Adaptive fuzzy approach for a class of uncertain nonlinear systems in strict-feedback form

Adaptive fuzzy control is proposed for a class of affine nonlinear systems in strict-feedback form with unknown nonlinearities. The unknown nonlinearities include two types of nonlinear functions: one satisfies the "triangularity condition" and can be directly approximated by fuzzy logic system, while the other is assumed to be partially known and consists of parametric uncertainties. Takagi-Sugeno type fuzzy approximators are used to approximate unknown system nonlinearities and the design procedure is a combination of adaptive backstepping and generalized small gain design techniques. It is proved that the proposed adaptive control scheme can guarantee the uniformly ultimately bounded (UBB) stability of the closed-loop systems. Simulation studies are shown to illustrate the effectiveness of the proposed approach.     

Finite-time stabilization for a class of stochastic nonlinear systems via output feedback

This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.     

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies.     

Global adaptive control for uncertain nonaffine nonlinear hysteretic systems

In this paper, the global output tracking is investigated for a class of uncertain nonlinear hysteretic systems with nonaffine structures. By combining the solution properties of the hysteresis model with the novel backstepping approach, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The proposed control scheme is further modified to tackle the bounded disturbances by adaptively estimating their bounds. It is rigorously proven that the designed adaptive controllers can guarantee global stability of the closed-loop system. Two numerical examples are provided to show the effectiveness of the proposed control schemes.     

Adaptive control for a class of MIMO nonlinear time delay systems against time varying actuator failures

This paper investigates an adaptive controller for a class of Multi Input Multi Output (MIMO) nonlinear systems with unknown parameters, bounded time delays and in the presence of unknown time varying actuator failures. The type of considered actuator failure is one in which some inputs may be stuck at some time varying values where the values, times and patterns of the failures are unknown. The proposed approach is constructed based on a backstepping design method. The boundedness of all the closed-loop signals is guaranteed and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark and a chemical reactor system. The simulation results show the effectiveness of the proposed method.     

Global adaptive output feedback control for a class of nonlinear time-delay systems

This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.     

A new discrete-time robust adaptive time-delay control for a class of uncertain nonlinear strict-feedback systems using sliding mode

This paper presents a new discrete-time adaptive second-order sliding mode control with time delay estimation (TDE) for a class of uncertain nonlinear time-varying strict-feedback systems. The existing researches on time delay control (TDC) are conventionally established based on a stability criterion that is subject to the infinitesimal time delay assumption. Recently, this criterion was rejected and a new criterion was proposed for the development of a controller for systems with fully known dynamics. In this study, this approach is extended to uncertain systems. Specifically, a new criterion is developed for the stability of the TDE-error within an adaptive robust controller design without the infinitesimal time delay assumption. With the proposed adaptive robust control, there is no need for determination of uncertainties upper-bounds. Simulation results illustrate the efficacy of the proposed controller.     

Fault diagnosis for a class of nonlinear systems via ESO

In this paper, a novel fault detection and identification (FDI) scheme for a class of nonlinear systems is presented. First of all, an augment system is constructed by making the unknown system faults as an extended system state. Then based on the ESO theory, a novel fault diagnosis filter is constructed to diagnose the nonlinear system faults. An extension to a class of nonlinear uncertain systems is then made. An outstanding feature of this scheme is that it can simultaneously detect and identify the shape and magnitude of the system faults in real time without training the network compared with the neural network-based FDI schemes. Finally, simulation examples are given to illustrate the feasibility and effectiveness of the proposed approach.     

Adaptive control of uncertain continuously stirred tank reactors with unknown actuator nonlinearities

Adaptive nonlinear control is investigated for continuously stirred tank reactor (CSTR) systems using neural networks. The CSTR plant under study belongs to a class of nonaffine nonlinear systems, and contains an unknown parameter that enters the model nonlinearly. Using adaptive backstepping and neural network (NN) approximation techniques, an alternative adaptive NN controller is developed that achieves asymptotic output tracking control. A novel integral-type Lyapunov function, which includes both system states and control input as its arguments, is constructed to solve the difficulty associated with the nonaffine control problem. Numerical simulation is performed to show the feasibility of the proposed approach for chemical process control.     

Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input

Based on the universal approximation property of the fuzzy-neural networks, an adaptive fuzzy-neural observer design algorithm is studied for a class of nonlinear SISO systems with both a completely unknown function and an unknown dead-zone input. The fuzzy-neural networks are used to approximate the unknown nonlinear function. Because it is assumed that the system states are unmeasured, an observer needs to be designed to estimate those unmeasured states. In the previous works with the observer design based on the universal approximator, when the dead-zone input appears it is ignored and the stability of the closed-loop system will be affected. In this paper, the proposed algorithm overcomes the affections of dead-zone input for the stability of the systems. Moreover, the dead-zone parameters are assumed to be unknown and will be adjusted adaptively as well as the sign function being introduced to compensate the dead-zone. With the aid of the Lyapunov analysis method, the stability of the closed-loop system is proven. A simulation example is provided to illustrate the feasibility of the control algorithm presented in this paper.     

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction

This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.     

Adaptive observer design for nonlinear systems using generalized nonlinear observer canonical form

In this paper, we present an adaptive observer for nonlinear systems that include unknown constant parameters and are not necessarily observable. Sufficient conditions are given for a nonlinear system to be transformed by state-space change of coordinates into an adaptive observer canonical form. Once a nonlinear system is transformed into the proposed adaptive observer canonical form, an adaptive observer can be designed under the assumption that a certain system is strictly positive real. An illustrative example is included to show the effectiveness of the proposed method.     

Adaptive nonlinear control using input normalized neural networks

An adaptive feedback linearization technique combined with the neural network is addressed to control uncertain nonlinear systems. The neural network-based adaptive control theory has been widely studied. However, the stability analysis of the closed-loop system with the neural network is rather complicated and difficult to understand, and sometimes unnecessary assumptions are involved. As a result, unnecessary assumptions for stability analysis are avoided by using the neural network with input normalization technique. The ultimate boundedness of the tracking error is simply proved by the Lyapunov stability theory. A new simple update law as an adaptive nonlinear control is derived by the simplification of the input normalized neural network assuming the variation of the uncertain term is sufficiently small.     

Adaptive output feedback tracking of nonlinear systems with uncertain nonsymmetric dead-zone input

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective.     

Indirect adaptive fuzzy fault-tolerant tracking control for MIMO nonlinear systems with actuator and sensor failures

In this paper, an active fuzzy fault tolerant tracking control (AFFTTC) scheme is developed for a class of multi-input multi-output (MIMO) unknown nonlinear systems in the presence of unknown actuator faults, sensor failures and external disturbance. The developed control scheme deals with four kinds of faults for both sensors and actuators. The bias, drift, and loss of accuracy additive faults are considered along with the loss of effectiveness multiplicative fault. A fuzzy adaptive controller based on back-stepping design is developed to deal with actuator failures and unknown system dynamics. However, an additional robust control term is added to deal with sensor faults, approximation errors, and external disturbances. Lyapunov theory is used to prove the stability of the closed loop system. Numerical simulations on a quadrotor are presented to show the effectiveness of the proposed approach.     

Command filter based adaptive control of asymmetric output-constrained switched stochastic nonlinear systems

In this paper, adaptive tracking control problem is investigated for a class of switched stochastic nonlinear systems with an asymmetric output constraint. By introducing a nonlinear mapping (NM), the asymmetric output-constrained switched stochastic system is first transformed into a new system without any constraint, which achieves the equivalent control objective. The command filter technique is employed to handle the “explosion of complexity” in traditional backstepping design, and neural networks (NNs) are directly utilized to cope with the completely unknown nonlinear functions and stochastic disturbances existing in systems. At last, on the basis of stochastic Lyapunov function method, an adaptive neural controller is developed for the considered system. It is shown that the designed adaptive controller can guarantee that all the signals remain semi-globally uniformly ultimately bounded (SGUUB), while the output constraint is satisfied and the desired signal can be tracked with a small domain of the origin. Simulation results are offered to illustrate the feasibility of the newly designed control scheme.     

Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints

This paper focuses on the problem of adaptive neural network tracking control for a class of discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints. Two novel state-feedback and output-feedback dynamic control laws are established where the function tanh() is employed to solve the saturation constraint problem. Implicit function theorem and mean value theorem are exploited to deal with non-affine variables that are used as actual control. Radial basis function neural networks are used to approximate the desired input function. Discrete Nussbaum gain is used to estimate the unknown sign of control gain. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of control schemes proposed in this paper.     

Finite-time stability and stabilization for stochastic markov jump systems with mode-dependent time delays

This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results.