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In this paper, an adaptive fixed‐time neural control scheme is proposed for a class of nonlinear uncertain systems with full‐state constraints. A novel asymmetric hyperbolic barrier Lyapunov function (AHBLF) is first constructed to handle time‐varying constraints of all the system states. EspecialLy, the AHBLF can not only be applied to unconstrained, symmetric‐constrained and asymmetric‐constrained systems simultaneously, but also the fixed time control can be realized by incorporating the AHBLF into each step of the backstepping method to design controller. The adaptive controller is presented to guarantee that the tracking errors converge into the neighborhood around the equilibrium point in a fixed time and all the system states can be restricted within the predefined time‐varying boundaries. With the proposed control scheme, the singularity problem is avoided without constructing multiple piecewise functions, and no prior knowledge on the bound of gain functions is required in the controller design. Comparative simulations illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the adaptive neural network event‐triggered control (ETC) problem for stochastic nonlinear systems with output constraint. The influence of stochastic disturbance inevitably exists in many practical systems, which leads to system instability. Meanwhile, a novel tan type barrier Lyapunov function (Tan‐BLF) structure is proposed to deal with the constraint requirements of stochastic systems. In the sense of probability, the output constraints will not be violated during the operation of the system. In addition, the ETC strategy is adopted to reduce the burden of communication. The asymptotic stability of the closed‐loop system is guaranteed without violating output constraints. Meanwhile, the tracking error converges to a small region of the origin. Two simulations results demonstrate the effectiveness of theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper investigates a novel distributed fuzzy adaptive iterative learning control protocol of exact consensus for second-order unknown nonlinear strict-feedback multi-agent systems with partially unknown time-varying control di- rections. Fuzzy logic system estimates the unknown nonlinear dynamics of each agent. Based on Nussbaum function, the control protocols of all follower agents with partially unknown virtual and actual control directions are designed by the backstepping method. The proposed protocol guarantees that the output of every follower agent could exactly track the desired output trajectory on a finite time interval. As an extension, the formation control results can also be solved. Finally, two simulation examples prove that the proposed control scheme is effective and rigorous. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of H ∞ optimal tracking control for a class of nonlinear state constrained systems with input delay and disturbances. With the aid of Pade approximation, an auxiliary variable is devised to eliminate the effects of input delay. Combining barrier Lyapunov functions (BLFs) with backstepping design technique, a feedforward adaptive controller is designed to transform the tracking control problem of nonlinear state constrained system into an equivalent H ∞ control problem of input-affine error system without state constraints, wherein neural networks (NNs) are employed to approximate unknown system dynamics. Then based on single-network adaptive dynamic programming (ADP), an H ∞ optimal feedback controller is developed by utilizing a single critic network to learn the Nash equilibrium related to Hamilton–Jacobi–Isaacs (HJI) equation. Therefore, the whole tracking controller can be constructed by integrating the feedforward adaptive controller with the optimal feedback controller. Moreover, it is proven by Lyapunov's theory that all signals within the closed-loop system are uniformly ultimately bounded (UUB), and the tracking error converges to a small neighborhood of the origin without violating any state constraints. Two simulation examples are also presented to validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper addresses the tracking control problem for a class of permanent magnet synchronous motors (PMSM) systems with asymmetric full-state constraints. To overcome the difficulty of controller design caused by the state constraint problems of system, a nonlinear transformation function i introduced to transform the state constraint problems into a non-constraint problems. Then, radial basis function neural networks (NN) is employed to approximate the uncertainties in the system. In addition, by combining the techniques of command filter and finite-time control, a novel virtual control signal and modified error compensation signals are proposed to construct the actual control law, which solves the problems of "explosion of complexity" and "singularity". It is shown that all signals of the closed-loop system are bounded and the tracking error remains in a small neighborhood of the origin in finite time. Finally, the simulations show the performance and feasibility of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of prescribed performance control (PPC) for a class of strict-feedback nonlinear systems, in which uncertain nonlinearity and uncertain disturbance exist in the considered nonlinear system at the same time, and the input control signal of the system is