturbance controller is constructed. By means of the backstepping technique, disturbance estimations are added in each virtual control to offset the unmatched disturbances, which results in the different coordinate transformations. At last, the availability of the proposed approach is illustrated by a mass-spring-damper system.     

Global fuzzy adaptive asymptotic tracking control for nonlinear reaction-diffusion equations with time-varying coefficients

This study focuses on the research of the globally asymptotic tracking problem of unknown nonlinear reaction-diffusion equations with time-varying coefficients and uncertain external disturbance. Firstly, fuzzy logic systems and adaptive bounding technique are used to deal with nonlinear reaction-diffusion equations with time-varying coefficients and uncertain external disturbance. Secondly, a novel global state feedback adaptive fuzzy control algorithm is proposed to make the nonlinear reaction-diffusion equations track the target systems globally and asymptotically. In addition, the globally asymptotic tracking condition can be obtained, which overcomes the semi-global results in the existing literatures. Finally, three simulation examples are given to illustrate the feasibility and effectiveness of the proposed control protocols.     

Adaptive fuzzy fixed-time dynamic surface control for stochastic nonstrict nonlinear systems with unknown dead-zones

This paper focuses on an adaptive fuzzy fixed-time control problem for stochastic nonstrict nonlinear systems with unknown dead-zones by using dynamic surface control (DSC) technology. Fuzzy logic systems (FLSs) and DSC technology are used to approximate nonlinear functions and reduce the computational complexity, respectively. At the same time, the influence of the dead-zone disturbance is offset by transforming the dead-zone model into the nonlinear model that can be approximated by the FLSs. Then, based on the fixed-time stability theory, an adaptive fuzzy fixed-time tracking control strategy is proposed, which can ensure semi-global practical fixed-time stability of the system and the tracking error converging to a small neighborhood near the origin. Finally, two simulation examples are given to prove the effectiveness of the proposed control strategy.     

Observer-based terminal sliding mode control of non-affine nonlinear systems: Finite-time approach

This paper studies the problem of observer based fast nonsingular terminal sliding mode control schemes for nonlinear non-affine systems with actuator faults, unknown states, and external disturbances. A hyperbolic tangent function based extended state observer is considered to estimate unknown states, which enhances robustness by estimating external disturbance. Then, Taylor series expansion is employed for the non-affine nonlinear system with actuator faults, which transforms it to an affine form system to simplify disturbance observer and controller design. A finite time disturbance observer is designed to address unknown compound disturbances, which includes external disturbances and system uncertainties. A fast nonsingular terminal sliding mode with exponential function sliding mode is proposed to address output tracking. Simulation results show the proposed scheme is effective.     

Robust adaptive finite-time stabilization control for a class of nonlinear switched systems based on finite-time disturbance observer

The problem of adaptive global finite-time stabilization control for a class of nonlinear switched systems in the presence of external perturbations and arbitrary switchings has been addressed in this research study. The proposed scheme has been designed based on a finite-time estimation technique in which during the control procedure, unknown imposed perturbations are accurately estimated by means of the designed finite-time disturbance observer (FTDO). Due to the exact estimation of the external disturbances within a given finite time, the encountered complications and adversities from loss of information in the Lyapunov parameter estimation (LPE) methods have been solved which are caused by the persistent switchings in the system. Furthermore, a new solution for the problem of chattering phenomenon in nonlinear switched systems has been presented by utilizing the designed FTDO, which can counteract the malfunctioning responses of the system caused by external disturbances and unmodeled dynamics. In this paper, an acknowledged class of nonlinear switched systems has been taken into account which is in the general form of canonical structure. In addition, the established design strategy is formulated for the control of perturbed nonlinear switched systems with one and only input and assures that the system states through the finite-time convergence characteristic, reach the equilibrium point of origin. Finally, numerical simulations are carried out on a mass-spring-damper (MSD) dynamical system to indicate advantages and superior efficiency of the suggested method.     

Adaptive dynamic surface tracking control for uncertain full-state constrained nonlinear systems with disturbance compensation

In this paper, an asymptotic adaptive dynamic surface tracking control strategy is investigated for uncertain full-state constrained nonlinear systems subject to parametric uncertainties and external disturbances. A novel disturbance estimator (DE) is firstly used to compensate for external disturbances. The parametric uncertainties are accordingly handled via a synthesized adaptive law. Then, by using the barrier Lyapunov function (BLF) and dynamic surface control (DSC), an appropriate backstepping design framework employing a novel adaptive-gain nonlinear filter is given, which avoids the “explosion of complexity” and relieves the conservatism of filter gain selection. The theoretical analysis reveals the asymptotic tracking performance is assured with the proposed controller. In the end, some simulation cases demonstrate the validity of the proposed controller.     

