Adaptive Tracking Control Approach Research Articles

Composite‐observer‐based asynchronous control for hidden Markov nonlinear systems with disturbances

SummaryIn this article, an asynchronous adaptive tracking control approach is presented for a type of hidden Markov jump nonlinear systems with external disturbances. In this joint jump process model, hidden Markov model signifies the dynamics of the actual system, whereas the signal emits from the detector symbolizes the transmitted information. This leads to the phenomenon of asynchronization between the modes of the system and that of the controller. Accordingly, an asynchronous observer is developed by using the mode information from the detector to develop an asynchronous control approach. The observer contains a disturbance estimation part, to compensate the unknown external inputs. Utilizing the backstepping scheme, a strict‐feedback asynchronous tracking controller is formulated, guaranteeing that all signals within the closed‐loop system are semi‐globally uniformly ultimately bounded in probability. Finally, the validity of the presented methodology is illustrated by means of a simulation example.

A finite-time path-tracking control algorithm for nonholonomic mobile robots with unknown dynamics and subject to wheel slippage/skid disturbances

Path planning and tracking control are two performance-critical tasks for wheeled mobile robots, particularly when nonholonomic constraints are imposed on robots in dynamically uncertain conditions. Accomplishing certain performance and safety considerations related to path-tracking, such as global stability, transient performance, and smooth finite-time convergence, becomes more difficult for nonholonomic robots. This paper is concerned with proposing a new adaptive robust finite-time tracking control approach for a large class of differential drive autonomous nonholonomic wheeled mobile robots (NWMRs) that are subject to structured uncertainties and extraneous disturbances with fully unknown dynamics. For this purpose, nonlinear kinodynamics of a type of rear-wheel drive NWMRs are developed by incorporating the skid/slippage constituents of the wheel motion. Then, a path-tracking controller is proposed using a continuous finite-time adaptive integral sliding mode control coupled with an integral backstepping approach (FTAISM-IBC). For the adaptive controller design, the entire nonlinear dynamics of the robot, including nonlinear vector functions and control gain functions, together with extraneous disturbances, are estimated by leveraging the universal approximation capabilities of radial basis neural networks (RBFNNs). The finite-time stability proof is presented by utilizing the Lyapunov stability theorem. Furthermore, the adaptive gains are derived to ensure the finite-time stability of the system subject to unknown functions, parametric variations, and unknown but bounded disturbances. Finally, the effectiveness of the proposed controller is evaluated through simulations in terms of several key performance indicators against several reported studies.

Adaptive Trajectory Tracking Control for the Quadrotor Aerial Transportation System Landing a Payload Onto the Mobile Platform

Recently, it is becoming increasingly possible to apply aerial transportation systems to real-world applications. However, current researches on cable-suspended transportation systems present practical limitations due to the fixed-length cable. With the introduction of the cable adjustment mechanism, various complicated tasks, such as limited space crossing, offshore sample collection, and even landing the payload on a mobile platform, can be accomplished by actively changing the distance between the quadrotor and the payload. In order to complete the aforementioned tasks, a trajectory tracking control method is in urgent need for the variable-length-cable-suspended aerial transportation systems. To this end, an adaptive tracking control approach with the consideration of unknown resistance coefficients is designed in this paper. Subsequently, Lyapunov techniques and Barbalat's Lemma are utilized to prove the convergence for the equilibrium point of the closed-loop system. Finally, hardware experiments are meticulously conducted based on a self-built experimental platform, which verify the satisfactory performance of the proposed method in anti-swing aerial transportation and payload landing onto the mobile platform.