constrained by saturation nonlinearity. The adaptive neural network is used to approximate all unknown nonlinearity of the closed-loop system. And a new class of error transformation functions is proposed for the first time, which is superior to other similar documents in that the output error can always be constrained by the prescribed band only according to the properties of the designed error transformation function without any additional conditions. The simulation results finally verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the fuzzy adaptive tracking control problem is studied for a class of nonlinear strict feedback systems with time-varying full state constraints. For the full state constraints problem, the nonlinear transformation function is used to transform the constraint problem into a non-constraint problem. A new adaptive control framework is proposed for asymptotic tracking of nonlinear systems with unknown virtual control coefficients (UVCC). Under the proposed control scheme, the effects of UVCC and unknown nonlinear functions are compensated by the introduction of some well-defined smoothing functions and boundary estimation methods. In addition, a new Lyapunov function is constructed, which successfully achieves the tracking error of the closed-loop system converge to zero and all the signals in the closed-loop systems are bounded. In the meanwhile, all states are always keep in their asymmetric time-varying constraints. Finally, a numerical example is presented to show the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of adaptive fault-tolerant control for a class of single-input and single-output nonlinear Itô stochastic systems with unknown dynamics and multiple sensor faults. Due to the partial loss of effectiveness of sensors, each measured state contains an unknown time-varying fault parameter. Then, to circumvent the main obstacle caused by the coupling of unknown fault parameters and real states, a new method of fault parameters separating of stochastic nonlinear systems is proposed. Combining with the modified backstepping design techniques, an adaptive state feedback controller is constructed recursively to estimate unknown fault parameters and guarantee the stabilisation of the stochastic system. By using quartic Lyapunov functions, it is proved that all signals of the closed-loop system are bounded in probability. Finally, simulation results are given to illustrate the effectiveness of the proposed controller design method. [ABSTRACT FROM AUTHOR]

The design of an attitude control system for an asteroid-orbiting satellite via immersion and invariance is the subject of this paper. It is assumed that the asteroid is rotating with a constant rate, and that the inertia parameters of the satellite and the coefficients in the spherical harmonic gravitational potential of the asteroid are not known. The objective is to regulate the quaternion trajectory of the satellite orbiting in an equatorial orbit. Based on the immersion and invariance (I&I) theory, a noncertainty-equivalence adaptive (NCEA) attitude control law is derived. For the design, a backstepping design process involving two steps is used, and filtered signals are constructed to overcome the difficulty in solving certain matrix inequalities of the I&I methodology. The control law includes a stabilizer and an identifier - designed separately. Unlike the classical certainty-equivalence adaptive (CEA) systems, here the estimated parameters include not only the signals obtained from an integral type update law, but also judiciously chosen nonlinear algebraic signals that yield stronger stability properties. By the Lyapunov stability analysis, it is shown that the quaternion trajectories of the disturbance input-free closed-loop system asymptotically converge to the equilibrium point. The control law is effective in regulating the attitude to the equilibrium point with minimal rotation of spacecraft. Also, for the model with disturbance input, uniform ultimate boundedness of system trajectories is established. Simulation results for the attitude control of spacecraft in orbit around asteroid 433 Eros are presented for illustration. These results show that the spacecraft achieves nadir pointing attitude despite uncertainties in the system dynamics. • Adaptive attitude control system for spacecraft orbiting around rotating asteroids. • Noncertainty-equivalence adaptive (NCEA) quaternion trajectory control law via immersion and invariance. • Lyapunov stability analysis estabilishing closed-loop system asymptotic stability. • Backstepping design accomplishing quaternion control with minimal rotation around 433 Eros asteroid. • Convergence of trajectories to an attractive manifold unlike traditional adaptive systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The development of an adaptive control system for the attitude control of spacecraft orbiting around uniformly rotating asteroids is the subject of this paper. It is assumed that inertia parameters of spacecraft, and zonal and sectorial harmonic coefficients associated with the gravitational field of asteroid are not known. The objective is to control the Euler (yaw, pitch, roll) angles of the spacecraft along prescribed reference attitude trajectories. Based on the immersion and invariance methodology, a noncertainty-equivalence adaptive (NCEA) control law for the trajectory control of the Euler angles is derived. The design is completed in two steps of a backstepping design process, and filtered signals are used for synthesis. Unlike traditional certainty-equivalence adaptive systems, the estimated parameters of this NCEA law consist of certain nonlinear algebraic functions as well as partial estimates, obtained by integral adaptation law. By the Lyapunov analysis, it is shown that in the closed-loop system, the yaw, pitch, and roll angles trajectory tracking errors asymptotically converge to zero. For the purpose of illustration, attitude control of a spacecraft orbiting around 433 Eros asteroid is considered. Simulation results confirm that this NCEA law can accomplish precise nadir pointing attitude of the spacecraft on elliptical prograde and retrograde orbits despite uncertainties in the spacecraft dynamics. [ABSTRACT FROM AUTHOR]

