Adaptive State Feedback Controller Research Articles

Fixed-time adaptive fault-tolerant output consensus control for heterogeneous multi-agent systems

Aiming at the fault-tolerant output consensus problem of heterogeneous multi-agent systems with external finite energy interference in the case of simultaneous additive and multiplicative faults of the actuators, this paper proposes a fault-tolerant output control strategy combining fixed-time feedforward control and adaptive state feedback control. First, a fully distributed adaptive fixed-time observer is designed for the follower, so that each follower can estimate the leader state and the state matrix within a fixed time. Then, combined with the output adjustment equation with fault matrix, a distributed adaptive fault-tolerant output consensus control scheme is proposed to compensate for the impact of fault on the system, and the sufficient conditions for consensus system output are deduced by using Lyapunov stability theory. Finally, the effectiveness and feasibility of the proposed method are verified by a heterogeneous multi-agent faulty system composed of a leader and four followers.

A multivariable adaptive formation control for multiple UAVs with external uncertain disturbances

Purpose A multivariable model reference adaptive control method is proposed to solve a distributed leader–follower formation control problem of unmanned aerial vehicles (UAVs) with uncertain parameters and unknown external disturbances for both leader and followers. Design/methodology/approach A case of uncertain stochastic external disturbances for UAVs is considered, and based on the distributed communication network of UAVs, a state-feedback adaptive controller is proposed to maintain the formation of UAVs consistently. Then, the stability and asymptotic tracking performance of the UAV formation control system are analyzed by the Lyapunov function. Findings The simulation results demonstrate that this formation control scheme can effectively solve the stochastic external disturbance problem of UAVs and ensure the stability of their formation. Originality/value The proposed multivariable model reference adaptive control method reduces the error of formation control system and improves the stability and control performance of UAV compared with fixed control.

Adaptive state-feedback control for nonlinear systems with input delay and state constraints

This paper investigates the adaptive tracking control for more general nonlinear systems that encompass input delay, state constraints, and parameter uncertainty. Firstly, the parametric nonlinearities of the system are addressed by adaptive control and parameter separation technique. By integrating the Pade approximation method with the barrier Lyapunov function in a unified framework, the uncertainties arising from input delay and state constraints are effectively tackled. Then, an adaptive state-feedback control strategy is constructed based on the backstepping design procedure and rigorous stability analysis. It is verified that all the signals in the closed-loop system are uniformly ultimately bounded, the tracking error of the system converges to a compact set of the origin, and the system state constraints are never violated. Finally, the designed controller is applied to a single-link robot system to demonstrate the effectiveness of the proposed control strategy.

Adaptive control for a class of stochastic nonlinear time-delay systems with unknown control coefficients

This paper mainly investigates the adaptive state feedback control problem for a class of stochastic nonlinear systems with time-delay and unknown control coefficients. The proposed control scheme leverages the dynamic gain technology and Nussbaum function to develop a state feedback controller, aiming to simplify its implementation and eliminate the influence of unidentified time-varying control coefficients. Through the utilization of suitable Lyapunov–Krasovskii (L–K) functionals and stochastic stability theories, it is demonstrated that the designed control mechanism guarantees the boundedness in probability for all closed-loop signals, ultimately regulating the state of the plant to zero. The availability and superiority of the developed adaptive management strategy are further certified through simulation results.

Fault-tolerant joint state feedback adaptive control for snake robots that move through random pole environments

ABSTRACT In unstructured terrain, snakes can move more efficiently by actively pushing and avoiding obstacles, a capability believed to be realized through a decentralized mechanism. Moreover, considering harsh and unpredictable rescue environments where snake robots are expected to be deployed, such as post-earthquake scenarios, some joint sensors are prone to failure. We propose a decentralized adaptation mechanism for snake robots to navigate through random pole environments. This mechanism integrates Fault-Tolerant Joint State Feedback Adaptive Control (FT-JSFAC) with Extended Curvature Derivatives control (ECD) and Angular Damping control (AD), leveraging the FT-JSFAC method to maintain operational robustness even when some joint sensors fail. To meet critical goals of adaptability, we utilize real-time angle and electrical current data from the robot's internal servo motors. Using this data, FT-JSFAC determines whether an obstacle is beneficial or detrimental to propulsion and then allows for decentralized torque adjustment to adapt to the environment. FT-JSFAC also employs historical data from functioning joints to compensate for erroneous sensor data, ensuring operational robustness even with joint sensor failure. Simulation experiments demonstrate that the proposed mechanism effectively adapts to environmental obstacles and maintains adaptability when one or two joint sensors fail.