Adaptive constrained tracking control for dynamical actuator driven linear 2 × 2 hyperbolic PDE systems with nonlinear uncertainties

The paper develops an adaptive constrained tracking control technique for a class of 2 × 2 hyperbolic partial differential equation (PDE) systems with boundary actuator dynamics, which are described by a set of ordinary differential equations (ODEs) in the presence of unknown parametric nonlinearities. Since the control input only appears in the uncertain ODE subsystem rather than directly on the boundary of PDE subsystem, the control task becomes quite difficult and the existing direct boundary control approaches are ineffective. Moreover, in this paper, a more challenging problem is considered such that the controlled output and the states of ODE actuators are constrained. To this end, by utilizing finite and infinite dimensional backstepping techniques, barrier Lyapunov functions (BLFs) and adaptive methods, a novel adaptive tracking control approach is proposed. It is the first time that such a constrained tracking control problem is addressed for the PDE-ODE coupled systems considered in this paper. On the basis of the presented method, the rigorous theoretical proof is provided to show that the PDE controlled output and all the states of the ODE actuator stay within the predefined compact sets. Finally, the results are illustrated via a comparative numerical simulation.

Adaptive asymptotic tracking control of autonomous underwater vehicles based on Bernstein polynomial approximation

In this article, an adaptive asymptotic tracking control approach is first proposed for the autonomous underwater vehicle (AUV) on the horizontal plane by using the Bernstein polynomial approximation. Bernstein polynomials aim to compensate for the synthetical uncertainties including unknown model dynamics and environmental disturbances. However, they cannot be directly used due to the unknown polynomial coefficients. To avoid this trouble, the adaptive backstepping technique is applied to estimation. Considering that the adaptive backstepping can only procure the bounded steady tracking errors and suffer from the redundancy of adaptive parameters, we further integrate the σ-modification and the minimum learning parameter (MLP) technique with the Bernstein polynomial approximation, so as to guarantee the high-precision tracking performance of AUVs with the asymptotic convergent tracking errors and less computation burden. The direct Lyapunov’s method and the Barbalat’s lemma are introduced for proving the stability of the control system. Finally, simulation reveals the advantage of the proposed scheme.

Neural networks-based adaptive tracking control for full-state constrained switched nonlinear systems with periodic disturbances and actuator saturation

In this paper, an adaptive tracking control approach is developed for full-state constrained switched nonlinear systems that have actuator saturation, periodic disturbances and unknown control direction. To deal with the full-state constraints, the Barrier Lyapunov functions are introduced to limit the state variables within the corresponding constraint conditions. Meanwhile, the Fourier series expansion technology is employed to deal with unknown periodic disturbances and unknown nonlinear dynamics jointly. Additionally, a Nussbaum-type function is used in the controller design to cope with the and unknown control gain and input saturation. On the basis of the Lyapunov stability theory, it is demonstrated rigorously that all signals of the closed-loop system are uniformly ultimately bounded, and the proposed controller ensures that the tracking error is kept within a compact set close to zero. In the end, the validity of the designed control protocol is verified by a simulation example.

Adaptive Neural Self-Triggered Bipartite Fault-Tolerant Control for Nonlinear MASs With Dead-Zone Constraints

An adaptive neural bipartite tracking control approach is proposed for nonlinear multi-agent systems in this article. In contrast to previous results, it is worth noting that this paper considers a cooperative-competitive relationship in multi-agent systems, which stands for a more common situation. In this paper, a distributed self-triggered communication strategy is designed to improve the transmission efficiency of the whole system. In addition, the designed controller can compensate the actuator failure and dead-zone nonlinearity, and increases the system fault-tolerance. The proposed method ensures the boundedness of all signals of the closed-loop system and the bipartite tracking performance. The effectiveness of the proposed method is verified by two simulation examples. <i>Note to Practitioners</i>&#x2014;Since complex modern engineering systems are difficult to be controlled by a single component, the cooperative control mode of multi-agent systems has become the mainstream trend. For multi-agent systems with cooperative-competitive relationships, the unique bipartite consensus will allow each agent to better complete the control objectives according to their respective advantages. In addition, for engineering systems such as automated manufacturing systems and transportation systems, fault problems are becoming more commonplace. These faults may make the system difficult to operate normally, and then affect the project progress. Therefore, how to guarantee the normal work of the control system when subject to faults has become a key topic. On the other hand, the channel bandwidth of the actual communication system is limited, and frequent updating of control signals will produce huge communication pressure in the traditional control scheme. Hence, it is challenging to design a control strategy that can achieve system stability and reduce communication resources simultaneously. This paper discusses the bipartite fault-tolerant control problem for nonlinear multi-agent systems. Meanwhile, a distributed adaptive self-triggered mechanism is designed to save communication resources.

