Nonsingular fractional-order integral fast-terminal sliding mode control for underactuated shipboard cranes

Lack of actuators creates many challenges in controlling underactuated systems. Additional difficulty arises when underactuated systems are subject to actuator faults, parametric uncertainties, and disturbances. We develop an adaptive robust controller for such systems by combining various advanced techniques with many benefits. The core of the controller, which is based on nonsingular integral fast-terminal sliding mode, ensures high robustness and quick finite-time convergence, reduces chattering, and prevents singularity. Fault-tolerant control provides good fault compensation. Fractional derivatives make the control structure flexible because fractional orders are adjustable gains. Self-tuning control creates an adaption mechanism that endows the system an intelligent behavior. Two layers of the sliding mode that contain fractional derivative, terminal power, and definite integral ensure terminal Mittag–Leffer stability. We test the proposed approach on an underactuated floating crane through a simulation and an experiment. A comparison with other methods shows the superiority of our approach.     

Adaptive control for uncertain nonlinear time-delay systems in a lower-triangular form

In the presence of uncertain time-varying control coefficients, structuring parameter uncertainty and unknown state time delay, this paper proposes a continuous feedback control scheme for highly nonlinear systems without extra nonlinear growth restriction. An expansion of the backstepping method is presented based on dynamic gains and tuning functions. By Lyapunov–Krasovskii functionals, a delay-free controller is designed to regulate the original system states to zero with the other states being globally bounded.     

Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction

This paper deals with the problem of adaptive output feedback neural network controller design for a SISO non-affine nonlinear system. Since in practice all system states are not available in output measurement, an observer is designed to estimate these states. In comparison with the existing approaches, the current method does not require any information about the sign of control gain. In order to handle the unknown sign of the control direction, the Nussbaum-type function is utilized. In order to approximate the unknown nonlinear function, neural network is firstly exploited, and then to compensate the approximation error and external disturbance a robustifying term is employed. The proposed controller is designed based on strict-positive-real (SPR) Lyapunov stability theory to ensure the asymptotic stability of the closed-loop system. Finally, two simulation studies are presented to demonstrate the effectiveness of the developed scheme.     

Adaptive quantized tracking control for a class of uncertain nonlinear systems with guaranteed transient performance

In this paper, an adaptive quantized control method with guaranteed transient performance is presented for a class of uncertain nonlinear systems. By introducing the Nussbaum function technique, the difficulty caused by quantization is handled and a novel adaptive control scheme is designed. In comparing with the existing adaptive control scheme, the key advantages of the proposed control scheme are that the controller needs no information about the parameters of the quantizer and the stability of the closed-loop system and the transient performance are independent of the coarseness of the quantizer. Based on Lyapunov stability theory and Barbalat’s Lemma, it is proven that all the signals in the resulting closed-loop system are bounded and the tracking error converges to zero asymptotically with the prescribed performance bound at all times. Simulation results are presented to verify the effectiveness of the proposed control method.     

Adaptive unit-vector control of an uncertain heat diffusion process

This paper deals with the distributed tracking control of a heat process having uncertain diffusivity and subject to a distributed disturbance whose L₂ norm is bounded by a constant which is not known a priori. Under certain regularity assumptions on the disturbance and on the chosen reference profile, a distributed unit-vector control, with an adaptive magnitude, is designed which provides the asymptotic tracking of the reference. The logic governing the gain adaptation is gradient-based and monodirectional, i.e. the gain cannot decrease over time. Lyapunov arguments are invoked to support the convergence properties of the proposed scheme, whose performance are also investigated by means of computer simulations.     

Adaptive neural finite-time control for space circumnavigation mission with uncertain input constraints

This paper explores the design of an anti-saturation adaptive finite-time control strategy with the neural network (NN) technique for the space circumnavigation mission. Before executing the controller design, the analytical solutions of the desired angular velocity and its derivative of the active spacecraft are calculated. Since there are uncertain saturation constraints on control forces and moments in the actual propulsion system, an auxiliary system compensated by an adaptive NN is adopted. The modified auxiliary system no longer needs the precise output values of the actuators. Besides, the hyperbolic tangent function is introduced to design the weight update law for the NN compensator, so that the derivative of the weight estimator will not be amplified by the quadratic of states when the system states are large. It is proved that tracking errors of the system states can converge to a residual set of the origin in finite time. Simulation results show that the maximum amplitudes of the control signals are greatly reduced compared to the classical non-singular terminal sliding-mode control scheme, and that the neural-based compensator can significantly weaken the overshoot and chattering.     