Adaptive state feedback controller design for efficient biodiesel production under kinetic uncertainty

In this study, we optimize the quality and economic performance of biodiesel production through a scenario-based adaptive state feedback control framework. Our goal is to maximize the operational efficiency while ensuring the production of on-spec biodiesel, despite uncertainties in reaction kinetics. A first-principle model is employed to describe the process dynamics, with kinetic parameters estimated online using a moving horizon estimator (MHE). A pool of state feedback controllers is created via off-line nonlinear optimization and metaheuristic algorithm based on sampled kinetic scenarios. Then, the uncertainty space is partitioned into several clusters, each linked to an optimal controller from the pool. During online operation, the appropriate controller is selected by matching the estimated kinetic parameters to the corresponding cluster. Simulation studies on a semi-batch reactor demonstrate that manipulating the methanol feed flow rate and heat duty with our control approach significantly improves operational efficiency, reduces online computational time, and enhances robustness to kinetic uncertainties compared to model predictive control (MPC).

Adaptive consensus control of uncertain nonlinear multi-agent systems with communication delays and relative output information

This paper explores the challenges of distributed adaptive consensus control problems in nonlinear multi-agent systems with unknown parameters and communication delays. To address these issues, a novel backstepping-based adaptive state feedback control protocol is proposed by utilizing a reference dynamic system. Furthermore, an output-feedback consensus control algorithm incorporating a state observer is introduced. Through the application of Laplace transformation, matrix properties, and graph theory, it is demonstrated that the closed-loop multi-agent system ensures the boundedness of all signals and achieves output consensus, even in the presence of nonuniform communication delays. Numerical simulations on a group of inverted pendulums illustrate the effectiveness of these algorithms.

Decentralized adaptive fault‐tolerant control for interconnected nonlinear time‐delay systems with uniform prescribed performance

AbstractIn this article, the prescribed performance tracking control problem is studied for interconnected nonlinear time‐delay systems with sensor and actuator faults. Based on the dynamic gain technique and the backstepping control method, a delay‐independent adaptive state feedback controller is designed. Besides, by embedding a smooth function into the controller, the unknown external disturbances, sensor and actuator faults are successfully compensated. Furthermore, we can deal with the asymmetric prescribed performance control with semi‐global or global requirements uniformly by selecting the initial value of the the scaling function. Based on Lyapunov theory, it is proved that the system output of each subsystem can closely track the desired signal and the boundedness of all signals in the closed‐loop systems can be ensured under the proposed control method. Finally, the effectiveness of the proposed control strategy is proved by two simulation examples.

Cooperative Adaptive Fuzzy Control for the Synchronization of Nonlinear Multi-Agent Systems under Input Saturation

This research explores the synchronization issue of leader–follower systems with multiple nonlinear agents, which operate under input saturation constraints. Each follower operates under a spectrum of unknown dynamic nonlinear systems with non-strict feedback. Additionally, due to the fact that the agents may be geographically dispersed or have different communication capabilities, only a subset of followers has direct communication with the leader. Compared to linear systems, nonlinear systems can provide a more detailed description of real-world physical models. However, input saturation is present in most real systems, due to various factors such as limited system energy and the physical constraints of the actuators. An auxiliary system of Nth order is introduced to counteract the impact of input saturation, which is then employed to create a collaborative controller. Due to the powerful capability of fuzzy logic systems in simulating complex nonlinear relationships, they are deployed to approximate the enigmatic nonlinear functions intrinsic to the systems. A distributed adaptive fuzzy state feedback controller is designed by approximating the derivative of the virtual controller by filters. The proposed controller ensures the synchronization of all follower outputs with the leader output in the communication graph. It is shown that all signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood around the origin. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Approximation-Based Approach to Adaptive Control of Linear Time-Varying Systems

An adaptive state-feedback control system is proposed for a class of linear timevarying systems represented in the controller canonical form. The adaptation problem is reduced to the one of Taylor series-based first approximations of the ideal controller parameters. The exponential convergence of identification and tracking errors of such an approximation to an arbitrarily small and adjustable neighbourhood of the equilibrium point is ensured if the condition of the regressor persistent excitation with a sufficiently small time period is satisfied. The obtained theoretical results are validated via numerical experiments.

