Output Feedback Tracking Control Problem Research Articles

Output Feedback Adaptive Optimal Control of Multiple Unmanned Marine Vehicles with Unknown External Disturbance

This paper presents an optimal output-feedback tracking control problem for multiple unmanned marine vehicles (UMVs) to track a desired trajectory. To guarantee the control objective in an optimal manner, adaptive dynamic programming (ADP) with optimal compensation terms is adopted. A neural velocity observer is designed based on a neural network (NN) to estimate the unmeasured system states and the unknown system dynamics. Furthermore, a disturbance observer (DO) is proposed to go against the effect of the unknown external disturbance of the sea environment. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded. Simulation results are given to demonstrate the effectiveness of the proposed control algorithm.

Global practical tracking for uncertain nonlinear systems with unknown control coefficients and polynomial growth

This paper studies the problem of global output-feedback tracking control for a class of uncertain nonlinear systems. The system studied in this paper has unknown time-varying control coefficients and unknown reference signal. Notably, the nonlinearities of the system are bounded by the lower triangular linear unmeasured states multiplying the unknown constant, the polynomial-of-output and the polynomial-of-input growth rates, which indicates the presence of serious uncertainties. Motivated by the closely related works, by combining the ideas of universal control and deadzone with backstepping technique, this paper presents a new adaptive tracking control scheme based on two dynamic high-gains in the new forms. The proposed control scheme ensures that the tracking error converges to a specified arbitrarily small interval range after a finite time while the state of the resulting closed-loop system is globally bounded. Finally, the effectiveness of the control scheme is verified by an illustrative example.

Output Feedback Tracking Control for Vessel with Collision-Avoidance and Performance Constraints

This manuscript investigates an output feedback-tracking control problem of a dynamically positioned vessel with an input constraint. The vessel is exposed to model uncertainty and external disturbances. Compared with the existing results, the primary contribution is to develop a switch-control strategy for achieving collision avoidance and performance constraints by using an extended state observer (ESO), a collision-avoidance controller (CAC), a prescribed performance controller, and an auxiliary dynamic system (ADS). The switch control strategy combined two different controllers, and an extended state observer (ESO) is designed. The ESO is employed to recover velocity information as well as unknown model uncertainty and external disturbances. A collision-risk-analysis module is introduced to evaluate whether there exists a risk of collision avoidance. Based on the analysis, the CASC can choose between a CAC and a PPC. An ADS is constructed to handle the input constraints. The CAC is employed by using an artificial potential function, the ADS, and the ESO. The PPC is designed based on an error constraint function, the ADS, and the ESO. The stability of the closed-loop control system is analyzed based on the Lyapunov direct method. Simulations prove the effectiveness of the presented control strategy.

Optimal Fuzzy Output Feedback Control for Dynamic Positioning of Vessels With Finite-Time Disturbance Rejection Under Thruster Saturations

This paper focuses on the problem of optimal fuzzy output-feedback tracking control for dynamic positioning of marine vessels simultaneously with model uncertainties, unknown disturbances, unavailable velocities and thruster saturations. The control scheme is built by integrating a fuzzy velocity observer, a finite-time disturbance observer, a dynamic auxiliary system, the optimal control strategy with the dynamic surface control. The fuzzy velocity observer is constructed to obtain the unavailable velocities without requiring the certain model dynamics. The finite-time disturbance observer is established to estimate the unknown disturbances. The dynamic auxiliary system is designed to compensate for thruster saturations effects. By incorporating these methods, a disturbance rejection adaptive controller is designed with dynamic surface control. The optimal compensation term is inserted to minimize the cost function of the tracking error system by adaptive dynamic programming. It is shown that the optimal control consisting of the adaptive controller and the optimal compensation term guarantees that all signals in the closed-loop dynamic positioning system are bounded. Finally, simulation results demonstrate the effectiveness of the proposed optimal control scheme.

Reduced-Order Observer-Based Output-Feedback Tracking Control for Nonlinear Time-Delay Systems With Global Prescribed Performance.

