Adaptive fuzzy control for nontriangular form systems with time-varying full-state constraints

This article investigates an adaptive fuzzy tracking control problem for a class of nontriangular form systems with asymmetric time-varying full state constraints. Unknown functions are approximated by the fuzzy logic systems. A domination approach is employed to tackle the nontriangular form structure. Time-varying asymmetric barrier Lyapunov functions (ABLFs) are adopted to ensure full-state constraints satisfaction. Based on the backstepping technique and time-varying ABLFs, an adaptive controller is proposed and guarantees that all the signals in the closed-loop system are ultimately bounded and the time-varying full state constraints are met. Simulation examples are presented to further demonstrate the effectiveness of the proposed approach.     

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.     

Adaptive fuzzy control for high-order nonlinear systems with time-varying full-state constraints and input saturation

The adaptive control for a class of high-order nonlinear systems with time-varying full-state constraints and input saturation is investigated in this paper. To deal with time-varying constraints, a type of high-order barrier Lyapunov functions(BLFs) are constructed. Its performance can be guaranteed with the disappearance of constraints. By building fuzzy systems, unknown functions can be approximated. Together with adding a power integrator technique and the gain-update law, an adaptive controller is designed. As a result, all the constraints are not breached, and the tracking error converges to an arbitrarily small zone around the origin. Finally, a practical example and a numerical example illustrate the effectiveness of the proposed method.     

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.     

A simplified adaptive tracking control for nonlinear pure-feedback systems with input delay and full-state constraints

This article investigated the adaptive backstepping tracking control for a class of pure-feedback systems with input delay and full-state constraints. With the help of mean value theorem, the system is transformed into strict-feedback one. By introducing the Pade approximation method, the effect of input delay was compensated. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. Furthermore, in order to reduce the computational burden by introducing backstepping design technique, dynamic surface control technique was employed. In addition, the number of the adaptive parameters that should be updated online was also reduced. By utilizing the barrier Lyapunov function, the closed-loop nonlinear system is guaranteed to be semi-globally ultimately uniformly bounded. Finally, a numerical simulation example is given to show the effectiveness of the proposed control strategy.     

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.     

Neuroadaptive output feedback control for nonlinear nonnegative dynamical systems with actuator amplitude and integral constraints

A neuroadaptive output feedback control architecture for nonlinear nonnegative dynamical systems with input amplitude and integral constraints is developed. Specifically, the neuroadaptive controller guarantees that the control amplitude as well as the integral of the control input over a given time interval are constrained, and the physical system states remain in the nonnegative orthant of the state space. The proposed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for noncardiac surgery in the face of infusion rate constraints and an integral drug dosing constraint over a specified time period. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Finite-time adaptive fuzzy control for a class of output constrained nonlinear systems with dead-zone

The article investigates the finite-time adaptive fuzzy control for a class of nonlinear systems with output constraint and input dead-zone. First, by skillfully combining the barrier Lyapunov function, backstepping design method, and finite-time control theory, a novel adaptive state-feedback tracking controller is constructed, and the output constraint of the nonlinear system is not violated. Second, the fuzzy logic system is used to approximate unknown function in the nonlinear system. Third, the finite-time command filter is introduced to avoid the problem of “complexity explosion” caused by repeated differentiations of the virtual control signal in conventional backstepping control schemes. Meanwhile, a new saturation function is added in the compensating signal for filter error to improve control accuracy. Finally, based on Lyapunov stability analysis, all the signals of the closed-loop are proved to be semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood region of the origin in a finite time. A simulation example is presented to demonstrate the effectiveness for the proposed control scheme.     

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.     

Neuro-adaptive finite-time optimal tracking control for permanent magnet synchronous motors with full-state constraints

In this article, the optimal tracking control problem is investigated for permanent magnet synchronous motors (PMSMs) with full-state constraints. By constructing multiple barrier-type performance index functions, a neuro-adaptive finite-time optimized control scheme is presented under identifier-actor-critic architecture, where the virtual control laws and the actual laws are designed to optimize corresponding subsystems. It is proven that all signals of the closed-loop system are uniformly ultimately bounded under the proposed control strategy, and the position tracking error converges to a small neighborhood of the origin in finite time. Besides, the system states are constrained to the effective operation range all the time. Finally, the simulation results and comparisons are carried out to further demonstrate the effectiveness of the proposed optimal control approach.     

Observer‐based fuzzy adaptive quantized control for uncertain nonlinear multiagent systems

This paper focuses on consensus quantized control design problem for uncertain nonlinear multiagent systems with unmeasured states. Every follower can be denoted through a system with unmeasurable states, hysteretic quantized input, and unknown nonlinearities. Fuzzy state observer and Fuzzy logic systems are employed to estimate unmeasured states and approximate unknown nonlinear functions, respectively. The hysteretic quantized input can be split into two bounded nonlinear functions to avoid chattering problem. By combining adaptive backstepping and first‐order filter signals, an observer‐based fuzzy adaptive quantized control scheme is designed for each follower. All signals exist in closed‐loop systems are semiglobally uniformly ultimately bounded, and all followers can accomplish a desired consensus results. Finally, a numerical example is employed to elaborate the effectiveness of proposed control strategy.     

Novel fuzzy adaptive finite-time nonsmooth control for uncertain nonlinear systems

In this article, a novel fuzzy adaptive finite-time nonsmooth controller is developed to handle the finite-time tracking problem for a class of uncertain nonlinear systems. Different from traditional fuzzy adaptive approximation methods, proposed method contains only one adaptive parameter, no matter how many states there are in the system. By constructing a new Lyapunov function with prescribed performance bound, the transient and steady performances of control system can be ensured. Further, based on a criterion of finite-time semiglobal practical stability and backstepping technology, a novel fuzzy adaptive finite-time nonsmooth control method is designed. It can be demonstrated that proposed control can effectively ensure tracking error tends to small neighborhood in a finite time. Finally, two examples have been simulated by the proposed control method, and it shows effective tracking performance.     

Adaptive fuzzy output feedback backstepping control of pure‐feedback nonlinear systems via dynamic surface control technique

In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure‐feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Prescribed performance adaptive fuzzy control for nonstrict-feedback nonlinear systems with dead zone outputs

This paper presents an adaptive fuzzy control scheme for a class of nonstrict-feedback nonlinear systems with dead zone outputs and prescribed performance. By utilizing the monotonically increasing property of system bounding functions and the Nussbaum function, the design difficulties caused by the nonstrict-feedback structure and dead zone output are overcome. Combining backstepping technique with prescribed performance algorithm, a feasible adaptive fuzzy controller is designed to guarantee the boundedness of all signals of the closed-loop system and the prescribed tracking performance of the system. Finally, simulation results are depicted to illustrate the effectiveness of the proposed control approach.     

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.     

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.