Adaptive control of output feedback nonlinear systems with unmodeled dynamics and output constraint

This paper is concerned with the adaptive control problem of a class of output feedback nonlinear systems with unmodeled dynamics and output constraint. Two dynamic surface control design approaches based on integral barrier Lyapunov function are proposed to design controller ensuring both desired tracking performance and constraint satisfaction. The radial basis function neural networks are utilized to approximate unknown nonlinear continuous functions. K-filters and dynamic signal are introduced to estimate the unmeasured states and deal with the dynamic uncertainties, respectively. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded, while the output constraint is never violated. Simulation results demonstrate the effectiveness of the proposed approaches.     

Observer-based decentralized adaptive control for large-scale nonlinear systems with mixed dynamic interaction

The problem of decentralized adaptive control is investigated for a class of large-scale nonstrict-feedback nonlinear systems subject to dynamic interaction and unmeasurable states, where the dynamic interaction is related to both input and output items. First, the fuzzy logic system is utilized to tackle unknown nonlinear function with nonstrict-feedback structure. Then, by combining adaptive and backstepping technology, the proper output feedback controller is designed. Meanwhile, a fuzzy state observer is proposed to estimate the unmeasurable states. The proposed controller could guarantee that all the signals of the resulting closed-loop systems are bounded. Finally, the applicability of the proposed controller is well carried out by a simulation example.     

Adaptive output feedback control of large-scale nonlinear time-delay systems with uncertain output equations

For a class of large-scale nonlinear time-delay systems with uncertain output equations, the problem of global state asymptotic regulation is addressed by output feedback. The class of systems under consideration are subject to feedforward growth conditions with unknown growth rate and time delays in inputs and outputs. To deal with the system uncertainties and the unknown delays, a novel low-gain observer with adaptive gain is firstly proposed; next, an adaptive output feedback delay-free controller is constructed by combining Lyapunov-Krasovskii functional with backstepping algorithm. Compared with the existing results, the controllers proposed are capable of handling both the uncertain output functions and the unknown time delays in inputs and outputs. With the help of dynamic scaling technique, it is shown that the closed-loop states converge asymptotically to zero, while the adaptive gain is bounded globally. Finally, the effectiveness of our control schemes are illustrated by three examples.     

Fuzzy adaptive output-feedback tracking control for nonlinear strict-feedback systems in prescribed finite time

The current paper addresses the fuzzy adaptive tracking control via output feedback for single-input single-output (SISO) nonlinear systems in strict-feedback form. Under the situation of system states being unavailable, the system output is used to set up the state observer to estimate the real system states. Furthermore, the estimation states are employed to design controller. During the control design process, fuzzy logic systems (FLSs) are used to model the unknown nonlinearities. A novel observer-based finite-time tracking control scheme is proposed via fuzzy adaptive backstepping and barrier Lyapunov function approach. The suggested fuzzy adaptive output feedback controller can force the output tracking error to meet the pre-specified accuracy in a fixed time. Meanwhile, all the closed-loop variables are bounded. Compared to some existing finite-time output feedback control schemes, the developed control strategy guarantees that the settling time and the error accuracy are independent of the uncertainties and can be specified by the designer. At last, the effectiveness and feasibility of the proposed control scheme are demonstrated by two simulation examples.     

Funnel-based adaptive fuzzy finite-time control for non-affine nonlinear systems preceded by unknown actuators

In this paper, an adaptive finite-time funnel control for non-affine strict-feedback nonlinear systems preceded by unknown non-smooth input nonlinearities is proposed. The input nonlinearities include backlash-like hysteresis and dead-zone. Unknown nonlinear functions are handled using fuzzy logic systems (FLS), based on the universal approximation theorem. An improved funnel error surface is utilized to guarantee the steady-state and transient predetermined performances while the differentiability problem in the controller design is averted. Using the Lyapunov approach, all the adaptive laws are extracted. In addition, an adaptive continuous robust term is added to the control input to relax the assumption of knowing the bounds of uncertainties. All the signals in the closed-loop system are shown to be semi-globally practically finite-time bounded with predetermined performance for output tracking error. Finally, comparative numerical and practical examples are provided to authenticate the efficacy and applicability of the proposed scheme.     