In this article, the output-feedback tracking control problem is considered for a class of nonlinear time-delay systems in a strict-feedback form. Based on a state observer with reduced order, a novel output-feedback control scheme is proposed using the backstepping approach, which is able to guarantee the system transient and steady-state performance within a prescribed region. Different from existing works on prescribed performance control (PPC), the present method can relax the restriction that the initial value must be given within a predefined region, say, PPC semiglobally. In the case that the upper bound functions for nonlinear time-delay functions are unknown, based on the approximate capacity of fuzzy-logic systems, an adaptive fuzzy approximation control strategy is proposed. When the upper bound functions are known in prior, or in a product form with unknown parameters and known functions, an output-feedback tracking controller is designed, under which the closed-loop signals are globally ultimately uniformly bounded, and tracking control with global prescribed performance can be achieved. Simulation results are given to substantiate our method.

Observer-Based Dynamic Event-Triggered Control for Multiagent Systems With Time-Varying Delay

This article is concerned with the dynamic event-triggered-based adaptive output-feedback tracking control problem of nonlinear multiagent systems with time-varying input delay. By utilizing the approximation capability of neural network (NN), a low-gain nonlinear observer is first established to estimate the immeasurable states. To mitigate the effect of time-varying input delay, an auxiliary system with communication information is designed to generate the compensation signals. Then, a distributed adaptive composite NN dynamic surface control (DSC) strategy is proposed to acquire the satisfactory tracking accuracy, where the filter errors are compensated by the introduced serial-parallel estimation model. Moreover, an effective switching dynamic event-triggered mechanism is developed to determine the communication instants and reduce the update frequency of the controller. It is proven that the consensus tracking error converges to a residual set of the origin. Finally, simulation results are presented to demonstrate the effectiveness of the proposed composite NN DSC scheme.

Non-Fragile Fuzzy Tracking Control for Nonlinear Networked Systems with Dynamic Quantization and Randomly Occurring Gain Variations

This paper investigates the observer-based non-fragile output feedback tracking control problem for nonlinear networked systems with randomly occurring gain variations. The considered nonlinear networked systems are represented by a Takagi–Sugeno (T–S) fuzzy model. The dynamical quantization methodology is employed to achieve the reasonable and efficacious utilization of the limited communication resources. The objective is to design the observer-based non-fragile output feedback tracking controller, such that the resulting system is mean-square asymptotically stable with the given H∞ tracking performance. Based on the descriptor representation strategy combined with the S-procedure, sufficient conditions for the existence of the desired dynamic quantizers and observer-based non-fragile tracking controller are proposed in the form of linear matrix inequalities. Finally, simulation results are provided to show the effectiveness of the proposed design method

Output feedback tracking control for polynomial nonlinear systems with measurement noises and mismatched disturbances

In this paper, the output feedback tracking control problem is investigated for polynomial nonlinear systems (PNSs) with measurement noises and mismatched disturbances. First, in order to suppress measurement noises, a polynomial observer is introduced to simultaneously estimate states and mismatched disturbances. Next, based on the idea of backstepping control, a novel output feedback controller is designed for PNSs to compensate mismatched disturbances. Command filters are employed to avoid the repeated derivatives of virtual control and measurement noises in the recursive controller design. Then, a sufficient condition in terms of the parameter-dependent linear matrix inequality (PDLMI) is derived to guarantee the boundedness of tracking errors and estimation errors. By utilizing the sum of squares (SOS) decomposition technique, the PDLMI is solved to obtain desired controller parameters. Finally, an example of dynamic point-the-bit rotary steerable drilling tool system is performed to demonstrate the effectiveness and feasibility of the proposed strategy.

Global Output-Feedback Prescribed Performance Control of Nonlinear Systems With Unknown Virtual Control Coefficients

This article is concerned with the output-feedback tracking control problem for a class of nonlinear systems. The challenge lies in how to drive the tracking error to a prescribed region in a given time globally, under both unknown nonlinear functions and unknown virtual control coefficients. To deal with the unknown control direction, an orientation function is exploited in lieu of the Nussbaum gain technique, the supervisory switching strategy, and the parameter estimation approach. To attain global tracking performance, a tuning function is employed to adjust the tracking error, and a barrier function is used to combat this error. The resulting controller guarantees the prescribed tracking performance and the boundedness of the signals in the closed loop for any initial condition.

