Adaptive neural output feedback control for stochastic nonlinear time-delay systems with unknown control directions

This paper first focuses on the problem of adaptive output feedback stabilization for a more general class of stochastic nonlinear time-delay systems with unknown control directions. By using a linear state transformation, the original system is transformed to a new system for which control design becomes feasible. Then a novel adaptive neural network (NN) output feedback control strategy, which only contains one adaptive parameter, is developed for such systems by combining the input-driven filter design, the backstepping technique, the NN’s parameterization, the Nussbaum gain function method and the Lyapunov–Krasovskii approach. The proposed control design guarantees that all signals in the closed-loop systems are 4-moment (or 2-moment) semi-globally uniformly bounded. Finally, two simulation examples are given to demonstrate the effectiveness and the applicability of the proposed control design.     

Robust adaptive NN control for a class of uncertain discrete-time nonlinear MIMO systems

A robust adaptive NN output feedback control is proposed to control a class of uncertain discrete-time nonlinear multi-input–multi-output (MIMO) systems. The high-order neural networks are utilized to approximate the unknown nonlinear functions in the systems. Compared with the previous research for discrete-time MIMO systems, robustness of the proposed adaptive algorithm is obvious improved. Using Lyapunov stability theorem, the results show all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero by choosing the design parameters appropriately.     

Adaptive neural network output feedback control of stochastic nonlinear systems with dynamical uncertainties

In this paper, a robust adaptive neural network (NN) backstepping output feedback control approach is proposed for a class of uncertain stochastic nonlinear systems with unknown nonlinear functions, unmodeled dynamics, dynamical uncertainties and without requiring the measurements of the states. The NNs are used to approximate the unknown nonlinear functions, and a filter observer is designed for estimating the unmeasured states. To solve the problem of the dynamical uncertainties, the changing supply function is incorporated into the backstepping recursive design technique, and a new robust adaptive NN output feedback control approach is constructed. It is mathematically proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing design parameters appropriately. The simulation example and comparison results further justify the effectiveness of the proposed approach.     

Adaptive Neural Network-Based Control for a Class of Nonlinear Pure-Feedback Systems With Time-Varying Full State Constraints

In this paper, an adaptive neural network (NN) control approach is proposed for nonlinear pure-feedback systems with time-varying full state constraints. The pure-feedback systems of this paper are assumed to possess nonlinear function uncertainties. By using the mean value theorem, pure-feedback systems can be transformed into strict feedback forms. For the newly generated systems, NNs are employed to approximate unknown items. Based on the adaptive control scheme and backstepping algorithm, an intelligent controller is designed. At the same time, time-varying Barrier Lyapunov functions (BLFs) with error variables are adopted to avoid violating full state constraints in every step of the backstepping design. All closedloop signals are uniformly ultimately bounded and the output tracking error converges to the neighborhood of zero, which can be verified by using the Lyapunov stability theorem. Two simulation examples reveal the performance of the adaptive NN control approach.      

Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems

In this paper, both full state and output feedback adaptive neural network (NN) controllers are presented for a class of strict-feedback discrete-time nonlinear systems. Firstly, Lyapunov-based full-state adaptive NN control is presented via backstepping, which avoids the possible controller singularity problem in adaptive nonlinear control and solves the noncausal problem in the discrete-time backstepping design procedure. After the strict-feedback form is transformed into a cascade form, another relatively simple Lyapunov-based direct output feedback control is developed. The closed-loop systems for both control schemes are proven to be semi-globally uniformly ultimately bounded.     

Multiple Lyapunov functions‐based adaptive neural network tracking control of uncertain switched nonlinear systems

In this paper, the problem of adaptive neural network (NN) tracking control of a class of switched strict‐feedback uncertain nonlinear systems is investigated by state‐feedback, in which the solvability of the problem of adaptive NN tracking control for individual subsystems is unnecessary. A multiple Lyapunov functions (MLFs)–based adaptive NN tracking control scheme is established by exploiting backstepping and the generalized MLFs approach. Moreover, based on the proposed scheme, adaptive NN controllers of all subsystems and a state‐dependent switching law simultaneously are constructed, which guarantee that all signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. The scheme provided permits removal of a technical condition in which the adaptive NN tracking control problem for individual subsystems is solvable. Finally, the effectiveness of the design scheme proposed is shown by using two examples.     

