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 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.     

Adaptive fuzzy constraint control for switched nonlinear systems in nonstrict feedback form

In this paper, the adaptive fuzzy controller design problem is investigated for a class of switched nonlinear systems in nonstrict feedback form, in which the unknown functions are considered and are approximated. Moreover, the system states are constrained in corresponding compact. By using Barrier Lypunov function method and backstepping technique, the adaptive fuzzy controller is designed such that all the signals in the closed-loop system are bounded, the system output can track the desired signal to small compact, and all the system states satisfy the constraint conditions. Finally, the simulation results show the effectiveness of the proposed method.     

Fuzzy approximation-based adaptive control of nonstrict feedback stochastic nonlinear systems with time-varying state constraints

This article develops an approximation-based fuzzy control scheme for nonstrict feedback stochastic nonlinear systems (NFSNS) with time-varying state constraints. The difficulty in constructing controller is how to conquer the algebraic loop problem caused by nonstrict feedback structure, as well as prevent the state constraints from violating. To dispose the time-varying state constraints, time-varying barrier Lyapunov function is incorporated into the backstepping design framework. The lumped uncertainties of NFSNS are approximated by the fuzzy logic systems. By virtue of fuzzy basis function, the algebraic loop problem is effectively handled. Theoretical analysis shows that the predefined state constraints are not violated and all signals of the closed-loop systems are bounded. Finally, simulation results substantiate the validity of the devised method.     

Adaptive fuzzy finite-time quantized control for stochastic nonlinear systems with full state constraints

This article studies the adaptive fuzzy finite-time quantized control problem of stochastic nonlinear nonstrict-feedback systems with full state constraints. During the control design process, fuzzy logic systems are used to identify the unknown nonlinear functions, integral barrier Lyapunov functions are employed to solve the state constrained problem. In the frame of backstepping design, an adaptive fuzzy finite-time quantized control scheme is developed. Based on the stochastic finite-time Lyapunov stability theory, it can be guaranteed that the closed-loop system is semiglobal finite-time stable in probability, and the tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to testify the effectiveness of the developed control scheme.     

Fuzzy adaptive optimal control for nonlinear switched systems with actuator hysteresis

This article considers the issue of fuzzy adaptive dynamic programming control of nonlinear switched systems with arbitrary switchings and unknown uncertain functions and actuator hysteresis nonlinearities. The whole control approach is made of switching feedforward controller and optimal switching feedback controller. To get over the hardness of arbitrary switching structure and the issue of “explosion of complexity”, the common Lyapunov function theory and dynamic surface control method are utilized in the recursive design technique. By using fuzzy logic systems to model unknown inner dynamics and unknown cost functions, a novel fuzzy adaptive optimal switching control strategy is developed. Meanwhile, uniformly ultimately boundedness of all weights in the controlled systems are proved by the proposed control method, and the tracking performance is guaranteed in an optimal manner. Subsequently, a numerical simulation study is used to test the effectiveness of the presented control strategy.     

Fuzzy adaptive two-bits-triggered control for nonlinear uncertain system with input saturation and output constraint

In this work, a fuzzy adaptive two-bits-triggered control is investigated for the nonlinear uncertain systems with input saturation and output constraint. The considered systems are more widespread. Without sufficient transmission resources, how to resolve the constraint issues while guarantee the control performance is difficult and challenging. Then, hyperbolic tangent function and barrier Lyapunov function are integrated with the designed auxiliary system to solve input saturation and output constraint. Meanwhile, faced with the transmission resources limitation, this work both considers the triggering condition and the control signal transmission bits. A two-bits-triggered control is proposed to economize the transmission resources. Furthermore, improved fuzzy logic systems are established to further promote the control performance. It combines with the time-varying approximation error for processing. The boundedness of all the system signals can be proved. Simulation results illustrate the validity of the proposed approach.     

Adaptive control for switched uncertain nonlinear systems with time‐varying output constraint and input saturation

This paper is concerned with adaptive tracking control for switched uncertain nonlinear systems, which contain the time‐varying output constraint (TVOC) and input asymmetric saturation characteristic. In response to the unknown functions, the fuzzy logic systems are adopted. The controller is constructed by the backstepping technique. Based on the Tangent Barrier Lyapunov Function (BLF‐Tan), an adaptive switched control scheme is designed. It is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded with TVOC under arbitrary switchings. Furthermore, the effectiveness of presented control method is validated via the simulation example.     