Switched-observer-based adaptive neural networks tracking control for switched nonlinear time-delay systems with actuator saturation

This paper deals with adaptive neural networks (NNs) output-feedback tracking control problem for a general class of switched nonlinear time-delay systems with actuator saturation. To estimate unmeasurable states, a constructive delay-independent switched-observer-based adaptive NNs control approach for solving the problem is provided by using the average dwell time (ADT) method and the backstepping technique. Design obstacles stemmed from unknown time delays and actuator saturation and unknown nonlinear functions are overcome by using appropriate multiple Lyapunov–Krasovskii functionals method, the Nussbaum gain technique, and neural network approximations, respectively. The proposed control strategy guarantees that i) all the closed-loop signals for the switched system are bounded in the semi-global sense under a class of switching signals with ADT, attaining semi-global uniformly ultimately boundedness (SGUUB); and, ii) the output tracking error is driven towards, and kept within, a small neighbourhood around the origin. Simulation results verify the effectiveness of the proposed control strategy on two numerical examples, including a practical switched continuous stirred tank reactor (CSTR) system.

Active disturbance rejection adaptive output feedback control of uncertain nonlinear systems

AbstractThis article concerns the output feedback tracking control problem for a class of single‐input‐single‐output (SISO) nonlinear systems in a semistrict feedback form, which possesses both matched and mismatched uncertainties, including parametric uncertainties and unknown nonlinear disturbances. An active disturbance rejection adaptive output feedback control scheme is proposed via backstepping method, in which parametric uncertainties are handled by adaptation law and disturbances are estimated by a series of linear extended state observers (LESOs). The learning burden of LESOs is much alleviated due to active compensation of parametric uncertainties via adaptation. In addition, both matched and mismatched disturbances are estimated in the construction of LESO for each channel of the considered nonlinear plant. Hence, all various of uncertainties can be mostly compensated. Consequently, prescribed transient performance and steady‐state tracking accuracy can be guaranteed. Theoretical analysis reveals the tracking error can be made arbitrarily small. Furthermore, exponentially asymptotic output tracking can be achieved when unknown disturbances are constants. Finally, comparative simulation studies are presented to illustrate the effectiveness of the proposed scheme.

Quantized Static Output Feedback Fuzzy Tracking Control for Discrete-Time Nonlinear Networked Systems With Asynchronous Event-Triggered Constraints

In this article, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> static output feedback tracking control problem is studied for discrete-time nonlinear networked systems subject to quantization effects and asynchronous event-triggered constraints. The Takagi-Sugeno (T-S) fuzzy model is utilized to represent the investigated nonlinear networked systems. A novel asynchronous event-triggered strategy is given to reduce the network communication burdens in both communication channels from the plant to the controller and from the reference model to the controller. The objective of this article is to design a quantized event-triggered tracking controller such that the resulting system is asymptotically stable and the given <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking performance is guaranteed. The sufficient design conditions for the tracking controller are formulated in the form of the linear matrix inequalities (LMIs). Furthermore, a simulation example will be utilized to show the effectiveness of the developed design strategy.

Neural network-based adaptive tracking control for switched nonlinear systems with prescribed performance: An average dwell time switching approach

This article investigates a problem of adaptive neural output-feedback tracking control for a class of switched uncertain nonlinear systems in nonstrict-feedback structure with average dwell time. For the system under study, many factors are taken into consideration, such as unknown nonlinearities, unmeasurable states, external disturbance, unknown dead-zone input, and prescribed performance bounds. A switched NN state observer is established to observe the unmeasurable states and alleviate the conservativeness induced by taking advantage of a common observer. In order to defeat the trouble originated from the nonstrict-feedback structure, an effective adaptive law is introduced by adopting the properties of NNs. The influence of dead-zone on control performance is restricted by designing a special adaptive law in the last step of the backstepping design frame. The stability of the closed-loop system is proved by average dwell time approach and Lyapunov stability theory. By utilizing the multiple Lyapunov function method and the backstepping technique together with the prescribed performance bounds, an adaptive NN controller is established which can ensure that all the signals in the closed-loop system are bounded under a class of switching signals with average dwell time and the tracking error converges to the predefined bounds. The feasibility of the presented control scheme is illustrated by the simulation results.

On Designing Event-Triggered Output Feedback Tracking Controller for Feedforward Nonlinear Systems

This brief investigates the output feedback tracking control problem for feedforward nonlinear systems subject to event-triggered input. Different from the existing results, it is the first time that an output feedback tracking control algorithm is proposed for feedforward nonlinear systems based on the relative threshold strategy. To estimate the unmeasured states, a novel dynamic observer is designed by using the information of the output and the tracking signal. By the low gain scaling technique, the event-triggered controller is designed based on the observer, which avoids the celebrated forwarding construct approach. Based on the constructed controller and the dynamic low gain, it is proved that all signals of the closed-loop system are globally bounded and the tracking error converges to a prescribed compact set and the Zeno-behavior is avoided. The novelty owes to a distinct perspective in coping with the measurement error such that the linear matrix inequality can be used in the design procedure. The effectiveness of the proposed algorithm is showed by a circuit system.

