Tracking Of Uncertain Nonlinear Systems Research Articles

Optimal trajectory tracking of uncertain nonlinear continuous-time strict-feedback systems with dynamic constraints

A novel method for optimal trajectory tracking of uncertain nonlinear systems by using adaptive dynamic programming (ADP)-based integral reinforcement learning (IRL) and neural networks (NNs) is proposed. The method utilises an actor-critic framework with optimal backstepping to minimise a discounted value function and uses a single-layer NN identifier for estimating the unknown dynamics. For safety assurance, a time-varying barrier Lyapunov function (TVBLF) is used in the control design to handle the constraints. A novel weight-tuning law by using the control input error, integral Bellman error, and the NN identifier is used for the actor-critic framework. A novel lifelong learning (LL)-based method for critic NN is utilised in an optimal framework by incorporating the Bellman error to mitigate catastrophic forgetting in multitasking scenarios. Stability analysis using Lyapunov stability theory is obtained for the overall closed-loop system. Simulations of leader-follower mobile robot formation control show a 25% reduction in the cost in multitasking scenarios.

Event-triggered prescribed-time tracking for uncertain nonlinear systems with unknown control gain and output constraints

This paper uses a prescribed-time event-triggered approach to explore the control of uncertain strict-feedback nonlinear systems with output constraints and an unknown time-varying control gain. The proposed method utilizes a universal barrier Lyapunov function (BLF) to ensure compliance with the output constraints. Furthermore, a technique known as congelation of variables is employed to handle the unknown time-varying control gain. Approximating the unknown dynamics using radial basis function neural network (RBFNN), a neural prescribed-time controller is designed based on the backstepping approach. Additionally, the event-triggered mechanism is employed to conserve computational and communication resources. With this scheme, all signals are guaranteed to converge to a compact set within the prescribed time frame. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed 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.

Adaptive asymptotic tracking for uncertain nonlinear systems with deferred full state constraints

Adaptive asymptotic tracking for uncertain nonlinear systems with deferred full state constraints

Command Filter Adaptive Asymptotic Tracking of Uncertain Nonlinear Systems With Time-Varying Parameters and Disturbances

This article is devoted to the adaptive asymptotic tracking for a class of uncertain nonlinear systems. The presence of unknown time-varying parameters and uncertain disturbances makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and command filter-based backstepping, a novel command filter adaptive tracking controller is successfully designed to achieve asymptotic tracking. The typical feature of the proposed controller lies in the introduction of a smooth function with positive integrable time-varying function, which makes the controller powerful enough to compensate the unknown time-varying parameters and uncertain disturbances. Remarkably, a novel Lyapunov function by incorporating the lower bounds of control gains is used to prove the stability of the closed-loop system. Compared with some existing command filter-based backstepping, the conditions on the virtual control coefficients and disturbances are relaxed. Finally, the effectiveness of the proposed method is shown by a simulation example.

An Enhanced Strategy for Adaptive Output-Feedback Control of Uncertain Nonlinear Systems

We are concerned with global practical tracking for uncertain nonlinear systems with intrinsic dependence on unmeasured states. Typically, we aim to remove the polynomial restrictions on system growth rates in relevant works, admitting the rates to be of arbitrary function-of-output type. Note that such highly nonlinear rates could alter so drastically in magnitude that no polynomial can upper bound them on any unbounded region, and would undermine the design rationale and the analysis route that are followed in polynomial rate scenarios. This entails refining/integrating state-of-the-art techniques and developing new ones, from design to analysis. Concretely, to circumvent the need for knowledge on polynomials, dual dynamic high gains are devised ingeniously which particularly incorporate certain highly nonlinear components to counteract the arbitrary function-of-output rates and other inherent nonlinearities and uncertainties. But unfavorable impacts of the components would also arise putting the effectiveness of the high gains at risk, which necessitates noticeable changes in the choice of vital variables/functions. In addition, to provide tractable observer error dynamics for control design and analysis, a nonlinear high-gain observer is pursued, which is filter based and of reduced order, following the design methodologies in relevant works. In terms of performance analysis, practical tracking suffers extra time variants and additive uncertainties which together with the highly nonlinear rates would carry over to stability analysis inevitably and in turn ruin the existing analysis routes. Hence, a new analysis route is paved to verify the anticipated performance. Notably, by unfolding an important implication, the performance verification boils down largely to the boundedness of the high gains. This makes plain and intelligible the verification, although sophisticated integration of multiple composite Lyapunov functions is still required. An exception, i.e., asymptotic stabilization, is presented to demonstrate its close connection with practical tracking.

Adaptive asymptotic fault-tolerant tracking of uncertain nonlinear systems with unknown control directions

In the article, the issues of asymptotic adaptive tracking control for the uncertain nonlinear systems in the presence of actuator faults and unknown control directions are investigated. By using the properties of the Nussbaum function and backstepping technique, the problems resulting from the unknown signs of the nonlinear control functions are circumvented successfully. Moreover, a new adaptive asymptotic tracking control method is presented with the fault-tolerant control framework, which is capable of realising zero-tracking performance. The stability of the controlled system is ensured through fractional Lyapunov stability analysis. Finally, the validity of the raised scheme is verified by a simulation example.

