Approximation-based decentralized output-feedback control for uncertain stochastic interconnected nonlinear time-delay systems with input delay and asymmetric input saturation

This paper proposes an adaptive observer-based neural controller for a class of uncertain large-scale stochastic nonlinear systems with actuator delay and time-delay nonlinear interactions, where drift and diffusion terms contain all state variables of their own subsystem. First, a state observer is established for estimating the unmeasured states, and a predictor-like term is utilized to transform the input delayed system into the delay-free system. Second, novel appropriate Lyapunov–Krasovskii functionals are used to compensate the time-delay terms, and neural networks are employed to approximate unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is driven to a small neighborhood of the origin. The simulation results are presented to further show the effectiveness of the proposed approach.     

Adaptive neural dynamic surface control for full state constrained stochastic nonlinear systems with unmodeled dynamics

This paper solves the problem of adaptive neural dynamic surface control (DSC) for a class of full state constrained stochastic nonlinear systems with unmodeled dynamics. The concept of the state constraints in probability is first proposed and applied to the stability analysis of the system. The full state constrained stochastic nonlinear system is transformed to the system without state constraints through a nonlinear mapping. The unmodeled dynamics is dealt with by introducing a dynamic signal and the adaptive neural dynamic surface control method is explored for the transformed system. It is proved that all signals of the closed-loop system are bounded in probability and the error signals are semi-globally uniformly ultimately bounded(SGUUB) in mean square or the sense of four-moment. At the same time, the full state constraints are not violated in probability. The validity of the proposed control scheme is demonstrated through the simulation examples.     

Output feedback control of electro-hydraulic servo actuators with matched and mismatched disturbances rejection

In this paper, two output feedback controllers are proposed for motion control of double-rod electro-hydraulic servo actuators with matched and mismatched disturbances rejection. All of them employ an linear extended state observer (LESO) to achieve real-time estimates of the unmeasured system states and matched disturbance, and a nonlinear disturbance observer (NDO) to estimate the largely unknown mismatched disturbance at the same time. Thus, the disturbances are compensated via their online estimates in a feedforward way when implementing the resulting control algorithms, respectively. Furthermore, a continuously differentiable friction model is employed to compensate the majority of nonlinear friction existing in the system and reduce the burden of the NDO. Specially, one of the proposed control schemes utilizes model-based compensation terms depending on the desired trajectory to be tracked instead of the estimated system states. By doing this, online computation burden can be reduced. The stability of the whole closed-loop system under each control scheme is guaranteed by theoretical analysis. Moreover, the applicability of each control scheme are validated by experiments in different working conditions.     

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.     

Output feedback control for stochastic nonlinear time delay systems using dynamic gain technique

This paper investigates the output feedback control for a class of stochastic nonlinear time delay systems based on dynamic gain technique. The nonlinear terms of the stochastic system satisfy linear growth condition on unmeasured state variables with the output dependent incremental rate, which makes the studied time delay stochastic system more general than the exiting results. Firstly, the full order dynamic gain observer is constructed. Then, the linear-like controller is designed without using recursive design method. Next, the stability analysis is given and a useful corollary is obtained. Finally, a simulation is given to illustrate the effectiveness of the proposed method.     

Command filter based adaptive DSC of uncertain stochastic nonlinear systems with input delay and state constraints

In this paper, a command filter based dynamic surface control (DSC) is developed for stochastic nonlinear systems with input delay, stochastic unmodeled dynamics and full state constraints. An error compensation system is designed to constrain the filtering error caused by the first-order filter in the traditional dynamic surface design. On this basis, the stability proof of DSC for stochastic nonlinear systems based on command filter is proposed. The definition of state constraints in probability is presented, and the problem of stochastic full state constraints is solved by constructing a group of coordinate transformations with nonlinear mappings. The Pade approximation is adopted to deal with input delay. The stochastic unmodeled dynamics is considered, which is processed by utilizing the property of stochastic input-to-state stability (SISS) and changing supply function. All the signals of the system are proved to be semi-globally uniformly ultimately bounded (SGUUB) in probability, and the full state constraints are not violated. The two simulation examples also verify the effectiveness of the proposed adaptive DSC scheme.     

Disturbance observer-based robust missile autopilot design with full-state constraints via adaptive dynamic programming

This paper aims to develop a robust optimal control method for longitudinal dynamics of missile systems with full-state constraints suffering from mismatched disturbances by using adaptive dynamic programming (ADP) technique. First, the constrained states are mapped by smooth functions, thus, the considered systems become nonlinear systems without state constraints subject to unknown approximation error. In order to estimate the unknown disturbances, a nonlinear disturbance observer (NDO) is designed. Based on the output of disturbance observer, an integral sliding mode controller (ISMC) is derived to counteract the effects of disturbances and unknown approximation error, thus ensuring the stability of nonlinear systems. Subsequently, the ADP technique is utilized to learn an adaptive optimal controller for the nominal systems, in which a critic network is constructed with a novel weight update law. By utilizing the Lyapunov's method, the stability of the closed-loop system and the convergence of the estimation weight for critic network are guaranteed. Finally, the feasibility and effectiveness of the proposed controller are demonstrated by using longitudinal dynamics of a missile.     