This paper investigates the fuzzy adaptive practical tracking problem for a class of nonlinear pure-feedback systems with quantized input signal. In the control scheme design process, the considered system is transformed into a plant with a strict-feedback form by borrowing the mean value theorem of differential, then fuzzy logic systems are used to compensate for some uncertain nonlinearities in the considered plant and the classical adaptive technique is employed to handle some unknown parameters. In the backstepping design, some non-negative switching functions are introduced to develop the desired fuzzy controller, and Barbalat’s lemma is used to analyze the stability and the control performance of the closed-loop system. It can be shown that under the novel adaptive fuzzy controller, all the closed-loop signals are semiglobally uniformly ultimately bounded, and especially the tracking error satisfies the accuracy assigned a priori. A simulation example is presented to verify the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper presents a solution to guarantee a fault-tolerant control (FTC) of dynamic positioning (DP) vessel in the presence of the position reference system (PRS) faults by using the backstepping technique. The faults modes of PRS are modeled as an additive uncertainty in the feedback loop of the DP control system, and the bounds of the additive uncertainty are unknown. Through estimating online the unknown bounds on the basis of the designed adaptive mechanism, the robust adaptive fault-tolerant controller (RAFTC), which takes the faulty PRS measurements as the inputs, is proposed rather than detecting and isolating them. Moreover, the developed RAFTC is proved by applying Lyapunov stability theory that the closed-loop DP control system is uniformly bounded and the tracking error can be converged to zero asymptotically despite of the PRS failures. A simulation scenario on an offshore supply vessel model is provided to validate the effectiveness of the designed RAFTC, and the results show that the RAFTC has better performance and robustness compared with the ordinary fine-tuned adaptive backstepping controller. [ABSTRACT FROM AUTHOR]

This paper considers the adaptive fuzzy output feedback control design problem for a class of switched nonlinear systems. The considered switched nonlinear systems contain unknown nonlinearities, the switching signals with average dwell time, and without requiring that state variables are available for measurement. Fuzzy logic systems are used to approximate the unknown nonlinearities, and a fuzzy switched state observer is designed to estimate the immeasurable states. In the framework of observer-based output feedback control design technique, and by introducing a command filter into the backstepping design algorithm, a command filter-based adaptive fuzzy backstepping output feedback control scheme is developed. The stability of the closed-loop system and the convergence of the tracking error are proved via average dwell time and multiple Lyapunov function. A numerical example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper proposes a novel decentralized adaptive excitation control scheme to globally stabilize large-scale power systems and enhance the transient stability. Two smooth functions are introduced to counteract the effect of unknown time-varying interactions, then a completely decentralized adaptive controller is constructed on the basis of the adaptive backstepping approach. The proposed controller utilizes only local measurements and has no requirement for the bounds of interconnections in the power system. All signals of the overall closed-loop large-scale power system are proved to be globally uniformly bounded. The proposed control scheme is tested on a two-area benchmark power system in the face of a symmetrical three-phase short circuit fault. Simulation results have showed better transient performances in comparison with existing controllers. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of tracking control for a class of uncertain nonlinear systems in strict-feedback form subject to completely unknown system nonlinearities, hard constraints on full states, and unknown time-varying bounded disturbances. Integral barrier Lyapunov functionals are constructed to handle the unknown affine control gains ( g(\cdot ) ) with state constraints simultaneously. This removes the need on the knowledge of control gains for control design and avoids the conservative step of transforming original state constraints into new bounds on tracking errors. Neural networks (NNs) are used to approximate the unknown continuous packaged functions. To enhance the robustness, adapting parameters are developed to compensate the unknown bounds on NNs approximations and external disturbances. Design parameters-dependent feasibility conditions are formulated as sufficient conditions for the existence of feasible design parameters to guarantee the state constraints, and an offline constrained optimization step is proposed to obtain the optimal design parameters prior to the implementation of the proposed control. It is proved that the proposed control can guarantee the semiglobal uniform ultimate boundedness of all signals in closed-loop system, all states are ensured to remain in the predefined constrained state space, and tracking error converges to an adjustable neighborhood of the origin by choosing appropriate design parameters. Simulations are performed to validate the proposed control. [ABSTRACT FROM PUBLISHER]

In this paper, a fuzzy adaptive switched control approach is proposed for a class of uncertain nonholonomic chained systems with input nonsmooth constraint. In the control design, an auxiliary dynamic system is designed to address the input nonsmooth constraint, and an adaptive switched control strategy is constructed to overcome the uncontrollability problem associated withx0(t0) = 0. By using fuzzy logic systems to tackle unknown nonlinear functions, a fuzzy adaptive control approach is explored based on the adaptive backstepping technique. By constructing the combination approximation technique and using Young's inequality scaling technique, the number of the online learning parameters is reduced tonand the ‘explosion of complexity’ problem is avoid. It is proved that the proposed method can guarantee that all variables of the closed-loop system converge to a small neighbourhood of zero. Two simulation examples are provided to illustrate the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive tracking control of flexible joint robots (FJR) is presented. By providing a simple error modification term in the neural networks (NNs) based adaptive backstepping design procedure, it is shown that the L∞ performance of system tracking error can be achieved and some restrictions on FJR in stability analysis of previous works are also removed. Besides, the dynamic surface control technique (DSC) and the minimal learning algorithm (MLP) are used to reduce the design procedure and the computational burden. The application of this scheme to a single-link robot system shows the efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, adaptive neural tracking control is proposed for a robotic manipulator with uncertainties in both manipulator dynamics and joint actuator dynamics. The manipulator joints are subject to inequality constraints, i.e., the joint angles are required to remain in some compact sets. Integral barrier Lyapunov functionals (iBLFs) are employed to address the joint space constraints directly without performing an additional mapping to the error space. Neural networks (NNs) are utilised to compensate for the unknown robot dynamics and external force. Adapting parameters are developed to estimate the unknown bounds on NN approximations. By the Lyapunov synthesis, the proposed control can guarantee the semi-global uniform ultimate boundedness of the closed-loop system, and the practical tracking of joint reference trajectory is achieved without the violation of predefined joint space constraints. Simulation results are given to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper provides observer-based sampled-data and event-triggered boundary control strategies for a class of reaction–diffusion PDEs with collocated sensing and Robin actuation. Infinite-dimensional backstepping design is used as the underlying control approach. It is shown that the continuous-time output feedback boundary control applied in a sample-and-hold fashion ensures global closed-loop exponential stability, provided that the sampling period is sufficiently small. Further, robustness to perturbations of the sampling schedule is guaranteed. For the event-triggered implementation of the continuous-time controller, a dynamic triggering condition is utilized. The triggering condition determines the time instants at which the control input needs to be updated. Under the observer-based event-triggered boundary control, it is shown that there is a minimal dwell-time between two triggering instants independent of initial conditions. Further, the global exponential convergence of the closed-loop system to the equilibrium point is established. A simulation example is provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an impulsive adaptive observer is proposed for online estimates of a class of hybrid cascade systems with uncertain parameters. The hybrid cascade system is formed by an ordinary differential equation (ODE) coupled with a partial differential equation (PDE) with uncertain parameters. In the hybrid cascade system, the state of the connection point between the two subsystems cannot be directly available, which makes it difficult to obtain online estimates of the inaccessible states. To deal with the complex observation problem, an impulsive adaptive observer is designed using the backstepping approach and the extended Kalman observer. In addition, the convergence of the proposed observer is examined. The backstepping transformation plays a crucial role in the convergence proof. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]