Adaptive leaderless consensus control of a class of strict feedback nonlinear systems with guaranteed transient performance under actuator faults

The problem of adaptive leaderless consensus control of a class of uncertain strict feedback nonlinear systems with guaranteed transient performance is investigated in this paper. The system model is a class of strict feedback nonlinear systems with parametric uncertainty, actuator fault and external disturbance. How to guarantee the transient performance of consensus error is involved. To solve this problem, the consensus is transmitted into stabilization of a new variable. Ultimately the consensus errors will asymptotically converge to zero and faster than a given exponentially converging variable. Finally, simulation results show the effectiveness of proposed control scheme.     

Command filter-based finite-time adaptive fuzzy control for nonlinear systems with uncertain disturbance

In this paper, a command filter-based adaptive fuzzy controller is constructed for a class of nonlinear systems with uncertain disturbance. By using the error compensation signals and fuzzy logic system, a command filter-based control strategy is presented to make that the tracking error converge to an any small neighborhood of zero and all closed-loop signals are bounded. In the design procedure, fuzzy logic system is employed to estimate unknown package nonlinear functions, which avoids excessive and burdensome computations. The control scheme not only resolves the explosion of complexity problem but also eliminates the filtering error in finite-time. An example has evaluated the validity of the control method.     

Adaptive fuzzy asymptotically tracking control of full state constrained nonlinear system based on a novel Nussbaum-type function

This study carries out the problem of adaptive backstepping fuzzy tracking control for a class of full state constrained uncertain nonlinear system with unknown control directions. Based on Nussbaum-type functions and tan-type Barrier Lyapunov functions, a novel adaptive fuzzy tracking controller is proposed to guarantee that the system output tracking error asymptotically converges to zero, while the constraints on the states of system will not be violated during operation. Compared with the existing results, a better convergence effect is obtained for this class of systems. Stability analysis of the proposed closed-loop control system is supported by the Lyapunov stability theory. Finally, a simulation example is presented to illustrate the effectiveness of the proposed control strategy.     

Fixed-time neuroadaptive practical tracking control based on extended state/disturbance observer for a QUAV with external disturbances and time-varying parameters

This paper investigates the fixed-time neural network adaptive (FNNA) tracking control of a quadrotor unmanned aerial vehicle (QUAV) to achieve flight safety and high efficiency. By combining radial basis function neural network (RBFNN) with fixed time adaptive sliding mode algorithm, a novel radial basis function neural network adaptive law is proposed. In addition, an extended state/disturbance observer (ESDO) is proposed to solve the problem of unmeasurable state and external interference, which can obtain reliable state feedback and interference input. Unlike most other ESO applications, this paper does not set the uncertainty model and external disturbances as total disturbances. Instead, the external disturbances are observed by extending the states and the observed states are fed back to the controller to cancel the disturbances. In view of the time-varying resistance coefficient and inertia torque in the QUAV model, the neural network is introduced so that the controller does not need to consider these nonlinear uncertainties. Finally, a numerical example is given to verify the effectiveness of the coupled non-simplified QUAV model.     

Online adaptive policy iteration based fault-tolerant control algorithm for continuous-time nonlinear tracking systems with actuator failures

In this paper, a novel tracking control scheme for continuous-time nonlinear affine systems with actuator faults is proposed by using a policy iteration (PI) based adaptive control algorithm. According to the controlled system and desired reference trajectory, a novel augmented tracking system is constructed and the tracking control problem is converted to the stabilizing issue of the corresponding error dynamic system. PI algorithm, generally used in optimal control and intelligence technique fields, is an important reinforcement learning method to solve the performance function by critic neural network (NN) approximation, which satisfies the Lyapunov equation. For the augmented tracking error system with actuator faults, an online PI based fault-tolerant control law is proposed, where a new tuning law of the adaptive parameter is designed to tolerate four common kinds of actuator faults. The stability of the tracking error dynamic with actuator faults is guaranteed by using Lyapunov theory, and the tracking errors satisfy uniformly bounded as the adaptive parameters get converged. Finally, the designed fault-tolerant feedback control algorithm for nonlinear tracking system with actuator faults is applied in two cases to track the desired reference trajectory, and the simulation results demonstrate the effectiveness and applicability of the proposed method.     

