Showing papers on "Lyapunov function published in 2022"

Observer-Based Neuro-Adaptive Optimized Control of Strict-Feedback Nonlinear Systems With State Constraints

Abstract: This article proposes an adaptive neural network (NN) output feedback optimized control design for a class of strict-feedback nonlinear systems that contain unknown internal dynamics and the states that are immeasurable and constrained within some predefined compact sets. NNs are used to approximate the unknown internal dynamics, and an adaptive NN state observer is developed to estimate the immeasurable states. By constructing a barrier type of optimal cost functions for subsystems and employing an observer and the actor-critic architecture, the virtual and actual optimal controllers are developed under the framework of backstepping technique. In addition to ensuring the boundedness of all closed-loop signals, the proposed strategy can also guarantee that system states are confined within some preselected compact sets all the time. This is achieved by means of barrier Lyapunov functions which have been successfully applied to various kinds of nonlinear systems such as strict-feedback and pure-feedback dynamics. Besides, our developed optimal controller requires less conditions on system dynamics than some existing approaches concerning optimal control. The effectiveness of the proposed optimal control approach is eventually validated by numerical as well as practical examples.

Floating Weighting Factors ANN-MPC Based on Lyapunov Stability for Seven-Level Modified PUC Active Rectifier

Abstract: Despite being cost-effective, seven-level Modified Packed U-Cell (MPUC7) active rectifier tends to be unstable due to unequal dc-links. Thus, a multiobjective controller is required to stabilize voltages and currents besides preserving efficiency and power quality. While conventional finite-set model predictive control (FSMPC) can deal with the multiobjective problem, it cannot assure the system stability, and its weighing factors tuning significantly becomes tiresome as the number of objectives increases. This article presents a low-frequency adaptive FSMPC (AMPC) stabilized based on Lyapunov stability theory to overcome the design problems of FSMPC. AMPC handles four control objectives and a decoupled stability objective. The control objectives assure the standard performance of MPUC7 in terms of switching losses, d v /d t , THD, and capacitors ripple. The stability objective guarantees the rectifier reliability under unstable conditions. The weighting factors in AMPC are floating to tackle the tuning challenges where a radial basis function neural network controller (RBFC) adjusts their variations. RBFC is trained by a novel self-training method including particle swarm optimization (PSO) algorithm and some mathematical analyses without using any training data. Experimental and simulation tests also evaluate AMPC in different conditions to confirm its reliability in fulfilling the desired objectives.

Adaptive Prescribed Performance Control of A Flexible-Joint Robotic Manipulator With Dynamic Uncertainties

Abstract: An adaptive fuzzy control strategy is proposed for a single-link flexible-joint robotic manipulator (SFRM) with prescribed performance, in which the unknown nonlinearity is identified by adopting the fuzzy-logic system. By designing a performance function, the transient performance of the control system is guaranteed. To stabilize the SFRM, a dynamic signal is applied to handle the unmodeled dynamics. To cut down the communication load of the channel, the event-triggered control law is developed based on the switching threshold strategy. The Lyapunov stability theory and backstepping technique are applied coordinately to design the control strategy. The semiglobally ultimately uniformly boundedness can be ensured for all signals in the closed-loop system. The designed control method can also guarantee that the tracking error can converge to a small neighborhood of zero within the prescribed performance boundaries. At the end of the article, two illustrative examples are shown to validate the designed event-triggered controller.

Desired tracking of delayed quadrotor UAV under model uncertainty and wind disturbance using adaptive super-twisting terminal sliding mode control

Abstract: In this study, the fully-actuated dynamic equation of quad-rotor as a type of Unmanned Aerial Vehicles (UAVs) is considered in the existence of input-delay, model uncertainty and wind disturbance. Then, a super-twisting terminal sliding mode control approach is planned with the aim of the finite-time attitude and position tracking of quad-rotor UAV considering input-delay, model uncertainty and wind disturbance. The finite time convergence of the tracking trajectory of quad-rotor is proved by Lyapunov theory concept. When the upper bound of the modeling uncertainty and wind disturbance is supposed to be unknown, an adaptive super-twisting terminal sliding mode control is proposed. Therefore, the unknown bounds of the model uncertainty and wind disturbance affecting the quad-rotor UAV are estimated using the adaptive-tuning control laws. Finally, simulation outcomes and experimental verifications are provided to demonstrate the validation and success of planned control technique.