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.     

Consensus tracking control for nonlinear multiagent systems with asymmetric state constraints and input delays

In this paper, the consensus tracking problem is studied for a group of nonlinear heterogeneous multiagent systems with asymmetric state constraints and input delays. Different from the existing works, both input delays and asymmetric state constraints are assumed to be nonuniform and time-varying. By introducing a nonlinear mapping to handle the problem caused by state constraints, not only the feasibility condition is removed, but also the restriction on the constraint boundary functions is relaxed. The time-varying input delays are compensated by developing an auxiliary system. Furthermore, by utilizing the dynamic surface control method, neural network technology and the designed finite-time observer, the distributed adaptive control scheme is developed, which can achieve the synchronization between the followers’ output and the leader without the violation of full-state constraints. Finally, a numerical simulation is provided to verify the effectiveness of the proposed control protocol.     

Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization

This paper proposes an observer-based fuzzy adaptive output feedback control scheme for a class of uncertain single-input and single-output (SISO) nonlinear stochastic systems with quantized input signals and arbitrary switchings. The SISO system under consideration contains completely unknown nonlinear functions, unmeasured system states and quantized input signals quantized by a hysteretic quantizer. By adopting a new nonlinear disposal of the quantized input, the relationship between the control input and the quantized input is established. The hysteretic quantizer that we take can effectively avoid the chattering phenomena. Furthermore, the introduction of a linear observer makes the estimation of the states possible. Based on the universal approximation ability of the fuzzy logic systems (FLSs) and backstepping recursive design with the common stochastic Lyapunov function approach, a quantized output feedback control scheme is constructed, where the dynamic surface control (DSC) is explored to alleviate the computation burden. The proposed control scheme cannot only guarantee the boundedness of signals but also make the output of the system converge to a small neighborhood of the origin. The simulation results are exhibited to demonstrate the validity of the control scheme.     

Global sampled-data output feedback stabilization for a class of stochastic nonlinear systems with time-varying delay

This paper studies the global sampled-data output feedback stabilization problem for a class of stochastic nonlinear systems. The considered system is in non-strict feedback form with unknown time-varying delay. A state observer is introduced to estimate the unmeasured states. With the help of the backstepping method, a linear sampled-data output feedback controller is constructed. By choosing an appropriate Lyapunov–Krasoviskii functional and an allowable sampling period, it is shown that the stochastic system can be globally asymptotically stabilized in the mean square sense under the developed control scheme. Finally, two examples are presented to verify the effectiveness of the designed control scheme.     

Barrier Lyapunov function-based decentralized adaptive neural control for uncertain high-order stochastic nonlinear interconnected systems with output constraints

Decentralized adaptive neural backstepping control scheme is developed for uncertain high-order stochastic nonlinear systems with unknown interconnected nonlinearity and output constraints. For the control of high-order nonlinear interconnected systems, it is assumed that nonlinear system functions are unknown. It is for the first time to control stochastic nonlinear high-order systems with output constraints. Firstly, by constructing barrier Lyapunov functions, output constraints are handled. Secondly, at each recursive step, only one adaptive parameter is updated to overcome over-parameterization problems, and RBF neural networks are used to identify unknown nonlinear functions so that the difficulties caused by completely unknown system functions and stochastic disturbances are tackled. Finally, based on the Lyapunov stability method, the decentralized adaptive control scheme via neural networks approximator is proposed, ultimately reducing the number of learning parameters. It is shown that the designed controller can guarantee all the signals of the resulting closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB), and the tracking errors for each subsystem are driven to a small neighborhood of zero. The simulation studies are performed to verify the effectiveness of the proposed control strategy.     

Reduced-order K-filters-based event-triggered adaptive command filtered tracking control for stochastic constrained nonlinear systems

To ensure better performance and simultaneously save resources, an event-triggered adaptive command filtered dynamic surface control (ACFDSC) method for uncertain stochastic nonstrict-feedback nonlinear systems with dynamic output constraints and prescribed performance is designed in this article. Firstly, with the help of reduced-order K-filters, linearly parameterized neural networks and specific coordinate transformation technique, the unmeasurable states, nonlinearities, two types of unmodeled dynamics and output constraints are dealt with respectively. Then, an event-triggered ACFDSC strategy is proposed to ensure that the tracking error reaches a specific bound within a finite time. By introducing the compensated signal into the complete Lyapunov function, and with the assistance of the compact set defined in the stability analysis, all signals are strictly demonstrated to be semi-globally uniformly ultimately bounded. The simulation results verify the effectiveness of the proposed method.     

