Control Of Uncertain Nonlinear Systems Research Articles

Global practical tracking via disturbance rejection control for uncertain nonlinear systems with quantized input and output

Global practical tracking via disturbance rejection control for uncertain nonlinear systems with quantized input and output

Fuzzy adaptive output feedback control for uncertain nonlinear systems with unknown control gain functions and unmodeled dynamics

In this work, the fuzzy adaptive robust output feedback control issues are investigated for single-input single-output (SISO) strict-feedback nonlinear systems. The controlled systems under consideration of this paper contain the unknown control gain functions, unmodeled dynamics and immeasurable states. The unknown nonlinear functions are be approximated by utilizing the fuzzy logic systems, and the immeasurable states are estimated by constructing a new fuzzy state observer. In order to handle the unknown control gain functions and the unmodeled dynamics problems, the Logarithm Lyapunov functions are constructed, under which a new fuzzy adaptive robust output feedback control scheme is proposed by using the adaptive backstepping control design technique and a dynamical signal function. The designed fuzzy adaptive control algorithm can ensure that the closed-loop system is semi-globally uniformly ultimately boundedness (SGUUB) and has the robustness to the unmodeled dynamics. Finally, a simulation example is considered to illustrate the availability of the designed controller.

Neural networks-based adaptive control of uncertain nonlinear systems with unknown input constraints

In this work, we solve the adaptive actuator backlash compensation control problem of uncertain nonlinear systems. A new generalized backlash model is first proposed, which takes both the actuator perturbation and unidentifiable coupling into account, and hence captures the practical backlash behavior more accurately. Nevertheless, such a model makes the adaptive control design difficult, where the most challenging one is that the unrecognizable coupling makes traditional compensation structure no more feasible. To address this issue, we propose an adaptive compensation control structure synthesizing neural networks learning and novel smooth backlash inverse model. With the established compensator and the iterative control design of compensator input, an adaptive neural controller is subsequently proposed to guarantee that all signals of the closed-loop system are bounded, and the tracking error converges to residual of zero asympotically. Simulation results are given to verify the effectiveness of the proposed control scheme.

Control of nonlinear uncertain systems by extended PID with differential trackers

Control of nonlinear uncertain systems by extended PID with differential trackers

Resilient Observer-Based H ∞ Control of Uncertain Nonlinear Networked Control Systems

This paper considers the resilient H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> dynamic control of nonlinear uncertain systems over a network assuming random communication packet dropouts, a subject which is seldom considered in the current literature for such uncertain systems. The uncertainties in the system and the controller are real, time-varying and norm bounded. Bernoulli distribution with white sequence is used to model the random packet losses with assumed conditions on the probability distribution. The resilient controller designed is an observer-based dynamic. The resulted closed-loop system is exponentially mean square stable and the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is less than a prescribed level γ for all admissible uncertainties. New sufficient conditions for the existence of such a controller are presented and proved based on the linear matrix inequalities (LMIs) approach. A numerical example is presented to demonstrate and show the effectiveness of the developed theory.

Fuzzy rule-based neural appointed-time control for uncertain nonlinear systems with aperiodic samplings

In this paper, a fuzzy rule-based neural appointed-time control scheme for uncertain nonlinear systems with aperiodic samplings is proposed. To guarantee tracking properties with preassigned convergence time and remove the high dependency on accurate initial states of system, we construct an improved prescribed performance control (IPPC) scheme on the basis of a hyperbolic cosecant performance function with a finite-time behavior. In light of the unavailability of partial states and uncertainties, by combining a fuzzy wavelet neural network (FWNN) with a state observer, a FWNN-based state observer is developed, which can simultaneously approximate unavailable system states and unknown lumped disturbances with a remarkable accuracy. In addition, aimed at eliminating the problem of parameter updating explosion caused by overlarge learning dimensions, a minimum-learning-parameter (MLP) technique is embedded in the FWNN-based state observer, where the norm of weight matrix is employed for online adaptive updating. Furthermore, an event-triggered control scheme with relative thresholds is synthesized within the framework of dynamic surface control (DSC), which can allow for aperiodic samplings to save communication and actuating resources. Meanwhile, a Nussbaum type function is introduced to solve the issue of unknown control coefficients. The significant features of our work are twofold: (1) Appointed-time tracking performances with much fewer sampling times are assured. (2) An enhanced robustness against uncertainties is achieved with a lower computational complexity and the requirement of full-state measurements is relaxed. Finally, two simulation examples are performed to validate the effectiveness and advantages of the proposed control scheme.

