Lyapunov-based Method Research Articles

Dynamic memory-based event-triggered security control for networked control systems subjected to false-injection-data attack

This study addresses the security control problem for networked control systems that are subjected to false-data-injection attacks. The designed controller rests on a dynamic memory-based event-triggered mechanism, which exploits historically transmitted data and an auxiliary term to improve transmission efficiency and ensure satisfactory control performance. Then, a controller that defends against the false-data-injection attacks is proposed by making full use of the historical information. With the aid of Cauchy–Schwarz and Gronwall–Bellman inequalities, the existence of such a controller is validated through a novel Lyapunov-based method, which allows the Lyapunov function to be nonpositive. Further, a test on a dynamic power system is provided to verify the effectiveness and superiority of the proposed method.

Backstepping-based adaptive control of underactuated AUV subject to unknown dynamics and zero tracking errors

This paper introduces a zero-error tracking control solution for underactuated autonomous underwater vehicle (AUV) facing unknown dynamic and environmental disturbances. The proposed approach integrates the backstepping method with adaptive techniques and neural networks to effectively address the challenges posed by uncertainties and external disturbances, thereby enhancing the robustness and adaptability of AUV. Subsequently, a boundary estimation method is employed to dynamically update a single adaptive parameter online, leading to a significant reduction in computational workload. To achieve superior asymptotic tracking performance, a different coordinate transformation of fusion scalar function is designed. Moreover, a rigorous analysis of the proposed control scheme is conducted using the Lyapunov-based method, establishing that the tracking error converges asymptotically to zero. Simulation experiments are executed to illustrate the efficacy of the proposed control scheme.

A Lyapunov-Based Method of Reducing Activation Functions of Recurrent Neural Networks for Stability Analysis

A Lyapunov-Based Method of Reducing Activation Functions of Recurrent Neural Networks for Stability Analysis

Finite-time synchronization control scheme for underactuated satellite formation reconfiguration

A synchronization control scheme for underactuated satellite formation reconfiguration in circular orbits is proposed in this paper. The main idea of the synchronization scheme is to control the satellite without radial or along-track thrust to track its desired configuration while synchronizing its motion with that of other underactuated satellites to maintain the predefined or time-varying formation. Firstly, a new underactuated control approach is presented for either underactuated case. Based on the inherent coupling of the system states, the finite-time convergence of the system trajectory could be guaranteed by the sliding mode-based underactuated controller. Secondly, to synchronize the reconfiguration motion between followers, the sum of the sliding mode errors of every two neighbor followers is defined as the synchronization control. The Lyapunov-based method proves the finite-time convergence of synchronization control. More importantly, the minimum nonzero eigenvalue of the Laplace matrix can reduce the system state convergence region. Numerical simulations also verify the performance of the proposed underactuated synchronization controller.

Real-Time Implementation of the Prescribed Performance Tracking Control for Magnetic Levitation Systems

For magnetic levitation systems subject to dynamical uncertainty and exterior perturbations, we implement a real-time Prescribed Performance Control (PPC). A modified function of Global Fast Terminal Sliding Mode Manifold (GFTSMM) based on the transformed error of the novel PPC is introduced; hence, the error variable quickly converges to the equilibrium point with the prescribed performance, which means that maximum overshoot and steady-state of the controlled errors will be in a knowledge-defined boundary. To enhance the performance of Global Fast Terminal Sliding Mode Control (GFTSMC) and to reduce chattering in the control input, a modified third-order sliding mode observer (MTOSMO) is proposed to estimate the whole uncertainty and external disturbance. The combination of the GFTSMC, PPC, and MTOSMO generates a novel solution ensuring a finite-time stable position of the controlled ball and the possibility of performing different orbit tracking missions with an impressive performance in terms of tracking accuracy, fast convergence, stabilization, and chattering reduction. It also possesses a simple design that is suitable for real-time applications. By using the Lyapunov-based method, the stable evidence of the developed method is fully verified. We implement a simulation and an experiment on the laboratory magnetic levitation model to demonstrate the improved performance of the developed control system.

