非仿射纯反馈不确定系统预设性能鲁棒自适应控制

针对一类结构和参数及控制方向均未知的非仿射纯反馈非线性不确定系统,提出了一种保预设性能鲁棒自适应控制方案。首先引入性能函数和误差转换函数,通过误差转换将原始的输出误差存在性能约束的受限系统转换为等价的非受限系统;其次,基于中值定理将非仿射型系统转化为具有线性结构形式的时变系统,并同时利用自适应投影算法对有界时变参数进行辨识,参数辨识误差和外界干扰采用非线性阻技术项进行补偿;随后综合运用反演技术和Nussbaum函数设计控制器并进行稳定性分析。所设计的控制器不仅能够保证闭环系统所有信号有界且输出误差满足预设的瞬态及稳态性能要求;最后,仿真结果验证了所设计控制方案的可行性与有效性。     

Adaptive finite-time consensus tracking control for nonlinear multiagent systems in nonstrict feedback form with full-state constraints

In this article, the fuzzy adaptive finite-time consensus tracking control problem for nonstrict feedback nonlinear multiagent systems with full-state constraints is studied. The finite-time control based on command filtered backstepping is proposed to guarantee the finite-time convergence and eliminate the explosion of complexity problem caused by backstepping process, and the errors in the filtering process are compensated by using error compensation mechanism. Furthermore, based on the fuzzy logic systems, the uncertain nonlinear dynamics are approximated and the problem of state variables in nonstrict feedback form is solved by using the property of basis functions. The barrier Lyapunov functions are introduced to guarantee that all system states and compensated tracking error signals are constrained in the designed regions. A simulation example is given to verify the superiority of the proposed algorithm.     

Adaptive finite-time tracking control for parameterized nonlinear systems with full state constraints

In this article, the issue of adaptive finite-time dynamic surface control (DSC) is discussed for a class of parameterized nonlinear systems with full state constraints. Using the property of logarithmic function, a one-to-one nonlinear mapping is constructed to transform a constrained system into an unconstrained system with the same structure. The nonlinear filter is constructed to replace the first-order linear filter in the traditional DSC, and the demand on the filter time constant is reduced. Based on finite-time stable theory and using modified DSC, the finite-time controller is designed via DSC. Theoretical analysis shows that all the signals in the closed-loop system are semiglobal practical finite-time stable. Furthermore, none of the states are outside the defined open set. In the end, simulation results are presented to demonstrate the effectiveness of the proposed control schemes with both linear filters and nonlinear filters.     

Adaptive neural network command filtered backstepping control of pure‐feedback systems in presence of full state constraints

An adaptive neural network (NN) command filtered backstepping control is proposed for the pure‐feedback system subjected to time‐varying output/stated constraints. By introducing a one‐to‐one nonlinear mapping, the obstacle caused by full stated constraints is conquered. The adaptive control law is constructed by command filtered backstepping technology and radial basis function NNs, where only one learning parameter needs to be updated online. The stability analysis via nonlinear small‐gain theorem shows that all the signals in closed‐loop system are semiglobal uniformly ultimately bounded. The simulation examples demonstrate the effectiveness of the proposed control scheme.     

Adaptive cross backstepping control for a class of nonstrict feedback nonlinear systems with partial state constraints

The tracking control problem for a class of partial state constrained nonlinear system is studied in this article. The system is divided into two semistrict feedback nonlinear subsystems, one is state constrained and the other is state free. By means of state transformation, the state constraint problem is transformed into the bounded problem of the transformed function. Compared with the barrier Lyapunov function (BLF) method, it not only solves the state constraint problem but also circumvents the feasibility check on virtual controllers. Based on the cross backstepping control, the constrained controller and unconstrained controller are designed simultaneously. It solves the coupling problem effectively in the design of cross processing control. On the other hand, dynamic surface control is used which effectively avoids “computation explosion” caused by backstepping control. The designed controllers can ensure the error signals converge to a small neighbourhood of zero and keep the asymmetric time-varying constraints on system partial states are satisfied for all the time. Finally, simulation experiments are carried out on a hyperchaotic Rössler system to verify the efficacy of the control scheme.     