Adaptive fuzzy control for high-order nonlinear systems with asymmetric time-varying full-state constraints and dead-zone input

The issue of adaptive fuzzy control for a category of high-order uncertain nonlinear systems is discussed in this paper. The time-varying full-state constraints are asymmetric, and the input is subjected to dead-zone. The asymmetric time-varying high-order barrier Lyapunov functions (BLFs) are constructed to depict the constraints characteristic and a controller design strategy is proposed. A dead-zone compensation mechanism is used to eliminate the influence of dead-zone input. Based on adding a power integrator technique and the adaptive control method, an adaptive state feedback controller is designed. As a consequence, all the constraints are not breached and the tracking error converges into a prescribed small region around the origin. Finally, a numerical example and a practical example are given to show the effectiveness of the proposed method.

Model-Free Adaptive State Feedback Control for a Class of Nonlinear Systems

This paper investigates state feedback control for a class of discrete-time multiple input and multiple output nonlinear systems from the perspective of model-free adaptive control and state observation. The design of a dynamic state feedback control can be efficiently carried out using dynamic linearization and state observation. The stability of the proposed method is guaranteed by theoretical analysis. Numerical simulation tests and experimentation on a continuous stirred tank reactor are carried out to validate the effectiveness of the proposed approach. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The growth in the scale of factories and the complexity of associated production processes increases the complexity and time involved in associated mathematical modelling. Data driven approaches to control remove the need to model processes. To the best of the authors’ knowledge, existing approaches to model-free adaptive control (MFAC) of general systems are all based on an input-output control paradigm. These methods thus cannot guarantee the stability of the system state. The purpose of this study is to develop a novel Model-Free Adaptive Control (MFAC) approach to achieve control of the system state. In this paper, the assumptions required to achieve model-free adaptive control by state feedback are presented mathematically. A controller design and the associated stability proof are then presented. Numerical simulation and experimentation is conducted to validate the effectiveness of the proposed approach. In future research, state feedback data control in the presence of random disturbances will be investigated.

Command filter-based event-triggered control for stochastic MEMS gyroscopes with finite-time prescribed performance

This paper proposes an adaptive neural control strategy for stochastic microelectromechanical system (MEMS) gyroscopes, aiming to achieve a prescribed performance in a finite time. The radial basis function neural network is introduced to address the system’s unknown nonlinear dynamics and stochastic disturbances. Then, the technology of finite-time prescribed performance function, along with the method of command-filtered backstepping design, is utilized to ensure both transient and steady-state performance and simultaneously solve the problem of "explosion of complexity." Moreover, a switching threshold event-triggered control law is proposed to cut down on communication resources and eliminate corresponding parametric inequality restrictions. The proposed adaptive state feedback control strategy is able to guarantee that the output tracking error converges to a prescribed, arbitrarily small residual set. Additionally, the closed-loop system’s signals can be semi-globally ultimately uniformly bounded in probability. Finally, numerical simulations demonstrate the effectiveness and superiority of the proposed strategy.

Adaptive neural control for delayed discrete-time switched systems under deception attacks

This paper focuses on the issue of adaptive neural control for discrete-time switched systems with time delay and deception attacks. Firstly, the switching signal is constrained by the dwell time. Considering that the deception attacks are unknown, the neural network technique is employed to approximate the attack signals. Then, an adaptive state feedback controller is established to compensate for the adverse effects of deception attacks for switched systems. Meanwhile, sufficient conditions for the boundedness of the switched system are given through the Lyapunov functional method, and the controller gains can be obtained by resolving the linear matrix inequality. Finally, the feasibility of the proposed method is illustrated via a numerical example.

Robust [formula omitted] synchronization for parabolic complex networks with coupling time-varying delays

This paper delves into the robust H∞ synchronization for diffusion-type parabolic complex networks (PCNs) characterized by second-order nonlinear partial differential equations (PDEs). Given that the potential deterioration of network performance or the loss of network synchronization caused by external disturbances and time delays, the analysis and synthesis results for the robust H∞ synchronization of the PCNs with coupling time-varying delays are derived with and without the utilization of the distributed adaptive state feedback control protocol. A numerical example is employed to validate the effectiveness of the acquired H∞ synchronization results and the adaptive protocol.