Error-driven nonlinear feedback-based fuzzy adaptive output dynamic surface control for nonlinear systems with partially constrained tracking errors

In this paper, a novel error-driven nonlinear feedback technique is designed for partially constrained errors fuzzy adaptive observer-based dynamic surface control of a class of multiple-input-multiple-output nonlinear systems in the presence of uncertainties and interconnections. There is no requirements that the states are available for the controller design by constructing fuzzy adaptive observer, which can online identify the unmeasurable states using available output information only. By transforming partial tracking errors into new error variables, partially constrained tracking errors can be guaranteed to be confined in pre-specified performance regions. The feature of the error-driven nonlinear feedback technique is that the feedback gain self-adjusts with varying tracking errors, which prevents high-gain chattering with large errors and guarantees disturbance attenuation with small errors. Based on a new non-quadratic Lyapunov function, it is proved that the signals in the resulted closed-loop system are kept bounded. Simulation and comparative results are given to demonstrate the effectiveness of the proposed method.     

Generation of stable limit cycles in nonlinear sandwich systems with dead-zone nonlinearity and input saturation

This paper is concerned with the problem of generating stable limit cycles for a class of nonlinear sandwich systems with the sandwiched dead-zone nonlinearity. In this study, the considered sandwich systems are restricted to the potential problems of non-symmetric input saturation nonlinearity and unknown parameters. In this regard, based on the set stabilization approach and the shape of the desired limit cycle, an adaptive state feedback controller is constructed by using the backstepping technique in such a way that forces the system's output to oscillate with the wanted amplitude and frequency. Besides, to estimate the value of unknown parameters, the adaptive laws are extracted and the problem of the explosion of complexity in the traditional backstepping approach is solved via an effective differentiator. The Lyapunov stability analysis proves that all signals of the closed-loop system keep bounded. Finally, the simulation results of a practical example are provided to demonstrate the effectiveness of the proposed method.     

Adaptive neural asymptotic tracking control for a class of stochastic non-strict-feedback switched systems

The adaptive asymptotic tracking control problem for a class of stochastic non-strict-feedback switched nonlinear systems is addressed in this paper. For the unknown continuous functions, some neural networks are used to approximate them online, and the dynamic surface control (DSC) technique is employed to develop the novel adaptive neural control scheme with the nonlinear filter. The proposed controller ensures that all the closed-loop signals remain semiglobally bounded in probability, at the same time, the output signal asymptotically tracks the desired signal in probability. Finally, a simulation is made to examine the effectiveness of the proposed control scheme.     

Fuzzy adaptive event-triggered control for uncertain nonlinear system with prescribed performance: A combinational measurement approach

This paper addresses the adaptive fuzzy event-triggered control (ETC) problem for a class of nonlinear uncertain systems with unknown nonlinear functions. A novel ETC approach that exhibits a combinational triggering (CT) behavior is proposed to update the controller and fuzzy weight vectors, achieving the non-periodic control input signals for nonlinear systems. A CT-based fuzzy adaptive observer is firstly constructed to estimate the unmeasurable states. Based on this, an output feedback ETC is proposed following the backstepping and error transformation methods, which ensures the prescribed dynamic tracking (PDT) performance. The PDT performance indicates that the transient bounds, over-shooting and ultimate values of tracking errors are fully determined by the control parameters and functions chosen by users. The closed-loop stability is guaranteed under the framework of impulsive dynamic system. Besides, the Zeno phenomenon is circumvented. The theoretical analysis indicates that the proposed scheme guarantees control performance while considerably reducing the communication resource utilization and controller updating frequency. Finally, the numerical simulations are conducted to verify the theoretical findings.     

Observer-based adaptive fuzzy control of a class of MIMO non-strict feedback nonlinear systems

This paper investigates the adaptive fuzzy control design problem of multi-input and multi-output (MIMO) non-strict feedback nonlinear systems. The considered control systems contain unknown control directions and dead zones. Fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and the state observers are designed to estimate immeasurable states. By constructing a dead zone compensator and introducing a Nussbaum gain function into the backstepping technique, an adaptive fuzzy output feedback control method is developed. The proposed adaptive fuzzy controller is proved to guarantee the semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system, and can solve the control design problems of unmeasured states, unknown control directions and dead zones. The simulation results are given to demonstrate the effectiveness of the proposed control method.     