A3C-Based Intelligent Event-Triggering Control of Networked Nonlinear Unmanned Marine Vehicles Subject to Hybrid Attacks

Abstract: This paper is concerned with the intelligent event-triggering-based positioning control of networked unmanned marine vehicle (UMV) systems with hybrid attacks, where the UMV and control station is connected by a communication network and the DoS attack and Deception attack are studied. Firstly, a stochastic switched Takagi-Sugeno (T-S) fuzzy system model is proposed for the networked nonlinear UMV systems subject to aperiodic DoS attack and random Deception attack. Then, a novel asynchronous advantage actor-critic (A3C) learning-based event-triggering approach is introduced to alleviate the communication load. By using the Lyapunov stability theory and switched system analysis method, the mean-square exponential stability condition of the closed-loop system and the design method of observer-based controller are devised. Finally, an example of a networked UMV system is given to verify the effectiveness of the proposed resilient control strategy.

Applying Dynamic Systems to Social Media by Using Controlling Stability

Abstract: This study focuses on hybrid synchronization, a new synchronization phenomenon in which one element of the system is synced with another part of the system that is not allowing full synchronization and nonsynchronization to coexist in the system. When limt⟶∞Y−αX=0, where Y and X are the state vectors of the drive and response systems, respectively, and Wan (α = ∓1)), the two systems' hybrid synchronization phenomena are realized mathematically. Nonlinear control is used to create four alternative error stabilization controllers that are based on two basic tools: Lyapunov stability theory and the linearization approach.

Fixed-Time Event-Triggered Output Consensus Tracking of High-Order Multiagent Systems Under Directed Interaction Graphs

Abstract: This article investigates the problem of fixed-time event-triggered output consensus tracking for high-order multiagent systems (MASs) under directed interaction graphs. First, a fixed-time event-triggered distributed observer and triggering functions are proposed. Next, fixed-time convergence of the presented distributed observer is proved by the Lyapunov function approach, and an analysis is conducted to show the proposed distributed observer excludes zeno behavior. Then, an event-triggered adaptive dynamic surface fixed-time controller is designed to stabilize the tracking error system. Finally, simulation results are given to show the effectiveness and superiority of the consensus scheme developed. The contribution of this article is to present a novel event-triggered fixed-time distributed observer and a novel fixed-time controller, which can reduce frequency of communication and control update, avoid continuous monitor, exclude zeno behavior, eliminate the effect of mismatched disturbance caused by observation error, and achieve practical fixed-time output consensus tracking of high-order MAS under directed interaction graphs.

Fault-Tolerant Control of Switched LPV Systems: A Bumpless Transfer Approach

Abstract: For switched linear parameter-varying (LPV) systems with possible actuator failures, the parameter-dependent multiple piecewise Lyapunov function is constructed to handle the $H_\infty$ bumpless transfer fault-tolerant control problem. First, a generalized bumpless transfer concept is presented for switched LPV systems to describe the transient performance, for which only the local bumpless transfer condition is required. Second, an event-triggered switching law, depending on the system states, external parameters, and dwell time, is designed to ensure a time span among adjacent switchings. Third, a solvability condition of the $H_\infty$ bumpless transfer fault-tolerant control problem is developed. A family of time-driven switching controllers with bumpless transfer constraint and fault-tolerant requirement are also designed. Finally, an application example of an aero-engine is given to verify the effectiveness of the developed methods.

Command Filter Adaptive Asymptotic Tracking of Uncertain Nonlinear Systems With Time-Varying Parameters and Disturbances

Abstract: This article is devoted to the adaptive asymptotic tracking for a class of uncertain nonlinear systems. The presence of unknown time-varying parameters and uncertain disturbances makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and command filter-based backstepping, a novel command filter adaptive tracking controller is successfully designed to achieve asymptotic tracking. The typical feature of the proposed controller lies in the introduction of a smooth function with positive integrable time-varying function, which makes the controller powerful enough to compensate the unknown time-varying parameters and uncertain disturbances. Remarkably, a novel Lyapunov function by incorporating the lower bounds of control gains is used to prove the stability of the closed-loop system. Compared with some existing command filter-based backstepping, the conditions on the virtual control coefficients and disturbances are relaxed. Finally, the effectiveness of the proposed method is shown by a simulation example.

Trajectory Tracking Control for a Three-Dimensional Flexible Wing

Abstract: This brief mainly considers trajectory tracking and vibration suppression for a 3-D flexible wing. The dynamical model of the flexible wing is regarded as a distributed parameter system, which is described by partial differential equations and ordinary differential equations. A control strategy regulates the flexible wing to track the desired trajectory by controlling two angles. Meanwhile, two active boundary controllers are proposed to restrain the vibrations both in bending and twisting. By using Lyapunov’s direct method, the stability of the flexible wing system can be ensured. Numerical simulations based on the finite-difference method demonstrate the effectiveness of the proposed control schemes.