Tracking control based on adaptive Bernstein polynomial approximation for a class of unknown nonlinear dynamic systems

In this article, an adaptive tracking control approach using Bernstein polynomial approximation is firstly proposed for an unknown nonlinear dynamic system. Bernstein polynomial approximation aims to compensate the unknown nonlinear dynamic function. However, if Bernstein theorem is directly used, the Bernstein polynomial's coefficients need to be derived from the system dynamic function. Nevertheless, the dynamic function is presumed to be unknown, hence the polynomial approximation still cannot be used for designing this control. In order to obtain the available function approximation, adaptive strategy is considered to estimate these coefficients. Finally, by learning from the classical adaptive algorithm, the undetermined coefficient problem is addressed, so that the valid tracking control is found for the unknown nonlinear dynamic system. According to Lyapunov stability analysis and simulation experiment, it is concluded that the new adaptive scheme can realize the control objective.

Adaptive Fuzzy Control of Nonlinear Systems With Function Constraints Based on Time-Varying IBLFs

In this article, an adaptive tracking control approach is developed for a class of strict-feedback nonlinear systems with time-varying full state constraints. As a breakthrough in this system, the special function constraints (whose constraint boundary is relevant to both state variables and time) are considered, which are rarely studied by research work. And there is no doubt that this method increases the complexity of designing this scheme. Furthermore, the time-varying integral barrier Lyapunov functions combining with backstepping technique is introduced to break the limitation of traditional methods as well as achieve the full state constraints. Meanwhile, fuzzy logic systems are selected to approximate unknown nonlinear functions. It is verified that all closed-loop signals are bounded and all states are forced in the time-varying boundness. In addition, the proposed control strategy has a good performance. The effectiveness of the theoretical analysis results is proved via a simulation example.

Neural Adaptive Self-Triggered Control for Uncertain Nonlinear Systems With Input Hysteresis.

The issue of neural adaptive self-triggered tracking control for uncertain nonlinear systems with input hysteresis is considered. Combining radial basis function neural networks (RBFNNs) and adaptive backstepping technique, an adaptive self-triggered tracking control approach is developed, where the next trigger instant is determined by the current information. Compared with the event-triggered control mechanism, its biggest advantage is that it does not need to continuously monitor the trigger condition of the system, which is convenient for physical realization. By the proposed controller, the hysteresis's effect can be compensated effectively and the tracking error can be bounded by an explicit function of design parameters. Simultaneously, all other signals in the closed-loop system can be remaining bounded. Finally, two examples are presented to verify the effectiveness of the proposed method.

Adaptive Fuzzy Output-Feedback Control for Switched Uncertain Nonlinear Systems With Full-State Constraints.

This article investigates an adaptive fuzzy tracking control approach via output feedback for a class of switched uncertain nonlinear systems with full-state constraints under arbitrary switchings. The adaptive observer and controller are designed based on fuzzy approximation. The main characteristic of discussed systems is that the state variables are not available for measurement and need to be kept within the constraint set. In order to estimate the unmeasured states, the adaptive fuzzy state observer is constructed. To guarantee that all the states do not violate the time-varying bounds, the tangent barrier Lyapunov functions (BLF-Tans) are selected in the design procedure. Based on the common Lyapunov function method, the stability of considered systems is analyzed. It is demonstrated that all the signals in the resulting system are bounded, and all the states are limited in their constrained sets. Furthermore, the simulation example is used to validate the effectiveness of the presented control strategy.