Fault-tolerant practical tracking control for uncertain robotic system with general reference trajectory and output constraint

This paper is devoted to the fault-tolerant tracking control for a class of uncertain robotic systems under time-varying output constraints. Notably, both actuator fault and the disturbances are present while all the dynamic matrices are not necessarily to be parameterized by unknown parameters or have known nominal parts, and moreover, the reference trajectories as well as the output constraints functions are not necessarily twice continuously differentiable without any time derivatives of them being available for feedback. These remarkable characteristics greatly relax the corresponding assumptions of the related literature and in turn to bring the ineffectiveness of the traditional schemes on this topic. For this, a powerful adaptive control methodology is established by incorporating adaptive dynamic compensation technique into the backstepping framework based on Barrier Lyapunov functions. Then, an adaptive state feedback controller with the smart choices of adaptive law and virtual controls is designed which guarantees that all the states of the closed-loop system are bounded and the system output practically tracks the reference trajectory while not violates the output constraints.     

Adaptive fuzzy output feedback fault-tolerant tracking control of switched uncertain nonlinear systems with sensor faults

This paper investigates the adaptive fuzzy output feedback fault-tolerant tracking control problem for a class of switched uncertain nonlinear systems with unknown sensor faults. In this paper, since the sensor may suffer from an unknown constant loss scaling failure, only actual output can be used for feedback design. A failure factor is employed to represent the loss of effectiveness faults. Then, an adaptive estimation coefficient is introduced to estimate the failure factor, and a state observer based on the actual output is constructed to estimate the system states. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Based on the Lyapunov function method and the backstepping technique, the proposed control scheme with average dwell time constraints can guarantee that all states of the closed-loop system are bounded and the tracking error can converge to a small neighborhood of zero. Finally, two simulation examples are given to illustrate the effectiveness of the proposed scheme.     

Sampled observer-based adaptive output feedback fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the sampled outputs-based adaptive fault-tolerant control problem for a class of strict-feedback uncertain nonlinear systems, where the nonlinear functions are allowed to include the unmeasured system states. Within the framework, a sampled output observer is introduced to jointly estimate the system states and parameters. By combining the estimated states and the supervisory switching strategy, an adaptive fault-tolerant controller is designed to achieve the desirable tracking performance. By using Lyapunov stability theory, it is proved that all the signals of the closed-loop systems are bounded and the tracking error converges to an adjustable neighbourhood of the origin eventually both in the fault free and faulty cases. Especially, if the outputs are available all the time, the proposed output feedback fault-tolerant control method can ensure the tracking error satisfy the prescribed performance bounds regardless of the faults. Finally, two examples are used to illustrate the effectiveness of the proposed method.     

Predictor-based optimal robust guaranteed cost control for uncertain nonlinear systems with completely tracking errors constraint

In this paper, a novel composite controller is proposed to achieve the prescribed performance of completely tracking errors for a class of uncertain nonlinear systems. The proposed controller contains a feedforward controller and a feedback controller. The feedforward controller is constructed by incorporating the prescribed performance function (PPF) and a state predictor into the neural dynamic surface approach to guarantee the transient and steady-state responses of completely tracking errors within prescribed boundaries. Different from the traditional adaptive laws which are commonly updated by the system tracking error, the state predictor uses the prediction error to update the neural network (NN) weights such that a smooth and fast approximation for the unknown nonlinearity can be obtained without incurring high-frequency oscillations. Since the uncertainties existing in the system may influence the prescribed performance of tracking error and the estimation accuracy of NN, an optimal robust guaranteed cost control (ORGCC) is designed as the feedback controller to make the closed-loop system robustly stable and further guarantee that the system cost function is not more than a specified upper bound. The stabilities of the whole closed-loop control system is certified by the Lyapunov theory. Simulation and experimental results based on a servomechanism are conducted to demonstrate the effectiveness of the proposed method.     

Adaptive output-feedback control for nonlinear time-delay systems in pure-feedback form

The main contribution of this paper is to develop an adaptive output-feedback control approach for a class of uncertain nonlinear systems with unknown time-varying delays in the pure-feedback form. Both the non-affine nonlinear functions and the unknown time-varying delayed functions related to all state variables are considered. These conditions make the controller design difficult and challenging because the output-feedback controller should be designed using only the output information. In order to overcome these conditions, we design an observer-based adaptive dynamic surface controller where the time-delay effects are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique using neural networks. A first-order filter is added to the control input to avoid the algebraic loop problem caused by the non-affine structure. It is proved that all the signals in the closed-loop system are semi-globally uniformly bounded and the tracking error converges to an adjustable neighborhood of the origin.     