Fuzzy Adaptive Two-Bit-Triggered Control for a Class of Uncertain Nonlinear Systems With Actuator Failures and Dead-Zone Constraint.

This article investigates a fuzzy adaptive two-bit-triggered control for uncertain nonlinear systems with actuator failures and dead-zone constraint. Actuator failures and dead-zone constraint exist frequently in practical systems, which will affect the system performance greatly. Based on the improved fuzzy-logic systems (FLSs), a fuzzy adaptive compensation control is established to address these issues. The approximation error is introduced to the control design as a time-varying function. In addition, for the limited transmission resources of the practical system, a two-bit-triggered control mechanism is proposed to further save system transmission resources. It is proved that the proposed method can guarantee the system tracking performance and all the signals are bounded. Its effectiveness is verified by the simulation examples.

Adaptive Asymptotic Tracking Control of Uncertain Nonlinear Systems Based on Taylor Decoupling and Event-Trigger

This article studies the robust adaptive asymptotic tracking control problem for uncertain nonlinear systems with event-triggered inputs. Contrary to the existing results, a novel nonaffine nonlinear control input separated design scheme is developed based on the Taylor decoupling technique instead of the previous approximation ways. Correspondingly, the augmented dimension parameter updated laws and the unknown bound estimation of the compounded disturbance with a positive continuous integrable function are skillfully introduced. Also, by introducing a suitable decreasing function of tracking error variables, an improved adaptive event-triggered mechanism is constructed to achieve the asymptotic tracking and the communication load can be effectively alleviated. Moreover, it is shown that all the signals in the closed-loop system are uniformly bounded and the tracking errors converge to zero in a preset compact set. Finally, the validity of the proposed method is illustrated by simulation on an inverted pendulum model.

Improved Function Augmented Sliding Mode Control of Uncertain Nonlinear Systems with Preassigned Settling Time

This paper investigates the robust tracking control of second-order uncertain nonlinear systems by adopting the function augmented sliding mode control approach. An improved version of this approach is proposed such that the exact information of the initial tracking error is not required when generating the desired trajectory of the tracking error. This evidently enlarges the application scope of the function augmented sliding mode control approach. Performance functions are introduced to form the performance envelopes for the sliding mode variables. A robust sliding mode controller is constructed such that the sliding mode variables are confined within their performance envelopes. This further guarantees that the tracking error converges to the given neighbourhood of zero within the preassigned settling time provided that proper control parameters are selected. An application example on the rendezvous control of spacecraft is also employed to illustrate the effectiveness of the proposed control approach.

Robust stabilization control for uncertain nonlinear systems based on two-step coprime factorization

In this paper, nonlinear control for dealing with a class of uncertain nonlinear systems is discussed according to operator-based coprime factorization method. In detail, firstly, for guaranteeing internal-output stability of nominal nonlinear systems with left factorization, a simple and effective design scheme is proposed with a weak assumption. Simultaneously, based on the proposed scheme, the given nominal nonlinear systems are proved to be coprime. Secondly, tracking performance of the considered systems is obtained by designing a suitable Bezout identity without complicated calculation on the obtained left factorization. Thirdly, with respect to the considered nonlinear system, when it comes to appear perturbation, different adverse effects resulting from different perturbation are considered to guarantee robust stability. For the two different cases, two suffcient conditions using inherent characteristics are proposed for guaranteeing robust stability. Finally, two examples are shown to confirm effectiveness of the proposed design scheme of this paper.

