Fuzzy State Observer Research Articles

Observer-Based Event-Triggered Adaptive Fuzzy Control for Leader-Following Consensus of Nonlinear Strict-Feedback Systems.

In this article, the leader-following consensus problem via the event-triggered control technique is studied for the nonlinear strict-feedback systems with unmeasurable states. The follower's nonlinear dynamics is approximated using the fuzzy-logic systems, and the fuzzy weights are updated in a nonperiodic manner. By introducing a fuzzy state observer to reconstruct the system states, an observer-based event-triggered adaptive fuzzy control and a novel event-triggered condition are designed, simultaneously. In addition, the nonzero positive lower bound on interevent intervals is presented to avoid the Zeno behavior. It is proved via an extension of the Lyapunov approach that ultimately bounded control is achieved for the leader-following consensus of the considered multiagent systems. One remarkable advantage of the proposed control protocol is that the control law and fuzzy weights are updated only when the event-triggered condition is violated, which can greatly decrease the data transmission and communication resource. The simulation results are provided to show the effectiveness of the proposed control strategy and the theoretical analysis.

Output Regulation for a Class of Uncertain Nonlinear Time-delay Systems by Output Feedback Control

This paper is concerned with the output regulation problem for a class of uncertain nonlinear systems with time-delay and immeasurable states. The nonlinear system is driven by an unknown linear system. By virtue of solutions of regulator equation and canonical internal model, the output regulation problem is converted to a stabilization problem of the augmented system. A novel fuzzy state observer independent of time-delay is proposed and the fuzzy adaptive output feedback controller and adaptive law are constructed such that all the solutions of the closed-loop system are ultimately uniformly bounded, and the tracking error e can asymptotically converge to a small neighborhood of the origin. Moreover the Lyapunov-krasovskii functional is chosen such that the stability analysis of the system can be performed. Finally a simulation example is provided to prove the efficiency of the proposed method.

Observer-Based Fuzzy Adaptive Event-Triggered Control for Pure-Feedback Nonlinear Systems With Prescribed Performance

This paper studies the problem of fuzzy adaptive event-triggered control for a class of pure-feedback nonlinear systems, which contain unknown smooth functions and unmeasured states. Fuzzy logic systems are adopted to approximate unknown smooth functions and a fuzzy state observer is designed to estimate unmeasured states. Via the event-triggered control technique, the control signal of the fixed threshold strategy is obtained. By converting the tracking error into a new virtual error variable, an observer-based fuzzy adaptive event-triggered prescribed performance control strategy is designed. The key advantage is that the proposed method does not require a priori knowledge of partial derivatives of system functions, i.e., it relaxes the restrictive condition that the partial derivatives of system functions need to be known for pure-feedback nonlinear systems. Simulation results confirm the efficiency of the proposed method.

Observer-Based Fuzzy Adaptive Dynamic Surface Control of Uncertain Nonstrict Feedback Systems With Unknown Control Direction and Unknown Dead-Zone

In this paper, an observer-based fuzzy adaptive controller for a class of uncertain nonstrict nonlinear systems with unknown control direction and unknown dead-zone is presented. First, by using equivalence dead-zone inverse and a linear state transformation, the original system is converted to a new one. Then, by using fuzzy logic systems, the unknown nonlinearities are approximated based on an adaptive mechanism, and a nonlinear fuzzy state observer is designed to estimate immeasurable states. The dynamic surface control technique is employed to solve the problem of explosion of complexity in the traditional backstepping approach, and then, this method is combined with Nussbaum gain function to address the problem of unknown control direction. Besides, barrier Lyapunov function is employed to overcome the violation of system output. The proposed controller guarantees that the closed-loop system is stable; all the system states are bounded, and tracking errors converge to a neighborhood of the origin. A numerical simulation is provided to confirm the usefulness of the proposed control design.

