Adaptive State Feedback Controller Research Articles

Adaptive stabilisation via passive identifier for an ODE system cascaded by coupled parabolic equations with serious uncertainties

Stabilisation via adaptive feedback is investigated for an ODE system cascaded by coupled parabolic equations. The remarkable characteristic of the system is the presence of serious uncertainties since no known or bounded intervals are needed for the unknown parameters. Besides, strong coupling exists in the PDE subsystem which brings essential difference compared with those of the related literature. For this, a passive identifier is skillfully constructed firstly, and in turn adaptive laws are given to compensate the serious parametric unknowns. Then, by constructing a backstepping transformation and its inverse one, the identifier joint with the original system is transformed into a new system. From the new system, an adaptive state-feedback controller is designed which ensures that all the states of the closed-loop system are bounded and particularly those of the original system converge to zero. Finally, a numerical example is provided to validate the proposed algorithm.

Design of an adaptive state feedback controller for a magnetic levitation system

This paper presents designing an adaptive state feedback controller (ASFC) for a magnetic levitation system (MLS), which is an unstable system and has high nonlinearity and represents a challenging control problem. First, a nonadaptive state feedback controller (SFC) is designed by linearization about a selected equilibrium point and designing a SFC by pole-placement method to achieve maximum overshoot of 1.5% and settling time of 1s (5% criterion). When the operating point changes, the designed controller can no longer achieve the design specifications, since it is designed based on a linearization about a different operating point. This gives rise to utilizing the adaptive control scheme to parameterize the state feedback controller in terms of the operating point. The results of the simulation show that the operating point has significant effect on the performance of nonadaptive SFC, and this performance may degrade as the operating point deviates from the equilibrium point, while the ASFC achieves the required design specification for any operating point and outperforms the state feedback controller from this point of view.

Barrier Lyapunov function-based tracking control for stochastic nonlinear systems with full-state constraints and input saturation

This paper investigates the adaptive tracking control problem of stochastic nonlinear systems under the conditions of full-state constraints and input saturation. The barrier Lyapunov function (BLF) is applied to handle the full-state constraints. To deal with the input saturation, a distinctive method of introducing an auxiliary system is adopted. Then, a systematic controller design procedure is given by combining a novel radial basis function neural network (RBF NN) approximation approach with backstepping technique.By this way, an adaptive state-feedback controller with only one adaptive law is obtained, which renders the closed-loop system semi-globally uniformly ultimately bounded. Meanwhile, the tracking error is bounded by an explicit function of the design parameters and saturated input error. In addition, the full-states are not violated. Finally, a simple pendulum system and a numerical example are simulated to demonstrate the effectiveness of the proposed scheme.

Hierarchical Decomposition-Based Distributed Full States Tracking Consensus for High-Order Nonlinear Multiagent Systems

This article studies the distributed adaptive leader-following control for high-order time-varying nonlinear multiagent systems (MASs) with uncertain parameters. The state feedback protocol and output feedback protocol are proposed, respectively, to render all states consensus errors to converge to zero asymptotically. First, the hierarchical decomposition algorithm is used to construct a refreshed communication graph to address the mutual dependence problem of controllers. Then, by introducing a local neighborhood consensus errors-based transformation, the leader-following consensus problem is converted into the stabilization problem for the consensus error system. Using the backstepping method and tuning function technique, the distributed adaptive state feedback controller is designed to render all followers' states to track the leader's ones. Further, by constructing the reduced-order dynamic gain k-filter to estimate unmeasured states, a distributed adaptive output feedback controller is designed. In both controller design methods, the traditional Lipschitz condition need not be satisfied any more for all time-varying nonlinear functions, and different from most of the existing results on the high-order nonlinear MASs, full states consensus can be obtained. Finally, a general numerical example is given to illustrate the effectiveness of the proposed methods.