An adaptive dynamic surface control of output constrained stochastic nonlinear systems with unknown control directions

This article is concerned about an adaptive dynamic surface control (DSC) of output constrained stochastic nonlinear systems with unknown control directions and unmodeled dynamics. Nonlinear mapping-based backstepping control design is presented for stochastic nonlinear systems with output constraint. The explosion of complexity exists in tradition backstepping method is avoided by using the DSC technique. The radial basis function neural networks are employed to deal with unknown nonlinear functions. Nussbaum gain technique is employed to handle the unknown control directions. And a dynamic signal is employed to dominate the unmodeled dynamics. The adaptive controller is designed can ensure that the tracking error converges on a small region of the origin. And all signals of the closed-loop systems are semiglobal uniformly ultimately bounded. Finally, the results of the simulation cases are provided to show the effectivity of the designed controller scheme.     

Adaptive control design for uncertain polynomial nonlinear systems with parametric uncertainties

In this paper, we will develop an adaptive ??_∞ control approach for a class of polynomial nonlinear systems with parametric uncertainties. Motivated by the dissipation theory and the vector projection technique, we propose a nonlinear adaptive ??_∞ controller and its associated parameter adaptation law. The proposed adaptive control strategy is capable of identifying unknown parameter values quickly and minimizing the effect of estimation error. To further improve adaptive controlled performance, the Lyapunov function will be relaxed from quadratic to higher‐order forms and the controller gains are generalized from constant to parameter‐dependent. All of the synthesis conditions are formulated in the framework of polynomial/constant linear matrix inequalities and solvable using available software packages. Copyright © 2010 John Wiley & Sons, Ltd.     

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

This work develops a robust adaptive control algorithm for uncertain nonlinear systems with parametric uncertainties and external disturbances satisfying an extended matching condition. This control method is implemented in the framework of a mapping filtered forwarding‐based technique. As an attractive alternative of the adaptive backstepping method, this bottom‐up strategy forms a virtual controller and a parameter updated law at each step of the design, where Lyapunov functions and the prior knowledge of system parameters are not required. The boundedness of all signals is guaranteed by using Barbalat's lemma. According to immersion relationship, a compliant behavior of systems behaves accordingly to the lower‐order target dynamics. Furthermore, input constraints are handled by estimating a saturated scaling. A spring, mass, and damper system is used to demonstrate the controller performances via simulation results.     

An approach to digital implementation of continuous backstepping adaptive control for linear systems

This paper presents a solution to the problem of digitally implementing backstepping adaptive control for linear systems. The continuous‐time system to be controlled is given a discrete‐time representation in the δ‐operator. A discrete adaptive backstepping controller is then designed for such a discrete‐time model. The effect of the modelling error, generated by the sampling process, is accounted for in the parameter update law by a σ‐modification. It is shown that all the signals (discrete and continuous) of the closed loop are uniformly bounded, with a region of attraction which is a K_∞ function of the sampling rate. An upper bound on the asymptotic tracking error is then given, and shown to be proportional to the sampling period. Copyright © 1999 John Wiley & Sons, Ltd.     

Adaptive control design for MIMO switched nonlinear systems with full state constraints

This paper presents an adaptive fuzzy control approach of multiple‐input–multiple‐output (MIMO) switched uncertain systems, which involve time‐varying full state constraints (TFSCs) and unknown disturbances. In the design procedure, the fuzzy logic systems are adopted to approximate the unknown functions in the systems. The adaptive fuzzy controller is set up by backstepping technique. According to the tangent barrier Lyapunov function (BLF‐Tan), a novel adaptive MIMO switched nonlinear control algorithm is designed. Under the rule of arbitrary switchings and the proposed control laws, it is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero with TFSCs. Furthermore, the simulation example validates the effectiveness of presented control strategy.     