Observer-Based Adaptive Fuzzy Containment Control for Multiple Uncertain Nonlinear Systems

The adaptive fuzzy containment control problem is addressed for multiple uncertain nonlinear strict-feedback systems with immeasurable states and multiple leaders under directed communication graphs. By utilizing fuzzy logic systems to model the followers’ dynamics, a distributed fuzzy state observer is designed for the state estimation using only the relative position information. Then, an observer-based containment control scheme is constructed by the adaptive fuzzy control technique as well as the command filter. The filtering error loop is introduced to compensate the error arising from the command filter. The proposed adaptive fuzzy containment control scheme guarantees that all followers are driven into the dynamic convex hull spanned by the leaders with a bounded containment error, if there exists at least one of the leaders who has a directed path to the follower. Simulation results are given to illustrate the control performance of the proposed containment control method.

Barrier Lyapunov Function-Based Adaptive Fault-Tolerant Control for a Class of Strict-Feedback Stochastic Nonlinear Systems.

This article investigates the adaptive fuzzy fault-tolerant control problem for a class of strict-feedback stochastic nonlinear systems with quantized input signal. A hysteretic quantizer is utilized to avoid chattering caused by quantized input signals. The fuzzy-logic systems are utilized to approximate the unknown nonlinear functions and also to construct the fuzzy state observer, which is used to estimate the immeasurable state vector. The actuator faults considered in this article are loss of effectiveness and lock-in-place faults. By using the Lyapunov stability theory, the closed-loop stochastic nonlinear system is guaranteed to be stable in probability, and all the signals of the closed-loop system are bounded in probability in the presence of quantized input and actuator faults. Finally, a simulation example is given to verify the validity of the proposed control strategy.

Event-triggered adaptive consensus for fuzzy output-constrained multi-agent systems with observers

The problem of distributed adaptive event-triggered consensus tracking control is investigated for a class of output-constrained uncertain nonlinear multi-agent systems (MASs). With the help of fuzzy logic systems (FLSs), the unavailable states are estimated by constructing a fuzzy state observer. In order to mitigate communication burden, the adaptive event-triggered controller is presented by employing the backstepping approach and dynamics surface control (DSC) technique, which guarantees the boundedness of all system signals. In view of the possible poor transient performance resulting from discontinuous control signal under the event-triggered mechanism, the barrier Lyapunov function combining exponential function is introduced to obtain better transient performance of systems by solving an output constraint problem, where the convergence rates and convergence bounds of tracking errors are precisely guaranteed. Simulation results demonstrate the effectiveness of the presented method.

Adaptive hybrid fuzzy output feedback control for fractional-order nonlinear systems with time-varying delays and input saturation

This paper studies the issue of adaptive hybrid fuzzy output feedback control for a class of commensurate fractional-order (FO) nonlinear systems with time-varying delays and input saturation. First, a hybrid fuzzy state observer is designed to estimate the unmeasured system states, where the neuro-fuzzy network systems (NFNSs) are introduced to handle the unknown nonlinear functions. Furthermore, based on DSC technique, a modified FO filter is designed to avoid the issue of the “explosion of complexity” generated by the traditional backstepping control design approach. Moreover, based on the recursive technique and an indirect Lyapunov method, an adaptive controller is constructed to ensure that all the signals of FO closed-loop systems are bounded. Finally, the simulation results are presented to demonstrate the effectiveness of the presented control scheme.

Observer-based adaptive fuzzy prescribed performance control for feedback linearizable MIMO nonlinear systems with unknown control direction

This paper investigates the prescribed performance tracking control problem for a class of feedback linearizable multi-input and multi-output (MIMO) nonlinear systems with immeasurable states and unknown control direction. The fuzzy systems are employed to approximate the unknown nonlinear functions, an adaptive fuzzy state observer is developed to estimate the unmeasured states. By utilizing the state observer, an adaptive fuzzy output-feedback controller equipped with the Nussbaum-type function is developed to solve the unknown control direction issues. It is proved that all the signals in the closed-loop systems are bounded and that the prescribed performance error constraints can be achieved. Simulation examples are provided to highlight the effectiveness of the proposed approach.

Observer-based adaptive fuzzy funnel control for strict-feedback nonlinear systems with unknown control coefficients

This paper proposes an adaptive fuzzy funnel controller for a class of strict-feedback nonlinear systems with unknown control coefficients. A fuzzy state observer is designed to estimate the unmeasurable system states. An improved funnel error is given and embedded in the procedure of control design. Furthermore, based on the backstepping method, an observer-based adaptive fuzzy funnel controller is constructed, which can guarantee that the output tracking error remains in a pre-set funnel and converges to a prescribed interval in finite time as long as the initial error is in the funnel. All the signals in the closed-loop system are also semi-globally uniformly and ultimately bounded. Simulation results demonstrate the effectiveness of the developed controller.

