Adaptive State Feedback Controller Research Articles

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.

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.

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.

Finite-time adaptive practical tracking control for high-order nonlinear systems with full-state constraints and input saturation

This paper focuses on finite-time adaptive practical tracking control for a class of high-order nonlinear systems with full-state constraints and input saturation. The state constraints are handled by applying nonlinear transformed functions (NTFs) and the input saturation is estimated by an auxiliary hyperbolic tangent function. On the basis of adding a power integrator technique and adaptive control method, an adaptive state feedback controller is designed for the closed-loop system. With the aid of finite-time stability theory, the tracking error converges to a bounded neighbourhood of the origin in a finite time, and all the signals in the closed-loop system are bounded. At last, a simulation example and a practical example are presented to show the effectiveness of the proposed control procedure.

Adaptive neural dissipative control for markovian jump cyber-Physical systems against sensor and actuator attacks

This work addresses the issue of adaptive neural dissipative control for Markovian Jump Cyber-Physical Systems subject to output-dependent sensor and state-dependent actuator attacks. Attackers can inject false information into feedforward and feedback signals to degrade system performance or even destabilize the system. To identify and approximate attack signals, neural network technique is employed. Attacks are successfully withstood by constructing the estimated signals of these approximate functions. New adaptive state and output feedback controllers are being developed in the meantime. Then, by adapting Lyapunov function technique, sufficient conditions are provided to achieve the stochastic stability of the considered system with extended dissipation. Last, two practical examples are applied to elucidate the effectiveness of the devised adaptive neural control approaches.

Adaptive quantized control for a class of high‐order nonlinear systems

AbstractIn this article, the adaptive stabilization problem is addressed for a class of nonlinearly parameterized systems with quantized input. The quantizer parameters and virtual control coefficients are unknown, and the linearization of the nonlinear systems is uncontrollable. A novel nonlinear time‐varying model is proposed to deal with the quantized input. Through the proposed nonlinear model, the quantized adaptive control problem is converted into the adaptive stabilization problem for nonlinear high‐order system with unknown virtual control coefficients. Then, based on the tuning function approach and adding power integrator technique, adaptive laws and an adaptive state feedback controller are designed. Further, it is shown that by adjusting some design parameters, the proposed scheme enables the stabilization error converges to an arbitrarily small neighborhood of the origin. Simulation is also provided to verify the validity of proposed scheme.

Adaptive control for heterodirectional 2 × 2 hyperbolic PDEs with spatially varying coefficients and uncertain nonlinear actuator dynamics

In this paper, we aim to develop adaptive asymptotic stability for heterodirectional 2 × 2 hyperbolic PDEs with parametric-strict-feedback nonlinear actuator dynamics. First, we transform the heterodirectional 2 × 2 hyperbolic PDEs with spatially varying coefficients into a stable target subsystem by utilizing the infinite-dimensional backstepping transformation. Second, an adaptive state feedback controller is constructed by combining finite-dimensional state transformation and adaptive compensation technology to assure the boundedness of all the signals in the closed-loop system. Meanwhile, we show that the PDE states converge to zero pointwise in space, the nonlinear ODE states and the control input also converge to zero. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method.

Adaptive tracking control for a class of stochastic nonlinear systems with full-state constraints and dead-zone

This paper seeks to address the problem of state-feedback tracking control for a class of stochastic systems whose states are constrained and input is perturbed by dead-zone. A tan-type barrier Lyapunov function (BLF) and a finite-time adaptive law are proposed such that all states of the system are constrained in the defined bounded compact sets. Based on stochastic Lyapunov theorem, an adaptive state-feedback tracking controller is designed to ensure that the considered stochastic system is semiglobally finite-time stable in probability (SGFSP) and the tracking error signal is bounded. Different from the existing control strategies for stochastic systems, the form of BLF can be used for asymmetric constraints without changing the controller, so the analysis of symmetric or asymmetric full-state constraints is unified. Finally, illustrative simulations are provided to verify the effectiveness of the proposed control strategy.

Fault-tolerant practical tracking control for uncertain robotic system with general reference trajectory and output constraint

This paper is devoted to the fault-tolerant tracking control for a class of uncertain robotic systems under time-varying output constraints. Notably, both actuator fault and the disturbances are present while all the dynamic matrices are not necessarily to be parameterized by unknown parameters or have known nominal parts, and moreover, the reference trajectories as well as the output constraints functions are not necessarily twice continuously differentiable without any time derivatives of them being available for feedback. These remarkable characteristics greatly relax the corresponding assumptions of the related literature and in turn to bring the ineffectiveness of the traditional schemes on this topic. For this, a powerful adaptive control methodology is established by incorporating adaptive dynamic compensation technique into the backstepping framework based on Barrier Lyapunov functions. Then, an adaptive state feedback controller with the smart choices of adaptive law and virtual controls is designed which guarantees that all the states of the closed-loop system are bounded and the system output practically tracks the reference trajectory while not violates the output constraints.

Predefined Time Synchronization of Multi-Agent Systems: A Passivity Based Analysis.

This paper deals with the predefined-time synchronization for a class of nonlinear multi-agent systems. The notion of passivity is exploited to design the controller for predefined-time synchronization of a nonlinear multi-agent system, where the time of synchronization can be preassigned. Developed control can be used to synchronize large-scale, higher-order multi-agent systems as passivity is an important property in designing control for complex control systems, where the control inputs and outputs are considered in determining the stability of the system in contrast to other approaches, such as state-based Control We introduced the notion of predefined-time passivity and as an application of the exposed stability analysis, static and adaptive predefined-time control algorithms are designed to study the average consensus problem for nonlinear leaderless multiagent systems in predefined-time. We provide a detailed mathematical analysis of the proposed protocol, including convergence proof and stability analysis. We discussed the tracking problem for a single agent, and designed state feedback and adaptive state feedback control scheme to make tracking error predefined-time passive and then showed that in the absence of external input, tracking error reduces to zero in predefined-time. Furthermore, we extended this concept for a nonlinear multi-agent system and designed state feedback and adaptive state feedback control scheme which ensure synchronization of all the agents in predefined-time. To further strengthen the idea, we applied our control scheme to a nonlinear multi-agent system by taking the example of Chua's circuit. Finally, we compared the result of our developed predefined-time synchronization framework with finite-time synchronization scheme available in literature for the Kuramoto model.