An indirect model reference adaptive controller based on the multirate sampling of the plant output

The use of sampled-data multirate-output controllers for model reference adaptive control of possibly non-stably invertible linear systems with unknown parameters is investigated. Multirate-output controllers contain a multirate sampling mechanism with different sampling period at each system output. Such a control allows us to assign an arbitrary discrete-time transfer function matrix for the sampled closed-loop system and does not make assumptions on the plant other than controllability, observability and the knowledge of two sets of structural indices, namely the controllability and the observability indices. An indirect adaptive control scheme based on these sampled-data controllers is proposed which estimates the unknown plant parameters (and consequently the controller parameters) on-line from sequential data of the inputs and the outputs of the plant, which are recursively updated within the time limit imposed by a fundamental sampling period T₀. Using the proposed adaptive algorithm, the model reference adaptive control problem is reduced to the determination of a fictitious static state feedback controller owing to the merits of multirate-output controllers. Known indirect model reference adaptive control techniques usually resort to the direct computation of dynamic controllers. The controller determination reduces to the simple problem of solving a linear algebraic system of equations, whereas in known indirect model reference adaptive control techniques, matrix polynomial Diophantine equations usually need to be solved. Moreover, persistent excitation of the continuous-time plant is provided without making any special richness assumption on the reference signals.     

Adaptive fuzzy finite-time decentralized control for large-scale stochastic nonlinear systems

An adaptive finite-time decentralized control algorithm for a class of large-scale stochastic nonlinear systems is presented. The fuzzy logic system is used to estimate uncertain nonlinearities. One advantage of the developed scheme is that each subsystem only needs to update one adaptive parameter, which alleviates the burden of online estimation. The dynamic surface control method is employed to reduce the “complexity explosion” caused by the repetitive derivation of the intermediate variable function in the backstepping control scheme. A new decentralized controller is designed so that all signals of the controlled system are bounded and the tracking error converges to a small residual set around the origin within a finite time. The simulation results of a numerical example illustrate the effectiveness of the method.     

A new decentralized retrofit adaptive fault‐tolerant flight control design

In this paper, we develop a new decentralized retrofit adaptive fault‐tolerant control design for a class of nonlinear models arising in flight control. The proposed adaptive fault‐tolerant controller is designed to accommodate loss‐of‐effectiveness (LoE) failures in flight control actuators and achieve accurate estimation of failure‐related parameters. The design is based on local estimation of LoE parameters and generation of local retrofit control signals to accommodate the failures. Using state‐dependent closed‐loop estimation errors, we show the overall system to be stable and demonstrate the tracking error to converge to zero asymptotically for any combination of actuator failures. Through computer simulation of F/A‐18 aircraft under actuator LoE failures, the proposed approach is also shown to achieve better parameter estimation performance compared to the fully centralized design and the design employing local observers and a centralized adaptive controller. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive control of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics

This paper focuses on the problem of adaptive control for a class of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics. By introducing a one-to-one nonlinear mapping, the constrained pure-feedback nonlinear system with state and input unmodeled dynamics is transformed into unconstrained pure-feedback system. The controller design based on the transformed novel system is proposed by using a modified dynamic surface control method. Dynamic signal and normalization signal are designed to handle dynamical uncertain terms and input unmodeled dynamics, respectively. By adding nonnegative normalization signal into the whole Lyapunov function and using the introducing compact set in the stability analysis, all signals in the whole system are proved to be semiglobally uniformly ultimately bounded, and all states can obey the time-varying constraint conditions. A numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Adaptive fuzzy finite-time fault-tolerant control of nonlinear systems with state constraints and input quantization

This article concentrates on an adaptive finite-time fault-tolerant fuzzy tracking control problem for nonstrict feedback nonlinear systems with input quantization and full-state constraints. By utilizing the fuzzy logic systems and less adjustable parameters method, the unknown nonlinear functions are addressed in each step process. In addition, a dynamic surface control technique combined with fuzzy control is introduced to tackle the variable separation problem. The problem for the effect of quantization and unlimited number of actuator faults is tackled by a damping term with smooth function in the intermediate control law. Finite-time stability is achieved by combining barrier Lyapunov functions and backstepping method. The finite-time controller is designed such that all the responses of the systems are semiglobal practical finite-time stable and ensured to remain in the predefined compact sets while tracking error converges to a small neighborhood of the origin in finite time. Finally, simulation examples are utilized to testify the validity of the investigated strategy.     