Disturbance and state observer-based adaptive finite-time control for quantized nonlinear systems with unknown control directions

This paper concentrates on proposing a novel finite-time tracking control algorithm for a kind of nonlinear systems with input quantization and unknown control directions. The nonlinear functions in the system are approximated by the means of strong approximation capability of the fuzzy logic systems. Firstly, the nonlinear system with unknown control directions is transformed into an equivalent system with known control gains by coordinate transformation. Secondly, the unknown system states are estimated by a designed fuzzy state observer, and the disturbance observer is constructed to track the external disturbances. The command filtering method is proposed to approach the problem of “explosion of complexity” existed in the conventional backstepping design process. In this system, the difficulties caused by unknown control directions are solved via the Nussbaum gain approach. Finally, based on the fuzzy state observer, the controller of the original system is obtained via using the transformed system by the backstepping method. The boundedness of all signals and the convergence of tracking and observer errors at the origin are ensured for the closed-loop system, and demonstrated by the simulation result in this paper.     

Adaptive-critic-based model reference control for unknown nonlinear systems with input constraints

In this paper, the optimal model reference adaptive control (MRAC) problem is studied for the unknown discrete-time nonlinear systems with input constraint under the premise of considering robustness to uncertainty. Through an input constraint auxiliary system, a new adaptive-critic-based MRAC algorithm is proposed to transform the above problem into the optimal regulation problem of the auxiliary error system with lumped uncertainty. In order to realize the chattering-free sliding model control for the auxiliary error system, an action-critic variable is introduced into the adaptive identification learning. In this case, the closed-loop control system is robust to the disturbance and the neural network approximation error. The uniformly ultimate bounded property is proved by the Lyapunov method, and the effectiveness of the algorithm is verified by a simulation example.     

Application of active disturbance rejection control in tank gun control system

The problem of position tracking for a tank gun control system with inertia uncertainty and external disturbance is investigated in this paper. The tank gun control system, demanding high tracking precision and stabilization precision, is a nonlinear system. Classical control methods are commonly used in the actual system, which is difficult to ensure high precision and high disturbance rejection capability. An active disturbance rejection control (ADRC) scheme is applied to guarantee the state variables of the closed loop system to converge to the reference state with the help of the extended state observer by estimating the inertia uncertainty and external disturbance. The basic theory of the ADRC is introduced here. According to the mathematical model, the parameters of ADRC are designed. Also, simulation results show that ADRC controller has advantages of high precision and high disturbance rejection ability. A comparison between ADRC and PID is also presented to show the effectiveness of the ADRC control strategy.     

Dual-Condition event-Triggered distributed adaptive neural control for multi-Agent systems with nonlinear fault

This paper studies the cooperative adaptive dual-condition event-triggered tracking control problem for the uncertain nonlinear nonstrict feedback multi-agent systems with nonlinear faults and unknown disturbances. Under the framework of backstepping technology, a new threshold update method is designed for the state event-triggered mechanism. At the same time, we develop a novel distributed dual-condition event-triggered strategy that combined the fixed threshold triggered mechanism acted on the controller with the new event-triggered mechanism, which can better reduce the waste of communication bandwidth. To deal with the algebraic loop problem caused by the non-affine nonlinear fault, the Butterworth low-pass filter is introduced. At the same time, the unknown function problems are solved by the neural network technology. All signals of the system are semiglobally uniformly ultimately bounded and the tracking performance is achieved, which proved by the Lyapunov stability theorem. Finally, the results of the simulation test the efficiency of the proposed control scheme.     

Fixed-time composite neural learning control of state-constrained nonlinear uncertain systems

This paper presents a fixed-time composite neural learning control scheme for nonlinear strict-feedback systems subject to unknown dynamics and state constraints. To address the problem of state constraints, a new unified universal barrier Lyapunov function is proposed to convert the constrained system into an unconstrained one. Taking the unconstrained system, a modified fixed-time convergence state predictor is explored, enabling the prediction error for compensating the neural adaptive law to be obtained and improving the learning ability of online neural networks (NNs). Without employing fractional power terms or a complicated switching strategy to build the control law, a new method of constructing a smooth fixed-time dynamic surface control scheme is proposed. This overcomes the potential singularity problem and the explosion of complexity often encountered in fixed-time back-stepping designs. The representative features of our design are threefold. First, it is free of the fractional power terms, yet offers fixed-time convergence. Second, it addresses the state constraint problem without requiring a feasibility check. Third, it constructs a new state-predictor and enhances the approximation accuracy of NNs. The stability of the proposed control scheme is analyzed using the Lyapunov technique. Simulation results are presented to illustrate the effectiveness of the proposed controller.     