Adaptive state feedback control of output‐constrained stochastic nonlinear systems with stochastic integral input‐to‐state stability inverse dynamics

AbstractThis article studies the adaptive state‐feedback control problem of output‐constrained stochastic high‐order nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics. A key nonlinear transformation function is constructed to convert the original output‐constrained stochastic nonlinear system into an equivalent form without any output constraint. By subtly using the SiISS small‐gain condition and fully extracting the characteristics of system nonlinearities, two new control design and analysis methods are developed to guarantee that the closed‐loop system has an almost surely unique solution, all the closed‐loop signals are bounded almost surely, and the equilibrium point is stable in probability without the violation of output constraint. A simulation result is provided to show the effectiveness of this control method.

Synchronization of stochastic fractional-order model of muscular blood vessels

This study deals with the synchronization problem of the stochastic fractional-order biomathematical model of muscular blood vessels (SFOMBVs) with nonlinear inputs using a state-feedback adaptive control law, in which the effects of uncertainties and external disturbances are considered in the modeling. The linear state feedback and adaptive laws are combined via an adaptive update law, leading to a simple and robust adaptive feedback scheme. The synchronization and tracking performances of the SFOMBV master and slave systems are investigated, and the stability of the proposed control system is proved based on stochastic analysis techniques and Lyapunov theory. The simulation results show that the proposed control method can lead an abnormal muscular blood vessel to a normal trajectory with good robustness by reducing the tracking error.

Finite-Time Passivity for Coupled Fractional-Order Neural Networks With Multistate or Multiderivative Couplings.

This article mainly delves into the finite-time passivity (FTP) for coupled fractional-order neural networks with multistate couplings (CFNNMSCs) or coupled fractional-order neural networks with multiderivative couplings (CFNNMDCs). Distinguishing from the traditional FTP definitions, several concepts of FTP for fractional-order systems are given. On one hand, we present several sufficient conditions to ensure the FTP for CFNNMSCs by artfully designing a state-feedback controller and an adaptive state-feedback controller. On the other hand, by utilizing some inequality techniques, two sets of FTP criteria for CFNNMDCs are also established on the basis of the state-feedback and adaptive state-feedback controllers. Finally, numerical examples are used to demonstrate the validity of the derived FTP criteria.

Adaptive stabilisation of output-constrained high-order nonlinear systems with high-order and low-order nonlinearities

This paper investigates the adaptive stabilisation of output-constrained high-order nonlinear systems with more general high-order and low-order nonlinearities. By skilfully introducing nonlinear mappings, a key coordinate transformation, integral Lyapunov functions and the sign function into the adding a power integrator technique, and combining a novel analysis method, a continuous adaptive state-feedback controller is constructed. When the initial value of system states lies in the constrained set, it is rigorously proved that all the closed-loop signals are uniformly bounded, the asymmetric output constraint isn't transgressed, and the equilibrium point of the closed-loop system is uniformly asymptotically stable. A simulation example shows the effectiveness of this control scheme.

Trajectory tracking controller of a robotized arm with joint constraints, a direct adaptive gain with state limitations approach

Motion restrictions in robotic devices may introduce complex requirements for any closed-loop control design, mainly when the robot joints must track reference trajectories that force the end-effector to perform planned motions. This study summarizes the comprehensive technical design of an adaptive state feedback controller for multi-link robotic manipulators that consider the effect of position and velocity restrictions on the tracking trajectory control approach. The proposed design is less conservative than other methods because of the explicit inclusion of state restrictions in the control gain dynamics. A logarithm barrier Lyapunov function class supports the design of the adaptive gain for the manipulator. Sufficient conditions based on a Riccati equation simplify the implementation of the adaptive controller with gains depending on the distance between the current state and the restriction sets. Numerical simulations show the advantages of the proposed controller with adaptive gains concerning a similar adaptive controller that does not consider the restrictions and a proportional–integral–derivative form. An implementation for the motion control of a robotic arm is presented to demonstrate the development by implementing the proposed gain, which confirms the suggested improvements enforced by the proposed controller. The performed comparison shows the advantages of the suggested adaptive gain control form, inducing better tracking of reference trajectories and smaller control energy applications.