Fuzzy adaptive control of nonlinear MIMO systems with unknown dead zone outputs

This paper addresses a novel fuzzy adaptive control method for a class of uncertain nonlinear multi-input multi-output (MIMO) systems with unknown dead-zone outputs and immeasurable states. The immeasurable states under consideration are estimated by designing a fuzzy state observer. Based on the properties of the Nussbaum-type function, the difficulty of fuzzy adaptive control caused by the unknown dead zone outputs of MIMO nonlinear uncertain systems is overcome. The presented design algorithm not only guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, but also ensures that the outputs of the MIMO system converge to a small neighborhood of the desired outputs. The main contributions of this research lie in that the developed MIMO systems are more general, and an efficient design method of output-feedback controller is investigated for the studied MIMO systems, which is more applicable in practical environment. Simulation results illustrate the effectiveness of the proposed scheme.     

Sampled observer-based adaptive decentralized control for strict-feedback interconnected nonlinear systems

This paper investigates the decentralized tracking control problem for a class of strict-feedback interconnected nonlinear systems with unknown parameters, where the system states are unmeasurable and the interconnections are unknown. Different from the existing results, where the output is available all the time, we consider the case that the output is only available at the sampled instants, which means the failure of existing methods. By introducing a kind of sampled observer for each subsystem, the system states and unknown parameters are jointly estimated. Based on which, a totally decentralized output feedback control scheme is developed to achieve the desired tracking performance by applying backstepping technique, where a compensation mechanism is utilized to address the unknown interconnections from other subsystems. Subsequently, by using Lyapunov stability theory, it is proved that all the signals in the closed-loop system are bounded and the tracking errors converge to an adjustable neighbourhood of the origin. Finally, an example is used to illustrate the effectiveness of the proposed method.     

Fuzzy adaptive fault-tolerant tracking control of MIMO stochastic pure-feedback nonlinear systems with actuator failures

This paper studies the adaptive fuzzy fault-tolerant control design problem for a class of stochastic multi-input and multi-output (MIMO) nonlinear systems in pure-feedback form. The nonlinear systems under study contain unknown functions, unmeasured states and actuator faults, which are described by the loss of effectiveness and lock-in-place modes. With the help of fuzzy logic systems identifying uncertain stochastic nonlinear systems, a fuzzy state observer is established for estimating the unmeasured states. Based on the backstepping design technique with the nonlinear tolerant-fault control theory, an adaptive fuzzy output feedback faults-tolerant control approach is developed. It is proved that the proposed fault-tolerant control approach can guarantee that all the signals of the resulting closed-loop system are bounded in probability. Moreover, the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach.     

Multivariable uniform finite-time output feedback reentry attitude control for RLV with mismatched disturbance

A continuous multivariable uniform finite-time output feedback reentry attitude control scheme is developed for Reusable Launch Vehicle (RLV) with both matched and mismatched disturbances. A novel finite-time controller is derived using the bi-limit homogeneous technique, which ensures that the attitude tracking can be achieved in a uniformly bounded convergence time from any initial states. A multivariable uniform finite-time observer is designed based on an arbitrary order robust sliding mode differentiator to estimate the unknown states and the external disturbances, simultaneously. Then, an output feedback control scheme is established through the combination of the developed controller and the observer. A rigorous proof of the uniform finite-time stability of the closed-loop system is presented using Lyapunov and homogeneous techniques. Finally, numerical simulation is provided to demonstrate the efficiency of the proposed scheme.     

Predefined-time tracking of nonlinear strict-feedback systems with time-varying output constraints

In this paper, the problem of the predefined-time tracking with time-varying output constraints (TVOC) is investigated for a class of nonlinear strict-feedback systems. First, the sufficient conditions for the studied problem are presented. Then, a recursive design algorithm of the controller is proposed by backstepping technique. A novel stabilizing function is constructed by adding a fractional term, which is capable of decreasing the asymmetric time-varying Barrier Lyapunov Function (BLF) to the origin within any desired settling time. After that, it is shown that under our proposed control, all the closed-loop signals are bounded, and the tracking error converges to zero within any desired settling time and remains zero thereafter without the violation of the output constraint. The settling time in this paper is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Finally, two examples are given to illustrate the effectiveness of the proposed method.