Adaptive backstepping based consensus tracking of uncertain nonlinear systems with event-triggered communication

This paper investigates the consensus tracking problem for a class of uncertain high-order nonlinear systems with parametric uncertainties and event-triggered communication. Under a directed communication condition, a totally distributed adaptive backstepping based control scheme is presented. Specifically, a decentralized triggering condition is adopted in this paper such that continuous monitoring of neighboring states, as required in some existing results, can be avoided. Besides, to handle the non-differentiability problem of virtual controllers, which arises from the utilization of neighboring states collected only at the triggering instants, the virtual controllers in each recursive step are firstly designed with continuous communication. Then, the partial derivatives of these designed virtual controllers are adopted to construct distributed adaptive consensus controllers for the event based communication case. It is shown that with the presented distributed adaptive consensus control scheme and even-triggered communication mechanism, all the closed-loop signals are uniformly bounded and the output consensus tracking errors will converge to a compact set. Besides, the tracking performance in the mean square sense can be improved by appropriately adjusting design parameters.

Adaptive tracking of uncertain nonlinear systems under different types of input delays with urban traffic perimeter control application

AbstractPragmatic design method of direct model reference adaptive control (MRAC) is developed for a class of uncertain systems, where various input channels might have different delays and taking into account the effect of control saturation. To overcome the difficulty of directly predict the plant state and cope with different kinds of input delays, the proposed control design relies on implicit time‐delay prediction by using auxiliary linear Smith‐like dynamic units with adjustable gains. The design is unified to different time delay categories, that is, constant, time‐varying, or dependent on the current plant state. Within the context of the proposed approach, various adaptive control feedback strategies are designed for problems of continuous and sample‐and‐hold control implementations. Simulation results of a perimeter control for two interacting aggregate urban traffic regions are presented.

Adaptive Dynamic Surface Control for Finite-time Tracking of Uncertain Nonlinear Systems with Dead-zone Inputs and Actuator Faults

Adaptive Dynamic Surface Control for Finite-time Tracking of Uncertain Nonlinear Systems with Dead-zone Inputs and Actuator Faults

A new nonlinear extended state observer design for output tracking of uncertain nonlinear systems

SummaryIn this article, we develop a new nonlinear extended state observer (ESO) for output tracking of a class of uncertain nonlinear affine systems. Instead of using the linear functions of the error, the nonlinear functions of the properly magnified error are used in the proposed ESO. Compared with the linear ESO, the new ESO allows more accurate estimation and smaller peaking value. We also design an output‐feedback controller based on the proposed nonlinear ESO. The convergence of the new ESO is proved without assuming the boundedness of the system state. It is also proved that under the proposed output‐feedback controller, the system output is capable to track the given reference signal despite a large scope of nonlinear uncertainties. Simulation results illustrate the effectiveness of the new ESO with improved performance.

Fuzzy adaptive asymptotic tracking of uncertain nonlinear systems with full states constraints

ABSTRACT In this paper, the fuzzy adaptive tracking control problem is studied for a class of nonlinear strict feedback systems with time-varying full state constraints. For the full state constraints problem, the nonlinear transformation function is used to transform the constraint problem into a non-constraint problem. A new adaptive control framework is proposed for asymptotic tracking of nonlinear systems with unknown virtual control coefficients (UVCC). Under the proposed control scheme, the effects of UVCC and unknown nonlinear functions are compensated by the introduction of some well-defined smoothing functions and boundary estimation methods. In addition, a new Lyapunov function is constructed, which successfully achieves the tracking error of the closed-loop system converge to zero and all the signals in the closed-loop systems are bounded. In the meanwhile, all states are always keep in their asymmetric time-varying constraints. Finally, a numerical example is presented to show the effectiveness of the proposed control scheme.

Event-Based Adaptive Fuzzy Asymptotic Tracking Control of Uncertain Nonlinear Systems

This article proposed a novel adaptive ETC framework for asymptotic tracking of uncertain nonlinear systems in the presence of unknown virtual control coefficients (UVCC). More precisely, by introducing some well-defined smooth functions and the bounded estimation approach, the effects caused by the unknown UVCC and uncertainties are counteracted. Moreover, a novel Lyapunov function is constructed such that the asymptotical convergence to zero of the tracking error and boundedness of the closed-loop system are successfully achieved. Effectiveness of the proposed strategies is shown by using a simulation example.

Optimal Guaranteed Cost Tracking of Uncertain Nonlinear Systems Using Adaptive Dynamic Programming with Concurrent Learning

In this paper, based on adaptive dynamic programming (ADP) with concurrent learning, the problem of optimal guaranteed cost tracking is studied for a class of uncertain continuous-time nonlinear systems. First, the original uncertain system and a reference system are combined into an augmented uncertain system, and the performance index is transformed into the corresponding augmented form. Afterwards, the solution of the optimal control problem consisting of the nominal augmented system with the modified performance index is proven to be the optimal guaranteed cost tracking control law of the original uncertain system. Moreover, a concurrent learning tuning algorithm based on ADP is presented to approximate the solution of corresponding Hamilton-Jacobi-Bellman (HJB) equation, which relaxes the condition of persistent excitation (PE). A neural network-based approximate optimal guaranteed cost tracking design is developed not only to ensure tracking error convergence to zero for all admissible uncertainties but also to achieve the minimal guaranteed cost. Finally, two simulation examples are considered to verify the effectiveness of the theoretical results.