Adaptive Fuzzy Event-Triggered Control for High-Order Nonlinear Systems With Prescribed Performance.

This article focuses on the design of a novel adaptive fuzzy event-triggered tracking control approach for a category of high-order uncertain nonlinear systems with prescribed performance requirements, in which a high-order tan-type barrier Lyapunov function (BLF) is employed to handle and analyze the output tracking error, fuzzy systems are adopted to identify the totally unknown nonlinear functions, and only one gain function rather than parameter estimation functions is designed to cancel out all unknowns appearing in fuzzy systems. As a result, complicated calculations are avoided and a structured simple control is achieved. The proposed controller not only ensures that the tracking error is always within a predefined region but also reduces the communication burden from the controller to the actuator. Finally, comparison simulations are presented to verify the effectiveness of the proposed control schemes.

Adaptive Neural Tracking Control for a Two-Joint Robotic Manipulator with Unknown Time-Varying Delays

This paper presents an adaptive neural tracking control approach for a two-joint robotic manipulator with unknown time-varying delays. In order to work out the effect of unknown time-varying delays on the two-joint robotic manipulator, the appropriate Lyapunov–Krasovskii functionals (LKFs) and separation technology are chosen to settle this matter. The neural networks work as an approximator that has the advantage of estimating the unknown function in the system. In this paper, Lyapunov stability analysis can prove that all signals of the closed-loop system are semiglobal uniformly ultimately bounded and the tracking error can converge to a compact neighborhood with respect to zero. The simulation consequences demonstrate the availability of the feedforward control approach.

Neuroadaptive asymptotic consensus tracking control for a class of uncertain nonlinear multiagent systems with sensor faults

This paper proposes an adaptive neural consensus tracking control approach for a class of leader–follower uncertain multiagent systems with sensor faults. Based on backstepping technique, a new direct adaptive neural control scheme is proposed to adaptively approximate the sensor faults. In order to improve the stability of the system and transient performance, a series of smooth functions are incorporated into control design and Lyapunov analysis. In addition, a class of reduced-order smooth functions is introduced to achieve a simpler virtual controller implementation. It is proved that the closed-loop signals are bounded and the synchronization errors can converge to a preset interval. Besides the asymptotic performance, a tunable L2-norm transient performance is achieved. Finally, numerical and physical example are presented to validate the effectiveness of the proposed control scheme.

Adaptive Fuzzy Fast Finite-Time Dynamic Surface Tracking Control for Nonlinear Systems

In this paper, we investigate the adaptive fast finite-time tracking control problem for a class of uncertain nonlinear strict-feedback systems by using backstepping technique and fast finite-time stable theory. Dynamic surface control approach is introduced to reduce the computational complexity because of the repeated differentiation of virtual signals in the traditional backstepping algorithm. By employing the approximation of fuzzy logic systems, a fuzzy-based adaptive fast finite-time output tracking control approach is presented, which can guarantee the convergence of tracking error and the boundedness of all closed-loop signals in the fast finite-time. In the final, the validity of the developed control method is proved by the simulation results.

Prescribed performance adaptive fault tolerant control approach for nonlinear large‐scale systems with time delay interconnection and dead zone input

AbstractIn this study, a prescribed performance adaptive fault tolerant tracking control scheme is presented for a class of nonlinear large‐scale systems with time delay interconnection, dead zone input, and actuator fault. The radial basis function neural networks are used to approximate unknown nonlinear functions. Different from the barrier Lyapunov functions used to achieve the symmetrical prescribed performance, a new error transformation is introduced in this study to achieve the desired asymmetrical prescribed performance. In addition, Nussbaum function is introduced to solve the difficulties caused by dead zone input and actuator fault. Based on the appropriate Lyapunov–Krasovskii functions, the effect of time delay interconnection could be compensated. By using backstepping procedures, an adaptive fault tolerant tracking control approach is developed for the considered large‐scale systems, and the stability of the closed‐loop systems is analyzed by Lyapunov theory. Meanwhile, the prescribed performance of the tracking error could be guaranteed. Finally, the effectiveness of the proposed control approach is illustrated by two simulation examples.

