Adaptive Asymptotic Tracking Control for High-Order Nonlinear Systems With Prescribed Transient Performance

Adaptive asymptotic tracking control design for high-order uncertain nonlinear systems

Nonsingular recursive-structure sliding mode control for high-order nonlinear systems and an application in a wheeled mobile robot

This article studies full-state constrained control for high-order nonlinear systems with unknown multiple time-varying powers and serious parameter unknowns. Due to the simultaneous existence of unknown powers and full-state constraints, we construct a log-type quadratic barrier Lyapunov function (BLF) rather than a quadratic Lyapunov function. By skillfully combining the log-type BLF, adding a power integrator technique and adaptive technique, an adaptive state feedback controller is developed. Under feasibility conditions, which are provided as sufficient conditions for the existence of proposed full-state constrained control, it is proved that all the signals of the closed-loop system are bounded, original system states converge to zero and full-state constraints are not violated.

Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non-symmetric dead-zone nonlinearities

This article discusses the adaptive fuzzy asymptotic tracking control for high-order nonlinear time-delay systems with full-state constraints. Fuzzy-logic systems and a separation principle are utilized to relax growth assumptions imposed on unknown nonlinearities. The adverse effect caused by unknown time delays is eliminated by choosing appropriate Lyapunov-Krasovskii functionals. By integrating nonlinear-transformed functions with a key coordinate transformation into the control design and constructing a specific compact set on the initial values of system states, the desired trajectory and parameter estimates, it is rigorously proved that all closed-loop signals are semiglobally bounded, the fuzzy approximation is valid, the full-state constraints are not violated without feasibility conditions on virtual controllers, and asymptotic tracking is achieved. The effectiveness and advantages of this control scheme are confirmed by two examples including a single-link robotic system.

In recent decades, controller design has been attracted a great deal of interest of many researchers in control community which can make the job of many other researchers in different area of research easier. The present study aims to design a finite time adaptive control input for a high-order nonlinear system in presence of a variety of mismatched uncertainties and external disturbances. Adaptive terminal sliding mode control (ATSMC) method is used to design robust controller in a finite time. Also, adaptive concept is employed in ATSMC to estimate the upper bound of mismatched uncertainties and external disturbances and their estimations are used in control input. The finite time stability proof is performed by defining a proper candidate Lyapunov function. Numerical simulation results are carried out in Simulink/MATLAB to reveal the correctness of proposed design in this research. Finally, the performance criterion, integral of the square value (ISV), is defined to provide a numerical comparison between the proposed adaptive controller and non-adaptive controller.

Adaptive fuzzy finite-time tracking control of nonlinear systems with unmodeled dynamics

This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples.

In this article, the problem of event‐triggered adaptive asymptotic tracking control (ATC) for stochastic nonlinear systems with unknown control directions (UCDs) and full state constraints is concerned. It must be said that the controller design and system analysis is more complex and difficult since the existence of stochastic disturbances, UCDs and full state constraints simultaneously. By introducing the lower bound of the UCDs into the barrier Lyapunov functions, an event‐triggered adaptive MTN ATC scheme is proposed based on the boundary estimation method and a new event‐triggered control (ETC) strategy, which can achieve satisfactory asymptotic tracking performance and control performance of the system, while reduce the occupation of network resources. The simulation results not only verify the effectiveness of the proposed control scheme, but also present different tracking performances between three ETC strategies for comparison, further confirming the superiority of the proposed ETC strategy in achieving asymptotic tracking performance.

This paper proposes an adaptive fuzzy logic tracking control for unknown nonlinear systems having input time delay. In the controller design, a filtered tracking error to facilitate handling of the time delay and fuzzy approximation of nonlinear function are introduced. Lyapunov stability analysis shows that the designed tracking control yields bounded signals of the closed-loop system. Two simulation examples are provided to prove the effectiveness of the proposed controller in achieving tracking with bounded control signals.

Event-triggered adaptive optimal tracking control for nonlinear stochastic systems with dynamic state constraints

In this paper, an event-based adaptive fuzzy tracking control strategy for a class of uncertain nonlinear systems with limited control input and its rate of change is proposed. The unknown nonlinear function of the considered system is approximated by a fuzzy logic system (FLS). Furthermore, an event-triggered control method is developed to save the computing resources, in which the controller parameters are adaptively adjusted by a fuzzy controller. Moreover, it is proved by designing the Lyapunov function that the event-based controller can ensure that all signals of the controlled system are bounded. In addition, the tracking error can converge to a preset domain. Meanwhile, two practical simulations are given to demonstrate the effectiveness of the proposed method.

Due to the difficulty encountered in dealing with unstructured system dynamics with unmeasured system state variables, this paper presents a novel observer-based neural network finite-time output control strategy for general high-order nonlinear systems (HNSs). The suggested technique is performed based on the backstepping-like control (BSC) scheme with a hybrid nonlinear disturbance-state observer and norm estimation-based radial basis function neural network (RBFNN). This helps not only reduce the number of estimated parameters but also relax the restriction of using inequality when exploiting the norm estimation concept in a conventional way; thus, retaining the same properties of the original system. Therefore, an observer-based finite-time output feedback control is established to deal with the unstructured dynamical behaviors and satisfying the output tracking regulation with the semi-global practically finite-time stability (SGPFS) guaranteed for the closed-loop system. The effectiveness and workability of the proposed algorithm is verified by a numerical simulation on a specific practical application.

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.

In this brief, a novel prescribed-time output feedback control strategy is developed for high-order nonlinear systems. To begin with, a new coordinate transformation method is proposed, under which a time-varying gain that goes to infinity towards the terminal time and a constant scaling gain are simultaneously introduced into the system. Then, the reduced-order observer and output feedback controller are successfully constructed by using the homogeneous domination approach. Unlike many existing results, our proposed control strategy can ensure that the convergence time is independent of both the initial conditions and design parameters, and the convergence rate of the system is adjustable. Moreover, the design process is simplified and the control scheme can operate even after the prescribed-time. Finally, a simulation example is used to verify the validity of the proposed control strategy.