Tracking-Based Control for Constrained Nonlinear Systems Under Parametric Uncertainties

The adaptive tracking control is extended to the nonlinear system with multiple uncertainties consisting of input saturation, unknown parameter and full-state constraints. To deal with the input saturation, a distinctive method of introducing an auxiliary system is used instead of directly approximating it by a smooth function. Then, the adaptive backstepping technique is combined with the barrier Lyapunov function (BLF) to solve the parametric nonlinearities and give a systematic design procedure. Based on this design procedure, an adaptive state-feedback controller is obtained with rigourous stability analysis. It is verified that all the signals are uniformly ultimately bounded, the tracking error is bounded in a compact set of the origin, and the full-states are not violated. Finally, the proposed controller is used to a mass-spring mechanical system, and demonstrates the proposed scheme is effective.

Adaptive fault-tolerant control for a class of stochastic nonlinear systems with multiple sensor faults

This paper investigates the problem of adaptive fault-tolerant control for a class of single-input and single-output nonlinear Itô stochastic systems with unknown dynamics and multiple sensor faults. Due to the partial loss of effectiveness of sensors, each measured state contains an unknown time-varying fault parameter. Then, to circumvent the main obstacle caused by the coupling of unknown fault parameters and real states, a new method of fault parameters separating of stochastic nonlinear systems is proposed. Combining with the modified backstepping design techniques, an adaptive state feedback controller is constructed recursively to estimate unknown fault parameters and guarantee the stabilisation of the stochastic system. By using quartic Lyapunov functions, it is proved that all signals of the closed-loop system are bounded in probability. Finally, simulation results are given to illustrate the effectiveness of the proposed controller design method.

Consensus and $H_{\infty }$ Consensus of Nonlinear Second-Order Multi-Agent Systems

This paper investigates the consensus problem for a class of nonlinear second-order multi-agent system with and without external disturbances. First, by making use of some inequality techniques and the designed state feedback controller, a consensus criterion is presented for the multi-agent system. In addition, an adaptive control scheme is also developed to ensure the consensus of the multi-agent system. Moreover, we further discuss the $H_{\infty }$ consensus problem for the multi-agent system, and some $H_{\infty }$ consensus criteria are acquired by using the designed state feedback controller and adaptive state feedback controller. Finally, we propose two numerical examples to verify the effectiveness of these obtained results.

Passivity-Based Finite-Time Synchronization of Nonlinear Multi-Agent Systems

This paper investigates the finite-time synchronization (FTS) problem for a kind of nonlinear multi-agent systems by exploiting the finite-time passivity (FTP). Firstly, with the help of designed state feedback controller and the adaptive state feedback controller, two sufficient conditions for ensuring the FTP of single agent are proposed. Moreover, we prove that finite-time passive agent is finite-time attractive based on the designed controllers. By employing these conclusions, several FTS criteria for multi-agent systems with nonlinear and linear couplings are derived on the basis of the designed controllers. As an application of these obtained results, we solve the FTS problem for the Kuramoto model and coupled Chua's circuits.

Finite-Time Consensus and Finite-Time $H_{\infty }$ Consensus of Multi-Agent Systems Under Directed Topology

In this paper, we respectively discuss the finite-time consensus (FTC) and finite-time $H_{\infty }$ consensus (FTHC) problems for a kind of nonlinear multi-agent systems under directed topology. Firstly, with the help of some inequality techniques and the designed state feedback controller, a FTC criterion is presented for multi-agent system. In addition, two adaptive control strategies for ensuring the FTC of multi-agent system are also developed. Moreover, we further discuss the FTHC for multi-agent system with external disturbances, and some FTHC criteria are given by exploiting the designed state feedback controller and adaptive state feedback controllers. Finally, the effectiveness of these obtained results are verified by two numerical examples.

Adaptive finite-time synchronization of stochastic mixed time-varying delayed memristor-based neural networks

This paper focuses on the finite-time synchronization of stochastic memristor-based neural networks with time-varying discrete and distributed delays and discontinuous nonlinear functions via the adaptive state-feedback controller. Based on the theories of set-valued mappings and stochastic differential inclusions, the finite-time synchronization of the drive neural network and response neural network is transformed into the finite-time stabilization problem of the corresponding error stochastic neural network. By choosing an appropriate Lyapunov function and employing the theory of stochastic finite-time stability, we present a method to design the control gain parameters. Finally, an example verifies the validity of the proposed method.