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.     

Adaptive fuzzy tracking control for switched uncertain strict-feedback nonlinear systems

This paper concerns an adaptive fuzzy tracking control problem for a class of switched uncertain nonlinear systems in strict-feedback form via the modified backstepping technique. The unknown nonlinear functions are approximated by the generalized fuzzy hyperbolic model (GFHM). It is shown that if the designed parameters in the controller and adaptive laws are appropriately selected, then all closed-loop signals are bounded and the stability of the system can be kept under average dwell time methods. In the end, simulation studies are presented to illustrate the effectiveness of the proposed method.     

Fixed-time adaptive fuzzy control scheme with prescribed tracking accuracy for uncertain nonlinear hysteretic systems

When the Preisach operator, a commonly used hysteresis model, is coupled with uncertain unparametrizable nonlinear dynamics of systems, its tracking control problem in particular with the demands for prescribed tracking accuracy and finite convergence time is challenging, and has not yet been solved in the existing literature. In this study, we focus on the problem, and develop a fixed-time adaptive fuzzy control scheme as a solution to it, based upon a novel decomposition of the Preisach model, the design of a robust control framework, and the integration of a direct adaptive fuzzy control approach. With our scheme, it can be rigorously proved that the tracking error goes to a predefined interval around zero in a bounded convergence time, and all signals in the closed-loop system are bounded. Besides theoretical analysis, the obtained results are also confirmed by experimental tests based on a real-life piezoactuated positioner.     

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 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.     

Adaptive-observer-based formation tracking of networked uncertain underactuated surface vessels with connectivity preservation and collision avoidance

This paper investigates an adaptive output-feedback formation tracking problem for ensuring connectivity preservation and collision avoidance among networked uncertain underactuated surface vessels (USVs) with different communication ranges. An adaptive observer using neural networks is designed to estimate the velocity information of USVs where neural networks estimate unknown nonlinearities of USVs. Especially, contrary to the existing related work of USVs, a new state transformation technique for the adaptive observer design is presented to relax the condition requiring the boundedness of the yaw velocity of USVs. Then, the recursive tracker design strategy is established by using a unified error function for connectivity-preserving and collision-avoiding formation tracking, without employing any potential functions. The proposed formation tracker does not require additional neural networks to estimate unknown nonlinearities derived from the tracker design procedure. The proposed theoretical result is proved in the sense of Lyapunov.     

Adaptive neural network dynamic surface control of uncertain strict-feedback nonlinear systems with unknown control direction and unknown actuator fault

In this paper, the tracking control problem of a class of uncertain strict-feedback nonlinear systems with unknown control direction and unknown actuator fault is studied. By using the neural network control approach and dynamic surface control technique, an adaptive neural network dynamic surface control law is designed. Based on the neural network approximator, the uncertain nonlinear dynamics are approximated. Using the dynamic surface control technique, the complexity explosion problems in the design of virtual control laws and adaptive updating laws can be overcome. Moreover, to solve the unknown control direction and unknown actuator fault problems, a type of Nussbaum gain function is incorporated into the recursive design of dynamic surface control. Based on the designed adaptive control law, it can be confirmed that all of the signals in the closed-loop system are semi-global bounded, and the convergence of the tracking error to the specified small neighborhood of the origin could be ensured by adjusting the designing parameters. Finally, two examples are provided to demonstrate the effectiveness of the proposed adaptive control law.     

Adaptive single input sliding mode control for hybrid-synchronization of uncertain hyperchaotic Lu systems

This paper addresses the problem of hybrid synchronization for hyperchaotic Lu systems without and with uncertain parameters via a single input sliding mode controller (SMC). Based on the SMC approach, the proposed controller not only minimizes the influence of uncertainty but also enhances the robustness of the system. The uncertain parameters are estimated by using new adaptation laws which ensure the uncertain parameters convergence to their original value. A hybrid synchronization scheme is useful to maintain the vastly secured and secrecy in the area of secure communication by using the control theory approach. The proposed hybrid synchronization results are providing a superiority of forming a chaotic secure communication scheme. Finally, a numerical example is provided to demonstrate the validity of the theoretical analysis.     