Observer-Based Backstepping Adaptive Force Control of Electro-Mechanical Actuator with Improved LuGre Friction Model

A dynamic load simulator, which can reproduce on-ground aerodynamic hinge moment of control surface, is an essential rig for the performance and stability test of an aircraft actuation system. In this paper, an observer-based backstepping adaptive control (OBAC) strategy with an improved friction model is proposed to deal with the force tracking problem of an electro-mechanical actuator under the influence of nonlinear friction and lumped disturbances. First, The LuGre friction model is improved by introducing the load effect of electrical linear load simulator (ELLS), and both dynamic and static parameters are identified with experimental data. Then, the ELLS system is divided into a loading subsystem and actuation subsystem for backstepping controller deign. The estimation of the position disturbance is obtained using an extended state observer and used for feedforward compensation for the loading subsystem. To reject the disturbance of friction parameter uncertainties for actuation subsystem, a friction scale factor with a reasonable adaptive updating law is introduced during the friction compensation process. Finally, the stability of the whole closed-loop system is demonstrated using a Lyapunov-based method, and experiments are performed to validate the effectiveness of the developed algorithm.

Optimal consensus control of multi-agent systems based on the state-dependent riccati equation

This paper is concerned with optimal consensus control of a multi-agent system, leaderless or leader-follower control. The hierarchical state-dependent Riccati equation (SDRE) controller was the main framework. The Lyapunov-based method is used for solving time-varying systems. Not only positive definite solution of the related algebraic Riccati equation is realized by the SDRE method based on Lyapunov, but also the negative definite solution is realized. Furthermore, the leader-follower tracking structure is developed based on two nonlinear differential equations; the feedforward differential equation and the state-dependent Riccati differential equation, which consider the error in the cost function through the co-sate equation. The application of the proposed controller structure in controlling the lifting system of multiple 3D cranes is studied. The theoretical results have been verified by simulating the leaderless and leader-follower consensus control problem.

Robust Feedback Control for Discrete-Time Systems Based on Iterative LMIs with Polytopic Uncertainty Representations Subject to Stochastic Noise

This paper deals with the design of linear observer-based state feedback controllers with constant gains for a class of nonlinear discrete-time systems in the form of a quasi-linear representation in presence of stochastic noise. For taking into account nonlinearities in the design of linear observer-based state feedback controllers, a polytopic modeling approach is investigated. An optimization problem is formulated to reduce the sensitivity of the controlled system towards stochastic input, state, and output noise with a predefined covariance. Due to the nonlinearities, the separation principle does not hold, thus, the controller and the observer have to be designed simultaneously. For this purpose, a Lyapunov-based method is used, which provides, in addition to the controller and observer gains, a stability proof for the nonlinear closed loop in a predefined polytopic domain. In general, this leads to nonlinear matrix inequalities. To solve these nonlinear matrix inequalities efficiently, we propose an approach based on linear matrix inequalities (LMIs) with a superposed iteration rule. When using this iterative LMI approach, a minimization task can be solved additionally, which desensitizes the closed loop to stochastic noise. The proposed method additionally enables the consideration of different linear closed loop structures by a unified Lyapunov-based framework. The efficiency of the proposed approach is demonstrated and compared with a classical LQG approach for a nonlinear overhead traveling crane.

Minimum-energy synchronization for interconnected networks with non-periodical information silence

Minimum-energy synchronization control for interconnected networks is addressed, where network topologies contain leaderless and leader-follower structures and information transmission of the whole network is non-periodically silent. The key characteristic of the current work is that the total energy consumption is minimum in the sense of the linear matrix inequality, while both the guaranteed-cost synchronization and the limited-budget synchronization cannot make the total energy consumption be minimum. Firstly, the leaderless minimum-energy synchronization achievement problem is transformed into the asymptotic stabilization problem by the state decoupling strategy, and sufficient conditions of leaderless minimum-energy synchronization are presented by the Lyapunov-based method. Especially, those conditions can be solved by the generalized eigenvalue approach on the basis of the linear matrix inequality. Then, main results of leaderless minimum-energy synchronization are expanded to leader-follower interconnected networks, where the key challenge is that these networks are nonsymmetrical. Finally, two numerical examples are illustrated to verify main results.