Distributed Adaptive Control for Asymptotically Consensus Tracking of Uncertain Nonlinear Systems With Intermittent Actuator Faults and Directed Communication Topology.

In this article, we investigate the output consensus tracking problem for a class of high-order nonlinear systems with unknown parameters, uncertain external disturbances, and intermittent actuator faults. Under the directed topology conditions, a novel distributed adaptive controller is proposed. The common time-varying trajectory is allowed to be totally unknown by part of subsystems. Therefore, the assumption on the linearly parameterized trajectory signal in most literature is no longer needed. To achieve the relaxation, extra distributed parameter estimators are introduced in all subsystems. Besides, to handle the actuator faults occurring at possibly infinite times, a new adaptive compensation technique is adopted. It is shown that with the proposed scheme, all closed-loop signals are globally uniformly bounded and asymptotically output consensus tracking can be achieved.

Development of an adaptive radial basis function neural network estimator-based continuous sliding mode control for uncertain nonlinear systems

In this paper an adaptive neural network (NN)-based nonlinear controller is proposed for trajectory tracking of uncertain nonlinear systems. The adopted control algorithm combines a continuous second-order sliding mode control (CSOSMC), the radial basis function neural network (RBFNN) and the adaptive control methodology. First, a second-order sliding mode control scheme (SOSMC), which is published recently in literature for linear uncertain systems, is extended for nonlinear uncertain systems. Second, an adaptive radial basis function neural network estimator-based continuous second order sliding mode control algorithm (CSOSMC-ANNE) is adopted. In CSOSMC-ANNE control methodology, a radial basis function neural network with adaptive parameters is exploited to approximate the unknown system parameters and improve performance against perturbations. Also, the discontinuous switching control of SOSMC is supplanted with a smooth continuous control action to completely eliminate the chattering phenomenon. The convergence and global stability of the closed-loop system are proved using Lyapunov stability method. Numerical computer simulations, with dynamical model of the nonlinear inverted pendulum system, are presented to demonstrate the effectiveness and advantages of the presented control scheme.

Robust output tracking of uncertain nonlinear systems with completely unknown dead‐zone input: A self‐tuning design approach

SummaryThe main purpose of this paper is to propose a direct and simple approach, called a self‐tuning design approach, to dealing with any nonsymmetric dead‐zone input nonlinearity where its information is completely unknown. In order to describe the approach, the output tracking problem is considered for a class of uncertain nonlinear systems with any nonsymmetric dead‐zone input. First, a dead‐zone input is represented as a time‐varying input‐dependent function such that the considered dynamical system with dead‐zone input can be transfered into an uncertain nonlinear dynamical system subject to a linear input with time‐varying input coefficient. Then, by making use of the self‐tuning design approach, a class of adaptive robust output tracking control schemes with a rather simple structure is synthesized. Thus, the proposed direct and simple self‐tuning design approach can be easily understood by the engineering designers, and the resulting simple adaptive robust control schemes can be well implemented in most practical engineering control problems. By combining the proposed self‐tuning design approach with other control methods, one may expect to obtain a number of interesting results for a rather large class of uncertain nonlinear dynamical systems with dead‐zone in the actuators. Finally,the simulations of some numerical examples are provided to demonstrate the validity of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

Global output feedback practical tracking for time-delay systems with uncertain polynomial growth rate

In this paper, the problem of global practical output tracking is investigated by output feedback for a class of uncertain nonlinear time-delay systems. Compared with the existing results, we allow the nonlinearities to nonlinearly grow in unmeasured free-delay and time-delay states with the uncertain time-delay output polynomial growth rate. Based on the ideas of universal adaptive control and dead zone, we develop an adaptive high-gain observer with a novel monotone non-decreasing dynamic law. By the Lyapunov–Krasovskii theorem, a memoryless controller is constructed to achieve global practical output tracking for uncertain nonlinear systems with multiple time delays. Finally, two examples are given to illustrate the usefulness of our results.

Robust adaptive tracking of uncertain nonlinear systems by output feedback

Summary We investigate the problem of robust adaptive tracking by output feedback for a class of uncertain nonlinear systems. Based on the high-gain scaling technique and a new adaptive law, a linear-like output feedback controller is constructed. Only one dynamic gain is designed, which makes the controller easier to implement. Furthermore, by modifying the update law, the adaptive controller is robust to bounded external disturbance and is able to guarantee the convergence of the output tracking error to an arbitrarily small residual set. A numerical example is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

Special issue on ‘new results on neuro‐fuzzy adaptive control systems’

Special issue on ‘new results on neuro‐fuzzy adaptive control systems’