Adaptive State Feedback Controller Research Articles

Adaptive State-Feedback Shared Control for Constrained Uncertain Mechanical Systems

This study develops two kinds of adaptive state feedback shared-control algorithms for a class of nonlinear mechanical systems in the presence of output constraints described by a set of linear inequalities. The parametric uncertainties and unknown external disturbances in the dynamical model are compensated by the proposed adaptive control laws for the feedback controller. In particular, an adaptive fixed-time state-feedback control law is also developed after the classical robust adaptive state-feedback control law design. The properties of the closed-loop shared-control systems are studied by using Lyapunov method. Simulation results demonstrate the effectiveness of the proposed approach.

Adaptive stabilization for a reaction–diffusion equation with uncertain nonlinear actuator dynamics

This paper is devoted to the stabilization of a reaction–diffusion equation with uncertain nonlinear actuator dynamics described by a cascaded parabolic PDE–ODE system. Essentially different from the systems in the related literature, control input appears in the ODE subsystem rather than in the PDE one, and moreover, the actuator dynamics are nonlinear and possess uncertainties rather than linear without uncertainty. Note that the existing control schemes so far are ineffective to handle such systems, and hence the stabilization problem for these systems is still unsolved. For this, backstepping approaches in both infinite and finite-dimension are smartly combined with the adaptive dynamic compensation technique in order to solve the control problem. Specifically, by using an infinite-dimensional backstepping transformation and its inverse, the original PDE subsystem is first changed to a new one from which control design is much convenient. Then, based on the new system together with the actuator dynamics, an adaptive state-feedback controller is explicitly constructed by using a couple of finite-dimensional backstepping transformations, which guarantees that all the states of the resulting closed-loop systems are bounded. Moreover, both the control input and the states of the original system converge to zero ultimately. Finally, a simulation example is provided to validate the effectiveness of the established theoretical results.

L1 Adaptive integrated guidance and control for flexible hypersonic flight vehicle in the presence of dynamic uncertainties

In this article, an integrated guidance and control design method for general nonlinear flexible hypersonic flight vehicles in the presence of dynamic uncertainties based on the [Formula: see text] adaptive state feedback control approach is presented. Initially, the 6-degree-of-freedom integrated guidance and autopilot dynamic model is organized using the combination of flexible uncertain hypersonic flight vehicle dynamic model and hypersonic flight vehicle-target relative motion model whereas aerodynamic and model uncertainties, cross-coupling effects, and disturbances are considered. The proposed integrated guidance and control method based on [Formula: see text] adaptive control scheme afterward is designed to realize control objectives including closed-loop stability, high-performance target interception, state regulation, uncertainties compensation, and reduction of the adverse flexibility effects on the overall performance. The whole Targets are proven thereupon based on the Lyapunov theory. Finally, the three-dimensional simulation results confirm the effectiveness of suggested integrated guidance and control law not only in closed-loop stability but also in high-performance target interception using the smooth control input.

Adaptive Robust Control for a Class of Uncertain Neutral Systems with Time Delays and Nonlinear Uncertainties

The problems of robust stabilization and adaptive robust controller design are considered for a class of uncertain neutral systems with time delays and nonlinear uncertainties. In this paper, Pade approximation is used to deal with input-delays, and the adaptation laws are proposed to estimate the norm of the unknown parameter uncertainties. Based on the improved Razumikhin-type theorem and the updated values, a class of delay-independent adaptive robust state feedback controllers is constructed to guarantee the uniform ultimate boundedness of uncertain neutral systems with input-delays and nonlinear uncertainties. Finally, the chemical two-stage dissolution tank is used to illustrate the effectiveness of the proposed method.

Adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations

The problem of adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations is studied in this paper. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller is skillfully designed by using the input-state scaling technique and an adaptive backstepping control approach. Then, by adopting the switching strategy to eliminate the phenomenon of uncontrollability, the proposed adaptive state-feedback controller can guarantee that the closed-loop system has an almost surely unique solution for any initial state, and the equilibrium of interest is globally asymptotically stable in probability. Finally, the simulation example shows the effectiveness of the proposed scheme.

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.

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.

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.

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.