Voltage Control of Flexible-Joint Robot Manipulators using Singular Perturbation Technique for Model Order Reduction

Background and Objectives: Robot manipulator with flexible-joints is very complex nonlinear system whose control is one of the most challenging issues in the control word. Therefore, the design of voltage-based controller in addition, using of order reduction methods can reduce the complexity of the control law in such systems. Methods: This paper proposes a voltage controller for flexible-joint robot manipulators based on singular perturbation method. The presented control approach has all three advantages of the singular perturbation method for model order reduction, the proper structure of Port-Hamiltonian systems, and voltage control strategy (VCS). In this approach, the robot manipulator model is divided into three sub-systems, slow, medium and fast sub-systems. Each of the sub-systems is controlled using separate controller. In addition, the stability of these sub-systems and ultimately the whole system are proved. Unlike other related works, in this work the tracking error system is considered from the beginning, and by singular perturbation method, a controller is designed to stabilize the tracking system. Moreover, in the suggested voltage-based controller unlike torque control strategy, the electrical model of actuators is used. Results: The main advantages of proposed approach are simple structure, using only velocity of motors, the position of the joints as a control signal and considering the electrical model of the actuators. So, practical implementation of this controller will be with much less effort, compared to the methods like feedback linearization or other controllers in related works. Moreover, using the Lyapunov-based method, the ultimate bounded stability of the closed loop system is proved. Then, some simulations are provided for tracking, regulation, robustness and response speed purposes. Conclusion: Since, the controllers for every sub-system are designed separately, also, the control signal parameters such as joints position, motors velocity, and motors current can be simply measured, therefore, the structure of designed controller is very simple and practically implementable. As the simulation results confirm, the performance of this controller is appropriate, even when external disturbances are present or the frequency of reference signal increases. At last, by comparison and analysis of the simulation results between the presented approach and a related work, the suitable tracking performance of the suggested controller is shown.

Sampled-data event-triggered control with application to quadcopter formations

This paper proposes a novel distributed formation controller for general linear multi-agent systems with application to multiple quadcopters. First, a new locally computable state-estimate-based event-triggering communication condition is proposed for each agent. Then, the formation tracking problem is formulated as a stability analysis, controller gain and event-generator gain design problem of the closed-loop formation error dynamics. Sufficient conditions that guarantee the co-existence of a valid formation controller and an event-triggered communication mechanism are derived using a Lyapunov-based method and linear matrix inequality techniques. In addition, equivalent low (agent-sized) dimensional sufficient conditions are obtained to reduce the computational complexity. For the simulation conditions used in this research, the proposed estimate-based event-triggered communication mechanism generates less data communication instants when compared with traditional state-error-based mechanisms while still achieving similar control performance.

Adaptive Fault-Tolerant Boundary Control of an Autonomous Aerial Refueling Hose System With Prescribed Constraints

In this article, we propose a redundant fault-tolerant and boundary constraint control in the framework of adaptive method, the neural network approximation, and the barrier Lyapunov function (BLF) with a relaxed initial condition. The actuator failures are compensated by a combination of adaptive methods and redundant actuators when some actuators suffer from partial or even total loss of effectiveness. The radial basis function’s neural network structure is introduced to strengthen the adaptivity in various orientations of the hose and other additionally unmodeled dynamics. To maintain the boundary deflection within a predefined open set after a constraint time, a novel asymmetrical and time-varying BLF is constructed by applying a shifting function to transform the original state into a new state with zero value initially. The performance of the developed adaptive control is demonstrated by numerical simulations. Note to Practitioners—This article is motivated by the limited performances in the existing control designs for flexible unmanned aerial refueling hose systems with failed actuators and boundary constraints. This article considers a redundant actuator case to solve time-varying and partially and totally failed actuator failures that are not settled by adaptive and Nussbaum-based single control. Unlike conventional barrier Lyapunov functions (BLFs), in this article, we resort to a shifting function and propose a novelly asymmetric and time-varying BLF, which is well defined initially and capable to address a deferred constraint control problem. The control design and stability analysis of the actuated system is a Lyapunov-based method rather than relying on semigroup theory or functional analysis, which makes the developed method more engineering orientated. The proposed control strategy is tested to illustrate performances in numerical simulations with the finite difference method.