Dynamic event-triggered optimal tracking control for constrained nonlinear stochastic systems

This paper investigates the optimal tracking control problem (OTCP) for nonlinear stochastic systems with input constraints under the dynamic event-triggered mechanism (DETM). Firstly, the OTCP is converted into the stabilizing optimization control problem by constructing a novel stochastic augmented system. The discounted performance index with nonquadratic utility function is formulated such that the input constraint can be encoded into the optimization problem. Then the adaptive dynamic programming (ADP) method of the critic-only architecture is employed to approximate the solutions of the OTCP. Unlike the conventional ADP methods based on time-driven mechanism or static event-triggered mechanism (SETM), the proposed adaptive control scheme integrates the DETM to further lighten the computing and communication loads. Furthermore, the uniform ultimately boundedness (UUB) of the critic weights and the tracking error are analysed with the Lyapunov theory. Finally, the simulation results are provided to validate the effectiveness of the proposed approach.     

Barrier function-based nonsingular prescribed performance terminal sliding mode tracker for under-actuated nonlinear systems: Experimental study

In this paper, an adaptive concave barrier function scheme coupled with the non-singular terminal sliding mode control technique is proposed for finite-time tracking control of the under-actuated nonlinear system in the existence of model uncertainty, external disturbance and input saturation. Firstly, the dynamical equation of under-actuated nonlinear n-order system is expressed under model uncertainty, external disturbance and input saturation. Secondly, for the improvement of stability performance of the system in the existence of input saturation, a compensation system is designed to overcome the constraint on the control input. Afterward, the tracking errors between actual states of the system and differentiable reference signals are defined and the sliding surface based on the defined tracking errors is presented. Then, for gaining the better transient and steady-state performance of the closed-loop system, the prescribed performance control scheme is adopted. Based on this method, the transformed prescribed form of the previous determined sliding surface is obtained to ensure that the sliding surface can reach to a predefined region. Afterward, for assurance of the finite-time reachability of transformed sliding surface, the nonsingular terminal sliding surface is recommended. In addition, for the compensation of the model uncertainty and external disturbance existed in the system, the adaptive-based concave barrier function technique is used to estimate the unknown bounds of uncertainty and exterior disturbance. Finally, for demonstration of the proposed control method, the simulations and experimental implementation are done on the air levitation system.     

Quantized adaptive tracking control for nonlinear systems with actuator backlash compensation

In this paper, the problem of adaptive tracking control is investigated for nonlinear systems with asymmetric actuator backlash. We assume that the nonlinearities of the systems are unknown and the external disturbances are bounded. First, the control input will be quantized by a hysteresis-type quantizer, which can reduce the communication rate of the control signal. Then, the asymmetric actuator backlash is approximated to a new model, and a novel adaptive controller with the quantizer is designed via an adaptive backstepping technique to guarantee all the signals of the closed-loop tracking error system are uniform ultimate boundedness. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed algorithm.     

Interventional bipartite consensus on coopetition networks with unknown dynamics

In this paper, an interventional bipartite consensus problem is considered for a high-order multi-agent system with unknown disturbance dynamics. The interactions among the agents are cooperative and competitive simultaneously and thus the interaction network (just called coopetition network in sequel for simplicity) is conveniently modeled by a signed graph. When the coopetition network is structurally balanced, all the agents are split into two competitive subgroups. An exogenous system (called leader for simplicity) is introduced to intervene the two competitive subgroups such that they can reach a bipartite consensus. The unknown disturbance dynamics are assumed to have linear parametric models. With the help of the notation of a disagreement state variable, decentralized adaptive laws are proposed to estimate the unknown disturbances and a dynamic output-feedback consensus control is designed for each agent in a fully distributed fashion, respectively. The controller design guarantees that the state matrix of the closed-loop system can be an arbitrary predefined Hurwitz matrix. Under the assumption that the coopetition network is structurally balanced and the leader is a root of the spanning tree in an augmented graph, the bipartite consensus and the parameter estimation are analyzed by invoking a common Lyapunov function method when the coopetition network is time-varying according to a piecewise constant switching signal. Finally, simulation results are given to demonstrate the effectiveness of the proposed control strategy.