Adaptive distributed observer design for containment control of heterogeneous discrete-time swarm systems

This paper develops both adaptive distributed dynamic state feedback control law and adaptive distributed measurement output feedback control law for heterogeneous discrete-time swarm systems with multiple leaders. The convex hull formed by the leaders and the system matrix of leaders is estimated via an adaptive distributed containment observer. Such estimations will feed the followers so that every follower can update the system matrix of the corresponding adaptive distributed containment observer and the system state of their neighbors. The followers cooperate with each other to achieve leader–follower consensus and thus solve the containment control problem over the network. Numerical results demonstrate the effectiveness and computational feasibility of the proposed control laws.

Adaptive Tracking Control for Stochastic Nonlinear Systems with Full-State Constraints and Unknown Covariance Noise

Abstract This paper is devoted to the adaptive state-feedback tracking control for stochastic nonlinear systems disturbed by unknown covariance noise under the condition of full-state constraints and parametric uncertainties. Different from the related literatures, nonlinear functions in the diffusion terms are allowed to be unknown in this paper. The parametric uncertainties and unknown covariance noise are compensated with the aid of adaptive control design. By combining the backstepping technique with barrier Lyapunov function (BLF) in a unified framework, the full-state constraints can be dealt. Then, an adaptive state-feedback controller is constructed, which guarantees all the signals in the closed-loop system are uniformly ultimately bounded, the system states remain in the defined compact sets and the output tracks the reference signal well. Finally, stochastic noise is introduced to establish a stochastic simple pendulum system to show the effectiveness of the proposed controller.

Adaptive Fuzzy Decentralized Control for Nonstrict Feedback Nonlinear Systems With Unmodeled Dynamics

An adaptive fuzzy decentralized control algorithm is developed in this article for interconnected nonlinear large-scale systems with unmodeled dynamics. This method is proposed by applying a fuzzy logic system (FLS) to identify unknown nonlinear functions. In addition, dynamic signals are introduced in design process of the backstepping to compensate the effect of unmodeled dynamics. A novel adaptive state feedback control algorithm is proposed with the help of Lyapunov function. Then, the state feedback control algorithm is extended to the case of output feedback by constructing a fuzzy state observer with FLSs. The large-scale and closed-loop nonlinear system is ensured to be semi-global uniformly ultimately bounded (SGUUB). Apart from this, all signals are guaranteed to be bounded. Both numerical and practical simulation examples are utilized to elaborate the feasibility of the developed control algorithms.

Adaptive Finite-Time Stabilization of Stochastic Nonlinear Systems Subject to Full-State Constraints and Input Saturation

In this article, the adaptive finite-time tracking control is studied for state constrained stochastic nonlinear systems with parametric uncertainties and input saturation. To this end, a definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Lyapunov theorem is established and proved. To alleviate the serious uncertainties and state constraints, the adaptive backstepping control and barrier Lyapunov function are combined in a unified framework. Then, by applying a function approximation method and the auxiliary system method to deal with input saturation respectively, two adaptive state-feedback controllers are constructed. Based on the proposed stochastic Lyapunov theorem, each constructed controller can guarantee the closed-loop system achieves SGFSP, the system states remain in the defined compact sets and the output tracks the reference signal very well. Finally, a stochastic single-link robot system is established and used to demonstrate the effectiveness of the proposed schemes.

Adaptive Control of Uncertain Coupled Reaction–Diffusion Dynamics With Equidiffusivity in the Actuation Path of an ODE System

This article is devoted to the stabilization via adaptive feedback for a class of uncertain coupled reaction-diffusion dynamics in the actuation path of an ordinary differential equation (ODE) system. The system under investigation, a class of coupled parabolic partial differential equation (PDE)-ODE systems, is more representative since the dynamics in actuation path (i.e., the PDE subsystem) are coupled rather than uncoupled parabolic equations and hence includes those in the related literature as special cases. Moreover, serious parametric uncertainties are present in both PDE and ODE subsystems, which bring obstacles to the traditional methods on this issue. To solve the control problem, an infinite-dimensional backstepping transformation with time-varying matrix-valued kernel functions is adopted to change the original system into a new one. Then, an adaptive state-feedback controller is designed for the new system, which guarantees that all the closed-loop system states are bounded while regulating the original system states to zero. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results.