Switched-observer-based adaptive DSC design of nonstrict-feedback switched stochastic nonlinear time-delay systems

For switched stochastic nonlinear systems with time delay, an adaptive output-feedback tracking control problem is studied by using the dynamic surface control (DSC) method associated with a switched state observer. The time-varying delay terms are handled by constructing an appropriate stochastic Lyapunov–Krasovskii functional. The unknown nonlinearities in the considered systems are adaptively approximated by the function approximation approach—neural networks (NNs). It is shown that, under the average dwell time (ADT) method, the semiglobal uniformly ultimately boundedness (SGUUB) is guaranteed for all closed-loop signals by the developed switched controllers of different subsystems even in the presence of time delay, meanwhile, the tracking error is confined to a small residual set. A practical system example and a numerical example are provided to demonstrate the efficacy of the proposed scheme.

Anti-Disturbance Output Feedback Tracking Control for Switched Stochastic Systems With Multiple Disturbances via Mode-Dependent Average Time Method

The anti-disturbance output feedback tracking control problem is addressed for switched stochastic systems with multiple disturbances in this article. To deal with unknown disturbances and unmeasurable states, composite disturbance observer and state observer are designed simultaneously. Then, an output feedback tracking controller is designed based on outputs of two observers. By employing multiple Lyapunov function method, some sufficient conditions are given to analyse the mean square exponential stability with weighted H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for the closed-loop system. Furthermore, the controller and observer gains are solved by linear matrix inequalities. At last, the validity of the presented scheme is demonstrated via two examples.

Adaptive fuzzy output-feedback fault-tolerant tracking control of a class of uncertain nonlinear switched systems

ABSTRACT This paper considers the output-feedback fault-tolerant tracking control problem for a class of uncertain nonlinear switched systems with nonlinear faults and strict-feedback form, where the faults which are nonaffine occur on the actuator. As a kind of specialised function approximating tool, fuzzy logic systems (FLSs), are employed to approximate the unknown smooth nonlinear functions. A switched fuzzy observer is designed to address the problem of unmeasurable states, filtered signals are used to address algebraic loop problem and the average dwell time (ADT) method is further utilised to prove the stability of the resulting closed-loop systems under a type of slowly switching signals. Based on the backstepping recursive design technique and Lyapunov function method, an adaptive fuzzy output-feedback control scheme is developed. The developed control method can ensure all the signals are semi-globally uniformly ultimately bounded (SGUUB) and the system output tracks the reference signal tightly even if unknown fault occurs. A simulation carried on an example demonstrates the validity of the obtained control scheme.

Practical tracking control for stochastic nonlinear systems with polynomial function growth conditions

This paper mainly focuses on an output feedback practical tracking controller design for a class of stochastic nonlinear systems with polynomial function growth conditions. Mostly, there are some studies on an output feedback tracking control problem for general nonlinear systems with polynomial function growth conditions in existing achievements. Moreover, we extend it to stochastic nonlinear systems and construct an output feedback practical tracking controller based on dynamic and static phase combined, ensuring that all the states of the stochastic nonlinear system are bounded and the system tracking error can be made arbitrarily small after some large enough time. Finally, a simulation example is provided to illustrate the efficiency of the theoretical results.

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.

Less conservative output‐feedback tracking control design for polynomial fuzzy systems

In this study, the problem of output-feedback tracking control for polynomial-fuzzy-model-based systems is studied. In this problem, the objective is to drive the system states of a non-linear plant to follow the states of a given reference model using a fuzzy controller. The design problem is formulated as a sum-of-squares (SOS) optimisation, which can be solved efficiently using semidefinite programming. Here, unlike previous SOS-based tracking control approaches, Lyapunov matrix depends on all of the system states, which decreases the conservatism of the stability criteria. Moreover, the SOS conditions are derived to guarantee the system stability subject to a given H∞ performance. Two simulation examples are given to demonstrate the effectiveness and benefits of the proposed method.