Finite-time adaptive fuzzy command filtering control for stochastic nonlinear systems with input quantization

This article focuses on the finite-time adaptive fuzzy control problem based on command filtering for stochastic nonlinear systems subject to input quantization. Fuzzy logic systems are employed to estimate unknown nonlinearities. In the control design, the hysteretic quantized input is decomposed into two bounded nonlinear functions, which solves the chattering problem. Meanwhile, an adaptive fuzzy controller is presented by the combination of command filter technique and backstepping control, which eliminates the computational complexity existing in traditional backstepping design. Under the proposed adaptive mechanism, all the closed-loop signals remain bounded while the desired system performance can be realized within finite time. The main significance of this work is that (1) the filtering error can be solved on the basis of the designed compensating signals; (2) the requirement of adaptive parameters is decreased to only one, which simplifies the controller design process and may improve the control performance. Two simulation examples are used to validity of the developed scheme.     

一种新型的间接自适应模糊控制器

自适应模糊控制为复杂对象的控制提供了有效途径,引起控制领域的广泛关注。针对一类单输入单输出非线性不确定对象,利用Popov超稳定理论提出了一种新型的间接自适应模糊控制器设计方案。该方案首先采用对象模型构成理想的控制器,利用模糊系统的万能逼近特性构造若干模糊系统在线逼近未知的对象模型,然后将闭环系统转换为1个线性定常的前向环节和1个非线性时变的反馈环节组成的等效误差模型,通过Popov超稳定理论推导出稳定的参数自适应律。该方案能确保系统的输出渐近收敛到给定的参考信号,同时放宽了对最小逼近误差的限制,并且具有更广泛和灵活的参数调节形式。仿真结果验证了方案对非线性对象的有效性。     

Adaptive neural network control for stochastic constrained block structure nonlinear systems with dynamical uncertainties

Stochastic adaptive dynamic surface control is presented for a class of uncertain multiple‐input–multiple‐output (MIMO) nonlinear systems with unmodeled dynamics and full state constraints in this paper. The controller is constructed by combining the dynamic surface control with radial basis function neural networks for the MIMO stochastic nonlinear systems. The nonlinear mapping is applied to guarantee the state constraints being not violated. The unmodeled dynamics is disposed through introducing an available dynamic signal. It is proved that all signals in the closed‐loop system are bounded in probability and the error signals are semiglobally uniformly ultimately bounded in mean square or the sense of four‐moment and the state constraints are confirmed in probability. Simulation results are offered to further illustrate the effectiveness of the control scheme.     

考虑铁损的永磁同步电动机模糊自适应约束控制

针对考虑铁损的永磁同步电动机位置伺服控制中的状态约束问题,本文提出了一种基于势垒Lyapunov函数的模糊自适应反步控制策略。首先,选取模糊逻辑系统处理电动机系统中的未知非线性函数项;然后,将势垒Lyapunov函数与反步法结合对状态变量幅值进行约束,保证电动机系统的转子角速度、定子电流等状态量被限制在给定的区间内;最终构建基于势垒Lyapunov函数的模糊自适应反步控制器。仿真结果表明所设计的控制器不仅实现了有效的位置跟踪,并且将控制量和状态量都限制在合理区间内,避免了因违反状态约束而引发的安全性问题。     

Integral barrier Lyapunov function-based adaptive fuzzy output feedback control for nonlinear delayed systems with time-varying full-state constraints

In this article, an adaptive fuzzy output feedback control method is presented for nonlinear time-delay systems with time-varying full state constraints and input saturation. To overcome the problem of time-varying constraints, the integral barrier Lyapunov functions (IBLFs) integrating with dynamic surface control (DSC) are applied for the first time to keep the state from violating constraints. The effects of unknown time delays can be removed by using designed Lyapunov-Krasovskii functions (LKFs). An auxiliary design system is introduced to solve the problem of input saturation. The unknown nonlinear functions are approximated by the fuzzy logic systems (FLS), and the unmeasured states are estimated by a designed fuzzy observer. The novel controller can guarantee that all signals remain semiglobally uniformly ultimately bounded and satisfactory tracking performance is achieved. Finally, two simulation examples illustrate the effectiveness of the presented control methods.