Output-Feedback Based Simplified Optimized Backstepping Control for Strict-Feedback Systems with Input and State Constraints

In this paper, an adaptive neural-network (NN) output feedback optimal control problem is studied for a class of strict-feedback nonlinear systems with unknown internal dynamics, input saturation and state constraints. Neural networks are used to approximate unknown internal dynamics and an adaptive NN state observer is developed to estimate immeasurable states. Under the framework of the backstepping design, by employing the actor-critic architecture and constructing the tan-type Barrier Lyapunov function (BLF), the virtual and actual optimal controllers are developed. In order to accomplish optimal control effectively, a simplified reinforcement learning (RL) algorithm is designed by deriving the updating laws from the negative gradient of a simple positive function, instead of employing existing optimal control methods. In addition, to ensure that all the signals in the closed-loop system are bounded and the output can follow the reference signal within a bounded error, all state variables are confined within their compact sets all times. Finally, a simulation example is given to illustrate the effectiveness of the proposed control strategy.      

Output feedback control of a class of discrete MIMO nonlinear systems with triangular form inputs

In this paper, adaptive neural network (NN) control is investigated for a class of discrete-time multi-input-multi-output (MIMO) nonlinear systems with triangular form inputs. Each subsystem of the MIMO system is in strict feedback form. First, through two phases of coordinate transformation, the MIMO system is transformed into input-output representation with the triangular form input structure unchanged. By using high-order neural networks (HONNs) as the emulators of the desired controls, effective output feedback adaptive control is developed using backstepping. The closed-loop system is proved to be semiglobally uniformly ultimate bounded (SGUUB) by using Lyapunov method. The output tracking errors are guaranteed to converge into a compact set whose size is adjustable, and all the other signals in the closed-loop system are proved to be bounded. Simulation results show the effectiveness of the proposed control scheme.     

面向控制性能的一类非线性关联系统输出反馈动态面控制

针对一类含有完全未知关联项的多输入/多输出非线性系统,提出了输出反馈动态面自适应控制方案,克服了反推控制中的微分爆炸问题;利用神经网络逼近系统中的未知关联项,对于每个子系统只需对一个参数设计自适应律;引入性能函数和输出误差变换,跟踪误差信号的收敛速率、最大超调量和稳态误差等控制性能指标均可得到保证.理论证明了闭环系统的所有信号半全局一致有界,仿真结果验证了所提方案的有效性.     

Stabilization of uncertain chained nonholonomic systems using adaptive output feedback

In this paper, adaptive output feedback control is presented to solve the stabilization problem of nonholonomic systems in chained form with strong nonlinear drifts and uncertain parameters using output signals only. The objective is to design adaptive nonlinear output feedback laws which can steer the closed‐loop systems to globally converge to the origin, while the estimated parameters remain bounded. The proposed systematic strategy combines input‐state scaling with backstepping technique. Motivated from a special case, adaptive output feedback controllers are proposed for a class of uncertain chained systems. The simulation results demonstrate the effectiveness of the proposed controllers. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive NN prescribed performance control for nonlinear systems with output dead zone

This paper investigates adaptive neural network (NN) prescribed performance output tracking control problem for a class of strict-feedback nonlinear systems with output dead zone. By introducing a Nussbaum function, the problem of unknown virtual control coefficient is resolved, which is caused by the nonlinearity in the output dead zone. By designing the state observer and utilizing backstepping recursive design technique, a new adaptive NN control method is proposed. It is shown that all the signals of the resulting closed-loop system are bounded and the tracking error remains an adjustable neighborhood of the origin with the predefined performance under the effect of output dead zone. Finally, a simulation example is given at the simulation part, which further demonstrate the effectiveness of proposed control method.

     

Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

This paper addresses the distributed output feedback tracking control problem for multi-agent systems with higher order nonlinear non-strict-feedback dynamics and directed communication graphs. The existing works usually design a distributed consensus controller using all the states of each agent, which are often immeasurable, especially in nonlinear systems. In this paper, based only on the relative output between itself and its neighbours, a distributed adaptive consensus control law is proposed for each agent using the backstepping technique and approximation technique of Fourier series (FS) to solve the output feedback tracking control problem of multi-agent systems. The FS structure is taken not only for tracking the unknown nonlinear dynamics but also the unknown derivatives of virtual controllers in the controller design procedure, which can therefore prevent virtual controllers from containing uncertain terms. The projection algorithm is applied to ensure that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the proposed control law can guarantee that the output of each agent synchronises to the leader with bounded residual errors and that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation results have verified the performance and feasibility of the proposed distributed adaptive control strategy.     