Lyapunov-Based Real-Time and Iterative Adjustment of Deep Neural Networks

A real-time Deep Neural Network (DNN) adaptive control architecture is developed for general uncertain nonlinear dynamical systems to track a desired time-varying trajectory. A Lyapunov-based method is leveraged to develop adaptation laws for the output-layer weights of a DNN model in real-time while a data-driven supervised learning algorithm is used to update the inner-layer weights of the DNN. Specifically, the output-layer weights of the DNN are estimated using an unsupervised learning algorithm to provide responsiveness and guaranteed tracking performance with real-time feedback. The inner-layer weights of the DNN are trained with collected data sets to increase performance, and the adaptation laws are updated once a sufficient amount of data is collected. Building on the results in (Joshi and Chowdhary, 2019) and (Joshi et al., 2020), which focus on deep model reference adaptive control for linear systems with known drift dynamics and control effectiveness matrices, this letter considers general control-affine uncertain nonlinear systems. The real-time controller and adaptation laws enable the system to track a desired time-varying trajectory while compensating for the unknown drift dynamics and parameter uncertainties in the control effectiveness. A nonsmooth Lyapunov-based analysis is used to prove semi-global asymptotic tracking of the desired trajectory. Numerical simulation examples are included to validate the results, and the Levenberg-Marquardt algorithm is used to train the weights of the DNN.

A Material Selection Criterion for Electrostatic Switches Based on Stability Considerations

Recent impressive advances of MEMS technology thanks to integration of emerging materials exhibiting exclusive properties, has led to fabrication of numerous high performance devices. Further development of the field necessitates more accurate analytical models capable of precisely accounting for all existing physical phenomena affected by new materials properties. In this regard, the present paper investigates how finite electrical conductivity of the composing materials may affect the pull-in instability of an electrostatically actuated cantilever MEMS switch. The governing coupled nonlinear equations of an equivalent lumped parameter model are derived by introducing an assumed mode solution to the extended Hamilton’s principle. A Lyapunov-based method is then employed to derive an estimation for the basin of attraction of the stable equilibrium and determine the minimum voltage needed for the cantilever to escape the attractor and touch the contact. Results indicate the substantial effect of electrical resistivity on both instability range and maximum switching frequency of the device. As evidenced by the presented findings the material selection for this type of switches should be made with a broader view bringing into focus the effect of electrical conductivity of the material on stability characteristics of the device.

Bipartite consensus for multi-agent systems with noises over Markovian switching topologies

In this paper, we investigate the distributed control problem for multi-agent systems (MASs) subject to multiplicative and additive noises over switching networks, where both cooperative and antagonistic interactions coexist. The communication topology is governed by a continuous-time Markovian chain. A stochastic approximation technique is utilized to handle stochastic bipartite consensus with communication noises. The major challenge, due to the fact that the intensity of the multiplicative noise is nonlinearly coupled with the distance between agents, is that the coexistence of antagonistic information and multiplicative noise makes the multiplicative noise term impossible to be converted into an error form. This leads to the inapplicability of the Lyapunov-based method. To cope with this, we first show the boundedness of agents’ states where the second moment approach is employed. Based on it, the mean square and almost surely bipartite consensus are achieved under some mild requirements. The efficiency of the proposed method is supported by an example.

Robust adaptive anti-windup wheel slip tracking control for intelligent vehicle with fast terminal sliding mode observer

Aiming at the requirement of the intelligent vehicle for the fast and stable tracking control of the wheel slip, a novel robust adaptive anti-windup wheel slip tracking control method with fast terminal sliding mode observer is proposed. First, a fast terminal sliding mode observer based on equivalent control on the sliding surface is proposed to estimate the states of the wheel slip dynamic system to lay the foundation for the full state feedback control law design. Second, a robust adaptive anti-windup wheel slip tracking control law with lumped uncertainty observer and additional anti-windup dynamics is derived based on Lyapunov-based method. The lumped uncertainty observer utilizes the nonlinear mapping ability of the radius basis function neural network to estimate and compensate the lumped uncertainty of the system, and the unknown optimal weight vector of the radius basis function neural network is updated by adaptive law. The additional anti-windup dynamics is used to suppress the effect of the input saturation on the stability of the system. Finally, the performance of the proposed method is verified through simulations of various maneuvers on vehicle dynamics simulation software.