The composite-disturbance-observer based stochastic model predictive control for spacecrafts under multi-source disturbances

In this paper, the attitude control problem of the spacecraft system under input/state constraints and multi-source disturbances is investigated. A novel estimation method, composite-disturbance-observer (CDO), is proposed to provide an estimate for both modeled and unmodeled disturbances in an online manner. Based on the estimates provided by the CDO, the composite stochastic model predictive control (C-SMPC) scheme is designed for attitude control. The recursive feasibility of the C-SMPC method is guaranteed by reformulating the state and input constraints. Furthermore, the sufficient conditions are established to guarantee the stability of the overall closed-loop system. Finally, the simulation on the attitude control of the spacecraft is conducted to verify the effectiveness of the proposed method.     

Distributed observer-based consensus tracking for nonlinear MASs with nonuniform input delays and disturbances

In this paper, we investigate the consensus tracking problem of nonlinear MASs with nonuniform time-varying input delays and external disturbances. For each follower, the composited disturbance observer and the state observer are employed to estimate bounded composited disturbances and unmeasured states, and a distributed observer based on output-feedback is proposed to approximate the leader’s states approachably. Sequentially, the consensus tracking control is converted into a stability control problem for the nonlinear MASs with nonuniform time-varying input delays. Subsequently, a distributed controller based on the truncated prediction approach is presented, which only depends on the boundary value of time-varying input delays. The distributed controller can render each follower synchronically stable via the Lyapunov stability theory. Finally, a group of single-link manipulators is used as an example to verify the effectiveness of the theoretical results.     

Event-triggered adaptive NN control for MIMO switched nonlinear systems with non-ISpS unmodeled dynamics

This paper investigates the problem of event-triggered adaptive neural network (NN) control for multi-input multi-output (MIMO) switched nonlinear systems with output and state constraints and non-input-to-state practically stable (ISpS) unmodeled dynamics. A nonlinear mapping is firstly utilized to deal with output and state constraints. Also, by developing a new switching signal with persistent dwell-time (PDT) and a switching dependent dynamic signal, the difficulty caused by some non-ISpS unmodeled dynamics is overcome. Then, a type of switching event-triggering mechanisms (ETMs) and event-triggered adaptive NN controllers of subsystems are designed, which handle the issue of asynchronous switching without requiring any known restriction on maximum asynchronous time. A piecewise constant introduced into this ETM effectively ensures a strict positive lower bound of inter-event times. Zeno behavior is thus ruled out. Finally, by proposing a novel class of switching signals with reset PDT, it is ensured that all output and state constrains are never violated and all signals of the switched closed-loop system are semi-global uniform ultimate boundedness (SGUUB). A two inverted pendulum system and a numerical example are provided for illustrating the applicability and validity of the proposed method.     

H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance

Finite-time stability concerns the boundness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to H_∞ finite-time boundness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundness, the state feedback controller is designed to H_∞ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.     

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.     

Fraction dynamic-surface-based adaptive neural finite-time control for stochastic nonlinear systems subject to unknown control directions,time-varying input delay and state delay

In this paper, an adaptive neural finite-time tracking control is studied for a category of stochastic nonlinearly parameterized systems with multiple unknown control directions, time-varying input delay, and time-varying state delay. To this end, a novel criterion of semi-globally finite-time stability in probability (SGFSP) is proposed, in the sense of Lyapunov, for stochastic nonlinear systems with multiple unknown control directions. Secondly, a novel auxiliary system with finite-time convergence is presented to cope with the time-varying input delay, the appropriate Lyapunov Krasovskii functionals are utilized to compensate for the time-varying state delay, Nussbaum functions are exploited to identify multiple unknown control directions, and the neural networks (NNs) are applied to approximate the unknown functions of nonlinear parameters. Thirdly, the fraction dynamic surface control (FDSC) technique is embedded in the process of designing the controller, which not only the “explosion of complexity” problems are successfully avoided in traditional backstepping methods but also the command filter convergence can be obtained within a finite time to lead greatly improved for the response speed of command filter. Meanwhile, the error compensation mechanism is established to eliminate the errors of the command filter. Then, based on the proposed novel criterion, all closed-loop signals of the considered systems are SGPFS under the designed controller, and the tracking error can drive to a small neighborhood of the origin in a finite time. In the end, three simulation examples are applied to demonstrate the validity of the control method.     

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.