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

SummaryThis 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.

Adaptive output‐feedback finite‐time stabilisation of stochastic non‐linear systems with application to a two‐stage chemical reactor

In this study, the authors investigate the problem of the stochastically finite-time stability analysis and control design of an adaptive single-input and single-output (SISO) uncertain stochastic non-linear system via establishing a new stability criterion. Owing to the unknown dynamics and unmeasured system variables, fuzzy logic systems and a fuzzy state observer are constructed and applied to identify the stochastic system, respectively. Combining the finite-time definition, stochastic differential equation and o^ formula, a novel stochastically finite-time stability theorem is raised in this study. By utilising the novel criterion and adaptive backstepping intelligent control, a stochastically finite-time control method is proposed. It is illustrated that the controlled stochastic system is semi-global finite-time stable in probability and behaves excellent convergence. The simulation results of a two-stage continuous stirred tank reactor process reveal the validity and efficiency.

Fuzzy-reconstruction-based robust tracking control of an air-breathing hypersonic vehicle

This paper proposes a novel control scheme to address the robust tracking control problem of an air-breathing hypersonic vehicle subject to unknown dynamics and immeasurable states. The whole control architecture is constructed by fuzzy logic system based on the decomposition of the vehicle dynamics into the velocity and altitude subsystem. In order to improve control precision, a nonlinear observer is designed to estimate and further compensate the approximation error of fuzzy logic system. In addition, a fuzzy state observer is proposed to estimate the immeasurable states and reconstruct the full states of the system. Through Lyapunov stability analysis, the closed-loop system is guaranteed to be semi-globally uniformly ultimately bounded. Moreover, the tracking and estimate errors converge to an arbitrary small neighborhood around zero. Extensive simulation and evaluations illustrate effectiveness of the proposed scheme.

Observer-based adaptive fuzzy tracking control for a class of MIMO nonlinear systems with unknown dead zones and time-varying delays

ABSTRACTThe adaptive tracking control strategy is investigated for a class of multi-input and multi-output pure-feedback nonlinear delayed systems with unknown dead-zone inputs. This problem is challenging due to the existence of unknown dead zones, time-varying delays and unavoidable state variables. By constructing fuzzy approximators and state observers, the difficulties from unknown nonlinearities and unavailable state variables are surmounted, respectively. Lyapunov–Krasovskii functions are introduced to deal with the time-varying delays. The adaptive controllers are designed by a backstepping method and adaptive technique so that the closed-loop systems remain stable and the target signals can be tracked within a small error as well. At last, two examples are provided to show the effectiveness of the proposed scheme.

Finite-Time Adaptive Fuzzy Output Feedback Dynamic Surface Control for MIMO Nonstrict Feedback Systems

This paper investigates the finite-time adaptive fuzzy control problem for a class of multi-input and multi-output (MIMO) nonlinear nonstrict feedback systems. During the control design process, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and fuzzy state observer is constructed to estimate the unmeasured states. By combining adaptive backstepping with the dynamic surface control (DSC) technique, a finite-time fuzzy adaptive control scheme is presented to overcome the “explosion of complexity” problem. The stability of the close-loop systems can be proved based on the finite-time Lyapunov stability theory. The presented control scheme demonstrates that the closed-loop systems are semiglobal practical finite-time stability, and tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to show the effectiveness of the presented control method.

Fuzzy State Observer‐Based Adaptive Dynamic Surface Control of Nonlinear Systems with Time‐Varying Output Constraints

In this paper, a new fuzzy dynamic surface control approach based on a state observer is proposed for uncertain nonlinear systems with time‐varying output constraints and external disturbances. An adaptive fuzzy state observer is used to estimate the states that cannot be measured in the systems. In our method, a time‐varying Barrier Lyapunov Function (BLF) is used to ensure that the output does not violate time‐varying constraints. In addition, dynamic surface control (DSC) technology is applied to overcome the problem of “explosion of complexity” in a backstepping control. Finally, the stability and signal boundedness of the system are confirmed by the Lyapunov method. The simulation results show the effectiveness and correctness of the proposed method.