Adaptive Compensation Control under Constant False Data Injection Attack

In view of the false data injection attack of cyber physical systems (CPS), this paper aims to study the designing method of adaptive compensation controller for system executor when the system executor suffers from constant false data injection attack. The application of the adaptive compensation control algorithm to the false data injection attack shows that the designed adaptive law has the advantages of fast convergence speed and accurate parameter estimation. The compensation control algorithm can substantially compensate for the effects of false data injection attacks, and we can prove that all signals of the final closed-loop system are bounded and the state of the system can asymptotically converge to zero. Finally, we provide simulation examples to verify the effectiveness of the state feedback adaptive compensation controller proposed in this paper.

Real-time emulation of photovoltaic energy using adaptive state feedback control

The current paper presents an experimental validation of photovoltaic (PV) source emulation using a real-time dSpace controller. The PV source emulator is a nonlinear power electronic device used to provide in real-time the electrical behavior of PV panels by tracking the PV current–voltage (I–V) characteristic. It aims to deliver nearly the same current and voltage as an actual PV module without depending on atmospheric conditions. This innovative tool is able to aid researchers in PV systems to perform their tests and measurements at the desired weather parameters without time, space and cost constraints. The proposed PV emulator is based on a simple and efficient adaptive state feedback control that ensures good accuracy and high dynamic response compared to the existing commercial PV emulators based on the programmable power supply, which improves significantly the static and dynamic performances of existing PV emulators.

Adaptive State-Feedback Stabilization of Stochastic High-Order Nonlinear Systems With Time-Varying Powers and Stochastic Inverse Dynamics

This article investigates adaptive state-feedback stabilization problem for a class of stochastic high-order nonlinear systems with unknown time-varying powers and stochastic inverse dynamics for the first time. The existence of stochastic inverse dynamics, unknown parameters, and time-varying powers makes stochastic high-order nonlinear systems essentially different from the related papers, which brings a series of obstacles to achieve the control objective. By virtue of the parameter separation principle, adaptive technique and some flexible algebraic methods, a novel adaptive state-feedback controller is designed to guarantee that the equilibrium of the closed-loop system is globally stable in probability. Finally, a simulation is provided to demonstrate the effectiveness of the control scheme.

Command Filter-Based Adaptive Prescribed Performance Tracking Control for Stochastic Uncertain Nonlinear Systems

The issue of adaptive fuzzy prescribed performance tracking control is considered in this article for strict-feedback stochastic uncertain nonlinear systems. A novel adaptive tracking control design approach, in which the fuzzy systems are employed to approximate the totally unknown nonlinear terms, is proposed by incorporating the technology of prescribed performance control with the method of command filtered backstepping design. The proposed adaptive state feedback controller can ensure that the output tracking error converges to a predefined arbitrarily small residual set in probability and all the signals of the closed-loop system can be bounded in probability, meanwhile, the problem of “explosion of complexity” is solved. The effectiveness of the presented method is verified by two simulation examples.

Fast Adaptive Robust Differentiator Based Robust-Adaptive Control of Grid-Tied Inverters with a New L Filter Design Method

In this research, a new nonlinear and adaptive state feedback controller with a fast-adaptive robust differentiator is presented for grid-tied inverters. All parameters and external disturbances are taken as uncertain in the design of the proposed controller without the disadvantages of singularity and over-parameterization. A robust differentiator based on the second order sliding mode is also developed with a fast-adaptive structure to be able to consider the time derivative of the virtual control input. Unlike the conventional backstepping, the proposed differentiator overcomes the problem of explosion of complexity. In the closed-loop control system, the three phase source currents and direct current (DC) bus voltage are assumed to be available for feedback. Using the Lyapunov stability theory, it is proven that the overall control system has the global asymptotic stability. In addition, a new simple L filter design method based on the total harmonic distortion approach is also proposed. Simulations and experimental results show that the proposed controller assurances drive the tracking errors to zero with better performance, and it is robust against all uncertainties. Moreover, the proposed L filter design method matches the total harmonic distortion (THD) aim in the design with the experimental result.