Saturated adaptive backstepping control of uncertain nonlinear systems with validation using twin rotor system

This work investigates the semi-global tracking control of a class of uncertain nonlinear systems with input saturation, using adaptive backstepping controller and tuning function design. The control input has been represented as a product of a positive constant and a generalized saturation function of unit magnitude, where the constant parameter represents the saturation bound of the available input signal. It has been shown that the overall saturation problem can be realized as an equivalent problem involving no saturation if the system satisfies a sufficient condition. The condition represents a relationship between the saturation bound of the input signal and the upper bounds of tracking errors, disturbances, and uncertainties. To realize this fact physically, the proposed control algorithm has been implemented on a Twin Rotor Multi Input Multi Output System (TRMS). Experimental and simulation outcomes illustrate the validation of the derived control methodology along with robustness and performance analysis.

Event‐triggered adaptive finite‐time prescribed performance tracking control for uncertain nonlinear systems

SummaryThis article addresses the problem of adaptive finite‐time tracking control for unknown nonlinear systems based on event‐triggered and prescribed performance control. For the first time, a new adjustable finite‐time performance function is developed, whose parameters are adjusted online with the change of tracking errors so that it converges faster. Besides, a novel event‐triggered control method is introduced to switch smoothly between the fixed and relative threshold strategies. Finally, an adaptive finite‐time tracking controller is constructed, which ensures the boundness of all the signals in the closed‐loop system and elimination of the Zeno behavior. Simultaneously, the output tracking error falls in a fixed region at pre‐defined finite time.

Fixed-Time Adaptive Fuzzy Control for Uncertain Nonlinear Systems

Most current methodologies on fixed-time adaptive fuzzy control for uncertain nonlinear systems result in practical fixed-time stability but not fixed-time stability, or require prior knowledge of the system dynamics. To obviate such restrictions, a fixed-time adaptive fuzzy control scheme is newly proposed with the discoveries of a singularity-avoidance virtual control design, a modified class of tuning functions and a projection operator-based adaptation mechanism. Fixed-time stability is established in the sense that the tracking error asymptotically converges to a user-defined interval within a prescribed fixed time. Illustrative examples verify the approaches developed.

Adaptive nonsingular proportional–integral–derivative-type terminal sliding mode tracker based on rapid reaching law for nonlinear systems

This article deals with a novel adaptive robust controller for uncertain nonlinear systems relying on a proportional–integral–derivative-type nonsingular fast terminal sliding mode control. In this nonsingular proportional–integral–derivative-type terminal sliding mode controller nonsingular fast terminal sliding mode control, the nonsingular fast terminal sliding mode control sliding surface is modified with integral to match with the proportional–integral–derivative-type structure to obtain the essential attributes, namely, quick transient response, finite-time convergence, negligible steady-state error, and chattering cancellation. Furthermore, a novel rapid reaching law is also suggested with dynamic proof for providing the robustness during transient phase. The controller stability and convergence is mathematically analyzed using the Lyapunov theory. The overall control structure is simulated on MATLAB® software and tested for trajectory tracking of a two-degree-of-freedom revolute–prismatic joint industrial robotic manipulator. The rigorous test results show the performance efficacy of the innovative controller.

Event-triggered neural intelligent control for uncertain nonlinear systems with specified-time guaranteed behaviors

In this paper, an event-triggered neural intelligent control for uncertain nonlinear systems with specified-time guaranteed behaviors is proposed. To cope with constrained communication resources, an event-triggered mechanism using switched thresholds is devised without involving input-to-state stability assumption, such that a better design flexibility and freedom can be provided. In addition, a minimum-learning-parameter-based state observer is developed to online estimate the unavailable states and uncertainties at the same time, which effectively eliminates the issue of learning explosion without sacrificing the identification precision. Furthermore, in pursuit of making a compromise between sampling cost and tracking performance, a modified barrier Lyapunov function based on a time-varying finite-time behavior boundary is constructed in the controller design, which can guarantee that the tracking error converges to a predetermined region within a specified time. Then by introducing the Nussbaum gain technique to handle the unknown control direction, an event-triggered neural output feedback control strategy is synthesized within the framework of dynamic surface control. Meanwhile, with the aid of Lyapunov synthesis, all the signals involved in the closed-loop system are proved to be bounded while Zeno phenomena is circumvented, and system outputs are well within the predefined region. Finally, an application on control design for a micro-electro-mechanical system gyroscope is given to validate the efficiency and superiority of proposed intelligent control scheme.