Observer‐based adaptive control for nonlinear strict‐feedback stochastic systems with output constraints

SummaryIn this paper, an adaptive output‐feedback control problem is investigated for nonlinear strict‐feedback stochastic systems with input saturation and output constraint. A barrier Lyapunov function is used to solve the problem of output constraint. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. To overcome the difficulties in designing the control signal in the saturation, we introduce an auxiliary signal in the n + 1th step in the deduction. By combining Nussbaum technique and the adaptive backstepping technique, an adaptive output‐feedback control method is developed. The proposed control method not only overcomes the problem of the compensation for the nonlinear term from the input saturation but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed‐loop system are semiglobally uniformly ultimately bounded. Finally, the effectiveness of the proposed method is verified by the simulation results.

A new combined actuator fault estimation and accommodation for linear parameter varying system subject to simultaneous and multiple faults: an LMIs approach

This paper proposes a novel fuzzy observer scheme-based active fuzzy fault-tolerant tracking control (FFTTC) combined with a parallel distributed compensation control law for a linear parameter varying system subject to actuator faults and noise measurement. This system consists of a doubly fed induction generator-based wind energy conversion system described by a Takagi–Sugeno fuzzy model. The developed scheme is able to force system states to track their desired reference signal in finite time and obtain a better dynamic response and performance. A fuzzy state observer is also developed to simultaneously estimate the generator states and the actuator faults. Based on the obtained online fault estimation information, the FFTTC will be reconfigured to compensate for the fault impact. The closed-loop stability is established based on a Lyapunov function. Sufficient conditions are formulated for the existence of fuzzy fault-tolerant control parameters in the form of linear matrix inequalities (LMIs), which can be easily solved by means of a standard YALMIP toolbox. The fuzzy observer and fuzzy fault-tolerant tracking control gains can be computed based on the solutions of a set of LMIs. Computer simulations were performed using the MATLAB/Simulink environment to highlight the performance and robustness of the proposed design procedure with respect to actuator fault occurrences.

Observer-based adaptive fuzzy quantized control of uncertain nonlinear systems with unknown control directions

This paper studies the output-feedback tracking control problem for a class of strict-feedback systems with input quantization and unknown control directions. A coordinate transformation is first introduced such that the unknown control coefficients are lumped together and the studied system is transformed into an equivalent system. Subsequently, a high-gain fuzzy state observer is designed to estimate unmeasurable states. Based on the high-gain fuzzy state observer, the adaptive backstepping design procedure is proposed for the new defined system. Then, by introducing a Nussbaum function and a smooth function, the obstacle caused by unknown control direction and input quantization is successfully circumvented, and a coarse quantization can be achieved. Moreover, the proposed adaptive controller can guarantee that the closed-loop system is bounded, and the tracking error converge to a predefined small residue set. The main advantages of our method are that: first, the restrictions on system control gains are relaxed. Second, the controller design does not depend on the quantization parameter. Finally, simulation results are provided to illustrate the effectiveness and benefits of the proposed results.

Adaptive Fuzzy Output Feedback Control for a Class of Nonlinear Systems With Full State Constraints

In the paper, the adaptive observer and controller designs based fuzzy approximation are studied for a class of uncertain nonlinear systems in strict feedback. The main properties of the considered systems are that all the state variables are not available for measurement and at the same time, they are required to limit in each constraint set. Due to the properties of systems, it will be a difficult task for designing the controller and the stability analysis. Based on the structure of the considered systems, a fuzzy state observer is framed to estimate the unmeasured states. To ensure that all the states do not violate their constraint bounds, the Barrier type of functions will be employed in the controller and the adaptation laws. In the stability analysis, the effect caused by the constraints for all the states can be overcome by using the Barrier Lyapunov functions. Based on the proposed control approach, it is proved that the system output is driven to track the reference signal to a bounded compact set, all the signals in the closed-loop system are guaranteed to be bounded, and all the states do not transgress their constrained sets. The effectiveness of the proposed control approach can be verified by setting a simulation example.