Networked load frequency control of multi-area uncertain power systems via adaptive event-triggered communication scheme

Load frequency control of power systems is a very important approach to keep stability and security. Unfortunately, the traditional load frequency control is not effective because of the introduction of communication networks in multi-area power systems. In order to overcome this difficulty, sampling-based load frequency control for multi-area power systems is studied via an event-triggered detector. Unlike published works, an adaptive law for event-triggered scheme is given. Since multi-area power systems with event-triggered scheme are hybrid systems, there are a lot of challenges for analysing load frequency control problem. Some lemmas and a new Lyapunov function are developed to overcome these challenges. The obtained stability and stabilization criteria can provide a tradeoff to balance the required communication resources and the desired control performance. Numerical examples verify effectiveness of the obtained results.     

Adaptive fuzzy fault-tolerant decentralized control for uncertain nonlinear large-scale systems based on dynamic surface control technique

In this paper, an adaptive fuzzy decentralized control method is proposed for accommodating actuator faults for a class of uncertain nonlinear large-scale systems. The considered faults are modeled as both loss of effectiveness and lock-in-place. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, the novel adaptive fuzzy faults-tolerant decentralized controllers are constructed by combining the backstepping technique and the dynamic surface control (DSC) approach. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop systems are bounded and the tracking errors converge to a small neighborhood of zero. Simulation results are provided to show the effectiveness of the control approach.     

Adaptive synchronization of uncertain chaotic systems with adaptive scaling function

The problem of adaptive synchronization for the uncertain chaotic systems with adaptive scaling function is investigated in this paper. In comparison to those of the existing scaling function synchronization, such as the presetting scaling function, the aim of this paper is focused not only on the scaling function but also on the identification of parameters of the chaotic system. Finally, to illustrate the implementation of the proposed method, some numerical simulations are given.     

Multi-channel transmission scheduling with hopping scheme under uncertain channel states

This paper investigates the multi-channel transmission scheduling problem for remote state estimation based on a hopping scheme in cyber-physical systems. The smart sensor sends multiple subpackets over different orthogonal channels to the remote end simultaneously. Owing to the randomness and vulnerability of transmission environments, the uncertain multi-channel states are considered in this paper, which relaxes the assumption of existing deterministic models. The objective is to find an appropriate hopping scheme that minimizes the remote estimation error covariance. First, the multi-channel selection problem is modeled as a multi-arm bandits (MAB) matrix via taking the packet receiving probability as the gain. From the perspective of strategy and channel, two exponential-weight online learning algorithms are designed with the assistance of transmission energy switching policy. Then, based on Bernstein’s inequality for martingales and mini-batching loop, the upper bounds of algorithms’ regret values are analyzed under stochastic and adversarial channel states, respectively. Further, the estimator expression in iterative form and a sufficient condition for the error covariance to be bounded are derived. Finally, an example of unmanned vehicle moving demonstrates all the theoretical results.     

Adaptive neural network control for nonstrict-feedback uncertain nonlinear systems with input delay and asymmetric time-varying state constraints

This paper is devoted to adaptive neural network control issue for a class of nonstrict-feedback uncertain systems with input delay and asymmetric time-varying state constraints. State-related external disturbances are involved into the system, and the upper bounds of disturbances are assumed as functions of state variables instead of constants. Additionally, during the approximations of unknown functions by neural networks, the online computation burdens are declined sharply, since the norms of neural network weight vectors are only estimated. In the process of dealing with input delay, an auxiliary function is applied such that the conditions for time delay are more general than the ones in existing literature. A novel adaptive neural network controller is designed by constructing the asymmetric barrier Lyapunov function, which guarantees that the output of system has a good tracking performance and the state variables never violate the asymmetric time-varying constraints. Finally, numerical simulations are presented to verify the proposed adaptive control scheme.