Adaptive event-triggered fuzzy tracking control of nonlinear systems with dead-zones and unmeasurable states

In this paper, the adaptive event-triggered tracking control of uncertain nonlinear systems with dead-zone inputs is developed based on fuzzy approximation technique. Firstly, a robust fuzzy state observer is constructed to effectively estimate all the unmeasurable states. Next, an adaptive output feedback controller with parameter updated law only containing one on-line adjusted variable is designed via the backstepping scheme. Concomitantly, a novel event-triggered condition related to the upper and lower bounds of dead-zone parameters and the decreasing function of tracking errors is given to substantially alleviate the computation load of the communication process. Moreover, the desired closed-loop stability of the resulting systems can be achieved by exploiting Lyapunov function analysis. Finally, simulation results verify the effectiveness of the proposed method.

Event-triggered adaptive prescribed performance control of uncertain nonlinear systems with unknown control directions

The problem of event-triggered prescribed performance control for a class of uncertain nonlinear systems with unknown control directions and faults is investigated. Compared with the existing methods, a new set of error transformation functions is defined for the first time. Although no approximate structure is adopted, prescribed performance control (PPC) and event triggered control (ETC) are realized simultaneously for the nonlinear system considered in this paper for the first time. The proposed control scheme can guarantee that all closed-loop signals are bounded, and the tracking error, as well as all state errors, converges within the adjustable constraint functions. Finally, two simulation experiments verify the effectiveness of the proposed algorithm.

Adaptive inverse multilayer fuzzy control for uncertain nonlinear system optimizing with differential evolution algorithm

This paper introduces a novel adaptive inverse multilayer T-S fuzzy controller (AIMFC) optimally identified with an optimization soft computing algorithm available for a class of robust control applied in uncertain nonlinear SISO systems. The parameters of multilayer T-S fuzzy model are optimally identified by the differential evolution (DE) algorithm to create offline the inverse nonlinear plant with uncertain coefficients. Then, the adaptive fuzzy-based sliding mode surface is applied to ensure that the closed-loop system is asymptotically stable in which the stability is satisfied using Lyapunov stability concept. The control quality of the proposed AIMFC algorithm is compared with the three recent advanced control algorithms applied in the Spring-Mass-Damper (SMD) benchmark system. Simulation and experiment results with different control parameters show that the proposed algorithm is better than the inverse fuzzy controller and the conventional adaptive fuzzy controller comparatively applied in both SMD system and the coupled-liquid tank system with the performance index using the least mean squares (LMS) error, which is investigated to demonstrate the efficiency and the robustness of the proposed AIMFC control approach.

Adaptive Output Feedback Funnel Control of Uncertain Nonlinear Systems With Arbitrary Relative Degree

This article considers the problem of output feedback funnel control for a class of uncertain nonlinear systems with arbitrary known relative degree. By utilizing the funnel control approach with a barrier Lyapunov function, a novel adaptive output feedback controller is constructed recursively, which accomplishes the output tracking with prescribed transient behavior. The developed control scheme features that the precise knowledge of system nonlinearities, including generally required bounding functions, is not needed. A physical example is performed to verify the effectiveness of the proposed theoretical findings.

Hybrid fuzzy direct/indirect adaptive controller for uncertain nonlinear systems

This paper describes a new approach to adaptive control of uncertain nonlinear systems. A fuzzy logic controller is used to combine both direct and indirect methods. Based on the fuzzy neural networks, the plant unknown nonlinear functions are estimated, and then combined to form the indirect control law. In parallel, another fuzzy neural network approximates the direct adaptive control. According to the modelling error and its derivatives, the fuzzy logic controller modulates between direct and indirect adaptive controllers. The global stability of the overall system is shown by constructing a Lyapunov function. The simulation results show that within this scheme, the control objectives can be achieved with a fast convergence and optimal control for different dynamic regimes.