Adaptive fuzzy backstepping output feedback control of nonlinear uncertain systems with unknown virtual control coefficients using MT-filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO nonlinear uncertain systems with unmeasured states and unknown virtual control coefficients. The fuzzy logic systems are used to model the uncertain nonlinear systems. The MT-filters and the state observer are designed to estimate the unmeasured states. Using backstepping design principle and combining the Nussbaum gain functions, an adaptive fuzzy output feedback control scheme is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of origin. A simulation is included to illustrate the effectiveness of the proposed approach.     

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

An adaptive neural network (NN)-based output feedback controller is proposed to deliver a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict feedback form. The NN backstepping approach is utilized to design the adaptive output feedback controller consisting of: (1) an NN observer to estimate the system states and (2) two NNs to generate the virtual and actual control inputs, respectively. The non-causal problem encountered during the control design is overcome by using a dynamic NN which is constructed through a feedforward NN with a novel weight tuning law. The separation principle is relaxed, persistency of excitation condition (PE) is not needed and certainty equivalence principle is not used. The uniformly ultimate boundedness (UUB) of the closed-loop tracking error, the state estimation errors and the NN weight estimates is demonstrated. Though the proposed work is applicable for second order nonlinear discrete-time systems expressed in non-strict feedback form, the proposed controller design can be easily extendable to an nth order nonlinear discrete-time system.     

Adaptive neural output feedback finite-time command filtered backstepping control for nonlinear systems with full-state constraints

In this paper, an adaptive neural finite-time control method via barrier Lyapunov function, command filtered backstepping, and output feedback is proposed to solve the tracking problem of uncertain high-order nonlinear systems with full-state constraints and input saturation. By utilizing the neural network (NN) to approximate unknown nonlinear functions, the finite-time command filters are used to filtering the virtual control signals and get the intermediate control signals in a finite time in the backstepping process. Because there are errors between the output of finite-time command filters and the virtual control signals, the error compensation signals are added to eliminate the influence of filtering errors. Based on the proposed control scheme, the states of the system can be constrained in the predetermined region, all signals in the system are bounded in finite time, and the tracking error can converge to the desired region in finite time. At last, a simulation example is given to show the effectiveness of the proposed control method.     

Cooperative learning neural network output feedback control of uncertain nonlinear multi-agent systems under directed topologies

Without assuming that the communication topologies among the neural network (NN) weights are to be undirected and the states of each agent are measurable, the cooperative learning NN output feedback control is addressed for uncertain nonlinear multi-agent systems with identical structures in strict-feedback form. By establishing directed communication topologies among NN weights to share their learned knowledge, NNs with cooperative learning laws are employed to identify the uncertainties. By designing NN-based κ-filter observers to estimate the unmeasurable states, a new cooperative learning output feedback control scheme is proposed to guarantee that the system outputs can track nonidentical reference signals with bounded tracking errors. A simulation example is given to demonstrate the effectiveness of the theoretical results.     

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.     

Adaptive Neural Dynamic Surface Control For Nonlinear Pure‐Feedback Systems With Multiple Time‐Varying Delays: A Lyapunov‐Razumikhin Method

This paper focuses on the problem of adaptive neural control for a class of uncertain nonlinear pure‐feedback systems with multiple unknown time‐varying delays. The considered problem is challenging due to the non‐affine pure‐feedback form and the unknown system functions with multiple unknown time‐varying delays. Based on a novel combination of mean value theorem, Razumikhin functional method, dynamic surface control (DSC) technique and neural network (NN) parameterization, a new adaptive neural controller which contains only one parameter is developed for such systems. Moreover, The DSC technique can overcome the problem of ‘explosion of complexity’ in the traditional backstepping design procedure. All closed‐loop signals are shown to be semi‐globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the proposed design.     

Adaptive output feedback control of uncertain nonlinear systems based on dynamic surface control technique

An adaptive output feedback control approach is studied for a class of uncertain nonlinear systems in the parametric output feedback form. Unlike the previous works on the adaptive output feedback control, the problem of ‘explosion of complexity’ of the controller in the conventional backstepping design is overcome in this paper by introducing the dynamic surface control (DSC) technique. In the previous schemes for the DSC technique, the time derivative for the virtual controllers is assumed to be bounded. In this paper, this assumption is removed. It can be proven that the resulting closed‐loop system is stable in the sense that all the signals are semi‐global uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set. A simulation example is given to verify the effectiveness of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.