Adaptive neural network asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints

This article addresses the issue of adaptive intelligent asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints. Unlike the existing systems in the literature in which the prior knowledge of the control gains is available for the controller design, the salient feature of our considered system is that the control gains are allowed to be unknown but have a positive sign. By introducing an auxiliary virtual controller and employing the new properties of Numbness functions, the major technique difficulty arising from the unknown control gains is overcome. At the same time, the -type barrier Lyapunov functions are introduced to prevent the violation of the state constraints. What's more, neural networks' universal online approximation ability and gain suppression inequality technology are combined in the frame of adaptive backstepping design, so that a new control method is proposed, which cannot only realize the asymptotic tracking control in probability, but also meet the requirement of the full state constraints imposed on the system. In the end, the simulation results for a practical example demonstrate the effectiveness of the proposed control method.     

Adaptive finite-time tracking control for output-constrained nonlinear systems with non-strict-feedback structure

This article investigates the issue of adaptive finite-time tracking control for a category of output-constrained nonlinear systems in a non-strict-feedback form. First, by utilizing the structural characteristics of radial basis function neural networks (RBF NNs), a backstepping design method is extended from strict-feedback systems to a kind of more general systems, and NNs are employed to approximate unknown nonlinear functions. In addition, the system output is constrained to the specified region by applying the barrier Lyapunov function (BLF) technique. Furthermore, the finite-time stability of the system is proved by employing the Bhat and Bernstein theorem. As a result, an adaptive finite-time tracking control scheme for the output-constrained nonlinear systems with non-strict-feedback structure is proposed by applying RBF NNs, BLF, finite-time stability theory, and adaptive backstepping technique. It is demonstrated the finite-time stability of the system, the prescribed convergence of the system output and tracking error, the boundedness of adaptive parameters and state variables. Finally, a simulation example is implemented to illustrate the effectiveness of the presented neural control scheme.     

Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

This paper considers the problem of adaptive fuzzy output‐feedback tracking control for a class of switched stochastic nonlinear systems in pure‐feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states. Based on these methods, an adaptive fuzzy output‐feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method.     

Passivity‐based adaptive output tracking control for switched nonlinear systems with uncertain parameters

This paper addresses the issue of the adaptive output tracking control for switched nonlinear systems with uncertain parameters. The solvability of the tracking control problem for each subsystem is not necessary to hold. Individual update laws corresponding to different unknown parameters are adopted to reduce the conservativeness produced from the adoption of a common undated law. By means of the dual design of the adaptive controllers and a state‐dependent switching law using multiple storage functions technique, several conditions are obtained under which the adaptive output tracking control problem for switched nonlinear systems is solvable. Finally, an example shows the effectiveness of the proposed method.     

一类切换系统的动态输出反馈控制器设计

针对一类非线性扰动项不满足匹配条件的蚤确定切换系统鲁棒动态输出反馈镇定问题,采用单李雅普诺夫函数方法和变量替换方法,研究了状态矩阵和控制输入矩阵同时带有未知、时变但有界的不确定性,且有外界干扰的切换系统,给出了不确定切换系统鲁棒可稳的充分备件。仿真结果表明,所设计的动态输出反馈控制器及相应的切换策略保证了闭环系统渐近稳定。     

Guaranteed cost control with pole constraints for uncertain discrete-time switched systems

For a class of discrete-time switched systems with norm-bounded uncertainties and a quadratic cost index, the problem of designing a guaranteed cost state feedback controller with pole constraints is considered. A sufficient condition on the existence of robust guaranteed controllers is derived by a quadratic Lyapunov function approach together with linear matrix inequality (LMI) technique. Based on a constructed switching law, the closed-loop system is quadratic D-stable and the closed-loop cost function value is not more than a specified upper bound. Furthermore, the design of suboptimal guaranteed cost controllers is turned into a convex optimization problem with linear matrix inequalities constraints. A numerical example demonstrates the effect of the proposed design approach. __________ Translated from Control and Decision, 2007, 22(11): 1269–1273 [译自: 控制与决策]     