Intelligent optimal tracking with asymmetric constraints of a nonlinear wastewater treatment system

AbstractThe wastewater treatment is an effective method for alleviating the shortage of water resources. In this article, a data‐driven iterative adaptive tracking control approach is developed to improve the control performance of the dissolved oxygen concentration and the nitrate nitrogen concentration in the nonlinear wastewater treatment plant. First, the model network is established to obtain the steady control and evaluate the new system state. Then, a nonquadratic performance functional is provided to handle asymmetric control constraints. Moreover, the new costate function and the tracking control policy are derived by using the dual heuristic dynamic programming algorithm. In the present control scheme, two neural networks are constructed to approximate the costate function and the tracking control law. Finally, the feasibility of the proposed algorithm is confirmed by applying the designed strategy to the wastewater treatment plant.

Model‐free adaptive consensus tracking control for unknown nonlinear multi‐agent systems with sensor saturation

AbstractThis article proposes a distributed model‐free adaptive consensus tracking control (DMFACTC) approach for a class of unknown heterogeneous nonlinear discrete‐time multi‐agent systems (MASs) with sensor saturation and measurement disturbance to perform consensus tracking tasks. Meanwhile, both fixed and switching topologies are considered, where only a subset of agents can acquire the desired trajectory information in each topology. A time‐varying linear data model for each agent is first established by utilizing the dynamic linearization method to formulate this algorithm. Merely, the input data and the saturated output data with measurement disturbance of each agent are applied to construct the DMFACTC algorithm without employing any dynamics model information of MASs. The convergence of the designed scheme is strictly proved. It illustrates that the output saturation and switching topologies do not affect the stability of MASs. Moreover, even if the sensor saturation, measurement disturbance, and switching topologies happen simultaneously, the DMFACTC also guarantees that the tracking errors of MASs converge to a small range around the origin. Furthermore, two numerical simulations and a realistic filling system simulation further verify the correctness and effectiveness of the theoretical results.

Adaptive neural tracking control for switched nonlinear systems with state quantization

In this study, an adaptive neural tracking control problem for uncertain switched nonlinear systems with state quantization under arbitrary switching is investigated. A command-filtered backstepping control design strategy is implemented to overcome the difficulty that the time derivate of common virtual control signals cannot be well defined. By deriving the closed-loop system quantized errors bounded, quantized states can be used to the control design and unquantized states can be applied to the stability analysis. And then, an adaptive neural tracking control approach for switched nonlinear systems with state quantization via common Lyapunov function is proposed, which guarantees that all the signals in the closed-loop system remain semiglobal uniform ultimate boundedness and the genuine output of system can well track the reference trajectory. Finally, the proposed method is demonstrated by two simulation results.

Dual-Rate Adaptive Optimal Tracking Control for Dense Medium Separation Process Using Neural Networks

Dense medium separation (DMS) is of great significance for coal cleaning. The DMS control system always involves dense medium density adjustment and ash content control that are operating on fast and slow time scales, respectively. The inherent time-varying and strongly nonlinear characteristics of the DMS process give rise to challenges for the design of this multitime scale control system. To address this issue, this article proposes a dual-rate adaptive optimal tracking control approach for the DMS system. For the basic loop process, a nonlinear adaptive PI controller containing a neural network (NN)-based unmodeled dynamics compensator is proposed. Then, a lifting technique is used to unify the time scales of the two loops accompanied by formulating a generalized controlled object, whose dynamics is completely unknown. On this basis, a data-driven operation optimization control method that combines adaptive dynamic programming algorithm and reference control is developed, which is implemented using NNs. Finally, the stability of the proposed method is analyzed. The simulation results indicate its effectiveness.