Robust adaptive control for continuous wheel slip rate tracking of vehicle with state observer

This article proposes a novel robust adaptive wheel slip rate tracking control method with state observer. First, a modified tracking differentiator is proposed based on a combination of tangent sigmoid function with terminal attraction factor and linear function to improve convergence speed and avoid chattering phenomenon, and then, the modified tracking differentiator is used as state observer to smooth and estimate the states of the system. Second, a robust adaptive wheel slip rate tracking control law with fuzzy uncertainty observer and modified adaptive laws is derived based on Lyapunov-based method. The fuzzy uncertainty observer is used for estimating and compensating the additive uncertainty, and the modified adaptive laws are used for estimating the unknown optimal weight vector of the fuzzy uncertainty observer and the multiplicative uncertainty. Finally, the performance of the robust adaptive wheel slip rate tracking control method is verified based on the model-in-the-loop simulation system.

Nonlinear robust wheel slip rate tracking control for autonomous vehicle with actuator dynamics

This article presents a novel nonlinear robust wheel slip rate tracking control strategy for autonomous vehicle with actuator dynamics. First, a simple yet effective wheel slip rate dynamic model with the lumped uncertainty is established as the basis of the nonlinear robust wheel slip rate tracking control strategy design. Second, a nonlinear robust wheel slip rate tracking control law with lumped uncertainty observer is derived via the Lyapunov-based method. The lumped uncertainty observer is used to estimate and compensate the lumped uncertainty of the system by combining the radial basis function neural network with the adaptive laws for the unknown optimal weight vector of the radial basis function neural network. Then, a novel tracking differentiator is designed to calculate the derivative of the desired wheel slip rate, which is an essential aspect of the proposed nonlinear robust wheel slip rate tracking control law. Finally, the performance of the proposed control strategy is verified based on straight line braking maneuvers with three typical signals.

Optimal spacecraft rendezvous using the combination of aerodynamic force and Lorentz force

This paper presents a propellantless spacecraft rendezvous method by using the optimal combination of aerodynamic force and Lorentz force. Aerodynamic force is provided by the rotations of the plates attached to the spacecraft, and Lorentz force is achieved by modulating spacecraft's electrostatic charge. Considering the limitation of the charging level of the spacecraft and physical constraints of the plates system, an optimal open-loop rendezvous trajectory is designed, which aims to minimize the energy consumed to actuate the hybrid system. The rotation rates of the plates and the electrostatic charge are constrained in the optimization problem, which is solved via the Gauss pseudospectral method. To track the open-loop trajectory in the presence of external perturbations, a novel adaptive nonsingular terminal sliding mode controller is designed. The stability of the closed-loop system is proved by the Lyapunov-based method. Several numerical examples are conducted to verify the validity of both the open-loop and closed-loop control strategy.

Implementation of an Adaptive Neural Terminal Sliding Mode for Tracking Control of Magnetic Levitation Systems

In this article, an adaptive neural terminal sliding mode is implemented for tracking control of magnetic levitation systems with the presence of dynamical uncertainty and exterior perturbation. By proposing a novel fast terminal sliding manifold function with the dynamic coefficients, the system state variables quickly converge the equilibrium point on the manifold function. Besides, an adaptive, robust reaching control law combined with radial basis function neural network compensator drives the system fast approaching the sliding manifold function regardless of whether the initial value is near or far from the sliding manifold and reduces the chattering of the conventional terminal sliding mode control. With a design approach based on the combination of the proposed sliding manifold and the combined control law, the implemented control method provides a control performance with significant improvement in the terms of chattering reduction, high tracking accuracy, fast convergence along with simple design for real applications. The experimental work is implemented for a real magnetic levitation system to demonstrate the superior efficiency of the proposed terminal sliding mode control. The stable evidence of the proposed method is also completely verified by Lyapunov-based method.