Adaptive fuzzy practical fixed-time control for uncertain nonlinear systems with actuator constraints

This article addresses an adaptive fuzzy practical fixed-time tracking control for nonlinear systems with unknown actuator constraints and uncertainty functions. First, fuzzy logic systems (FLSs) are used to identify uncertain functions. Then, by utilizing FLSs, backstepping technique, and finite-time stability theory, an adaptive fuzzy practical fixed-time control is proposed to obtain satisfactory tracking performance even when the actuator faults. The theoretical analysis verified that the closed-loop systems is practical fixed-time stable under the proposed control strategy, the tracking error converges to a small neighborhood of the origin in a fixed time, and the convergence time is independent of the state conditions. Finally, both numerical simulation and physical example demonstrates the effectiveness of the proposed control strategy.     

Fixed-time fault-tolerant control of uncertain MIMO switched interconnected systems subject to state delay,unknown control directions,and quantized nonlinear inputs

This paper investigates design of an adaptive fixed-time fault-tolerant decentralized controller for a class of uncertain multi-input multi-output (MIMO) switched large-scale non-strict interconnected systems under arbitrary switching subject to unknown control directions, quantized nonlinear inputs, actuator failures unknown external disturbances, and unmodeled dynamics. In addition to interconnected terms, time-varying delayed interconnected terms have been considered in the system model which makes it more general than previous works in the literature. The proposed controller can handle switched systems with unknown switching signal and different types of input nonlinearities including, saturation, backlash, and dead-zone. The singularity problem in designing the fixed time controller has been solved. The quantizer and actuators fault parameters are assumed to be unknown. The Razumikhin lemma has been used to deal with the delayed interconnected terms. To cope with the system unknown dynamics, neural networks (NNs) have been applied and by updating the maximum norms of the networks weight vectors the computational load has been reduced. The explosion of complexity occurring in the traditional back-stepping technique has been avoided by applying dynamic surface control (DSC). Finally, by defining an appropriate common Lyapunov function (CLF), fixed-time convergence of system outputs and the closed-loop system stability have been established. The effectiveness of the proposed controller has been shown via simulation study.     

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.     

带有非线性扰动的不确定切换系统鲁棒控制

针对一类非线性扰动项不满足匹配条件的不确定切换系统鲁棒状态反馈镇定问题,采用单李雅普诺夫函数和多李雅普诺夫函数方法,研究了状态矩阵和控制输入矩阵同时带有未知、时变但有界的不确定性,而且有外界干扰的切换系统,分别给出了不确定切换系统鲁棒可稳的充分条件。仿真结果表明,所设计的两类控制器及相应的切换策略均能保证闭环系统渐近稳定。     

Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function

In this paper, a novel indirect adaptive fuzzy controller is proposed for a class of uncertain nonlinear systems with input and output constrains. To address output and input constraints, a barrier Lyapunov function and an auxiliary design system are employed, respectively. The proposed approach is explored by employing fuzzy logic systems to tackle unknown nonlinear functions and combining the adaptive backstepping technique with adaptive fuzzy control design. Especially, the number of the online learning parameters are reduced to 2n in the closed‐loop system. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded, and the input and output constraints are circumvented simultaneously. A numerical example with comparisons is provided to illustrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

一类切换T-S型模糊系统二次镇定保成本控制

针对一类不确定切换T-S型模糊系统,对保成本鲁棒控制问题进行了研究。利用单Lyapunov函数法,给出了混杂状态反馈保成本控制器的设计方案,使得闭环系统对所有允许的不确定性,在所设计的混杂状态反馈控制器下是二次稳定的,应用线性矩阵不等式的可解性给出闭环系统二次稳定的充分条件,同时给出了二次型成本函数的一个上界。模型中的每个切换系统的子系统是不确定模糊系统,取常用的平行分布补偿PDC控制器,主要条件以凸组合的形式给出,具有较强的可解性。仿真结果验证了所设计方法的有效性。