Adaptive Neural Event-Triggered Control for Discrete-Time Strict-Feedback Nonlinear Systems.

In this paper, the design of a neural network (NN) based adaptive model-based event-triggered control of an uncertain single input single output (SISO) nonlinear discrete time system in affine form is presented. The controller uses an adaptive estimator consisting of a single-layer NN not only to approximate the internal dynamics of an affine nonlinear discrete-time system but also to provide an estimate of the state vector during inter event interval. The NN weights of the adaptive NN estimator are tuned in a aperiodic manner at the event trigger instants unlike periodic updates in standard adaptive neural network (NN) control. A dead zone operator is used to reset the event trigger error to zero as long as the system states continue to remain in a bounded region due to NN reconstruction errors. Lyapunov method is used to derive the event trigger condition, prove uniform ultimate boundedness (UUB) of the NN weight estimation error and system states.

In this paper, output feedback direct adaptive robust NN control is investigated for a class of nonlinear discrete-time systems in strict-feedback form. To construct output feedback control, the original strict-feedback system is transformed into a cascade form, which the output feedback of the nonlinear discrete-time system can be carried out. Then with employment of the inputs and outputs, the output feedback direct adaptive robust NN control is developed. The HONNs is exploited to approximate unknown function, and a stable adaptive NN controller is synthesized. The proposed algorithm improves the rubostness of the discrete-time nonlinear systems. It is proven that all the signals in closed-loop system are uniformly ultimately bounded (UUB). A simulation example is presented to illustrate the effectiveness of the proposed algorithm.Keywordsoutput feedbackrubostnessdirect adaptive NN controldiscrete-time nonlinear system

This article studies the fuzzy adaptive event-triggered (ET) consensus control issue of nonlinear multiagent systems (NMASs) under jointly connected switching networks. Since the leader and its high-order derivatives are unknown under jointly connected switching networks, a novel distributed ET reference generator equipped with an ET mechanism is constructed to estimate them. Meanwhile, the continuous information transmission among agents is avoided and the network channel utilization is optimized. Subsequently, fuzzy logic systems (FLSs) are employed to approximate unknown dynamics, and a fuzzy adaptive ET consensus control algorithm only using intermittent communication is designed by backstepping control methodology. It is demonstrated that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), with the tracking errors converging to a small neighborhood around zero. Finally, we apply the developed fuzzy adaptive ET consensus control algorithm to unmanned surface vehicles (USVs), and the simulation results verify the effectiveness of the proposed ET consensus control algorithm.

In this paper, we focus on the design of output feedback controller for a class of discrete-time nonlinear systems combined with event-triggered control approach. The designed event-triggered threshold is related to the output signal, which further reduces the tracking error. Besides, by co-designing backstepping control method and the event-triggered strategy, the corresponding assumptions for input-to-state stable (ISS) with respect to the measurement errors can be removed. The stability analysis result shows that all signals in the closed-loop system are bounded and the tracking error is bounded by a small constant depending on event-triggered threshold parameter. Simulation results show the performance and effectiveness of the designed controller.

This paper presents a neural network adaptive control scheme for the nonlinear systems in strict-feedback form, where the unstructured uncertainties are assumed to be unknown, though they still satisfy certain growth conditions characterized by 'bounding functions' composed of known functions multiplied by unknown constants. All adaptation laws for these unknown bounds are derived from Lyapunov based method as well as the adaptation laws for the networks' weights estimations. In addition, the unknown control gain functions are not approximated directly by neural networks. Therefore, we can avoid the possible controller singularity problems. Under a certain relaxed assumptions on the control gain functions, proposed control scheme can guarantee that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Simulation studies are included to illustrate the effectiveness of the proposed scheme, and some practical features of the control laws are also discussed.

In this paper, adaptive neural network (NN) control is investigated for a class of multiinput and multioutput (MIMO) nonlinear systems with unknown bounded disturbances in discrete-time domain. The MIMO system under study consists of several subsystems with each subsystem in strict feedback form. The inputs of the MIMO system are in triangular form. First, through a coordinate transformation, the MIMO system is transformed into a sequential decrease cascade form (SDCF). Then, by using high-order neural networks (HONN) as emulators of the desired controls, an effective neural network control scheme with adaptation laws is developed. Through embedded backstepping, stability of the closed-loop system is proved based on Lyapunov synthesis. The output tracking errors are guaranteed to converge to a residue whose size is adjustable. Simulation results show the effectiveness of the proposed control scheme.

Adaptive neural dynamic surface control for servo systems with unknown dead-zone

NN-adaptive predictive control for a class of discrete-time nonlinear systems with input-delay

This article is concerned with the exponential mean-square stabilization problem for a class of discrete-time strict-feedback nonlinear systems subject to multiplicative noises. The state-dependent multiplicative noise is assumed to occur randomly based on a stochastic variable obeying the Gaussian white distribution. To tackle the difficulties caused by the multiplicative noise, a novel backstepping-based control framework is developed to design both the virtual control laws and the actual control law for the original nonlinear system, and such a framework is fundamentally different from the traditional n-step predictor strategy. The proposed design scheme provides an effective way in establishing the relationship between the system states and the controlled errors, by which a noise-intensity-dependant stability condition is derived to ensure that the closed-loop system is exponentially mean-square stable for exactly known systems. To further cope with nonlinear modeling uncertainties, the radial basis function neural network (NN) is employed as a function approximator. In virtue of the proposed backstepping-based control framework, the ideal controller is characterized as a function of all system states, which is independent of the virtual control laws. Therefore, only one NN is employed in the final step of the backstepping procedure and, subsequently, a novel adaptive neural controller (with modified weight updating laws) is presented to ensure that both the neural weight estimates and the system states are uniformly bounded in the mean-square sense under certain stability conditions. The control performance of the proposed scheme is illustrated through simulation results.

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

A unified barrier function-based trajectory tracking control for hovercraft with asymmetric dynamic safety constraints

In this article, a model-free-adaptive-control-based (MFAC-based) event-triggered (ET) consensus output tracking problem for multiagent systems (MASs) is investigated. The dynamic models of agents are unknown, and only a subset of agents can acquire the reference trajectory. The consensus tracking algorithm is designed by the real-time input/output data and pseudo-partial-derivative (PPD), which is an important parameter of MFAC approach. An output observer is built to design the centralized ET mechanism. Then, the boundedness analysis that the tracking error is uniformly ultimately bounded (UUB) is given. Finally, a simulation experiment is provided to verify the feasibility of the ET consensus output tracking strategy for MASs.

A robust adaptive neural network control approach is presented for a class of uncertain strict-feedback nonlinear systems with unknown dead-zone and disturbances. In the controller design, a single neural network is used to approximate the lumped unknown part of the system. By the approach, only one actual control law is implemented at the last step, and all the virtual control laws at intermediate steps need not be implemented actually. Thus, the designed controller is simpler in structure. Furthermore, the actual control law and one adaptive law can be given directly for the class of systems under study. The result of stability analysis shows that the proposed scheme can guarantee the uniform ultimate boundedness of all the closed-loop system signals, and the steady-state tracking error can be made arbitrarily small by appropriately choosing control parameters. A simulation example is given to demonstrate the effectiveness and merits of the proposed approach.

Discrete time immersion and invariance adaptive control via partial state feedback for systems in block strict feedback form