New Adaptive Control Methods for $n$ -Link Robot Manipulators With Online Gravity Compensation: Design and Experiments

Abstract: For robot manipulators subject to unmeasurable/uncertain plant parameters, this article designs a new adaptive motion controller, which ensures positioning errors to converge to zero and provides accurate gravity compensation. Meanwhile, specific motion constraints are also satisfied during the entire control process. Additionally, the proposed controller is further extended to address output feedback control without velocity measurement/numerical differential operations. A useful feature of this article is that neither complicated gain constraints nor the upper/lower bounds of model parameters/matrices in the dynamics are required in controller design and analysis, which greatly facilitates practical applications. Meanwhile, by introducing a nonlinear auxiliary term (related to motion constraints and error signals) into the proposed controllers, all links accurately reach their desired positions without exceeding the preset constraints, while the gravity vector is estimated online to eliminate static errors. Additionally, the asymptotic stability of the system equilibrium point is strictly proven; more importantly, the difficulty of stability analysis is significantly decreased based on the elaborately constructed Lyapunov function candidate. Compared with existing controllers, the main merits of the designed control schemes include fewer control gain conditions, more concise closed-loop stability analysis, and higher safety satisfying specific constraints. Finally, some hardware experiments are carried out to validate the performance of the presented controllers.

Adaptive Second-Order Sliding Mode Control: A Lyapunov Approach

Abstract: This article proposes an adaptive second-order sliding mode (ASOSM) controller design by means of the Lyapunov method. The notable feature of the proposed algorithm is that it only needs boundedness of the uncertainties, whereas boundedness of the derivatives of uncertainties is not demanded. Under the proposed ASOSM control scheme, the gain can be dynamically tuned, which avoids gain overestimation. The finite-time stability of the closed-loop ASOSM dynamics is proved via the Lyapunov theory. Finally, the simulation results are shown to validate the theoretical analysis.

Non-fragile l 2-l ∞ state estimation for time-delayed artificial neural networks: an adaptive event-triggered approach

Abstract: In this paper, the state estimation problem is investigated for a kind of time-delayed artificial neural networks subject to gain perturbations under the adaptive event-triggering scheme. To avoid wasting resources, the event-triggering scheme is adopted during the data transmission process from the sensors to the estimator where the triggering threshold can be dynamically adjusted. By means of the Lyapunov stability theory, sufficient conditions are provided to ensure that the estimation error dynamics achieves both the asymptotical stability and the - performance. The desired non-fragile estimator gain is parameterised by solving certain matrix inequalities. At last, the usefulness of the proposed event-based non-fragile state estimator is shown via a numerical simulation example.

H ∞ state estimation for memristive neural networks with randomly occurring DoS attacks

Abstract: This study deals with the problem of the state estimation for discrete-time memristive neural networks with time-varying delays, where the output is subject to randomly occurring denial-of-service attacks. The average dwell time is used to describe the attack rules, which makes the randomly occurring denial-of-service attack more universal. The main purpose of the addressed issue is to contribute with a state estimation method, so that the dynamics of the error system is exponentially mean-square stable and satisfies a prescribed disturbance attenuation level. Sufficient conditions for the solvability of such a problem are established by employing the Lyapunov function and stochastic analysis techniques. Estimator gain is described explicitly in terms of certain linear matrix inequalities. Finally, the effectiveness of the proposed state estimation scheme is proved by a numerical example.

Decentralized Event-Triggered Adaptive Fuzzy Control for Nonlinear Switched Large-Scale Systems With Input Delay Via Command-Filtered Backstepping

Abstract: This article presents a decentralized fuzzy adaptive event-triggered command-filtered control scheme for switched large-scale nonlinear systems with input delay. Fuzzy logic systems are employed to approximate uncertain nonlinearities and a novel observer is constructed to estimate unmeasured states. The “explosion of complexity” defect inherent in the backstepping approach is overcome by employing command filter technology. An auxiliary system is designed to compensate for the effect of input delay, and a novel event-triggered decentralized controller is derived based on the common Lyapunov function method. This article shows that the presented strategy guarantees that all closed-loop variables are semiglobally uniformly ultimately bounded. Finally, simulation results are shown to further confirm the presented strategy’s validity.

Self-Triggered Sliding Mode Control for Networked PMSM Speed Regulation System: A PSO-Optimized Super-Twisting Algorithm

Abstract: This article is concerned with the design of a super-twisting algorithm (STA) based sliding mode controller for permanent magnet synchronous motor (PMSM) speed regulation system under the self-triggered mechanism. By using the strict Lyapunov function approach, it is shown that the tracking error converges to an ultimate domain within the finite-time sense under the proposed self-triggered STA. A feasible self-triggered strategy is designed for both cases with and without external perturbation. Moreover, a nonlinear optimization problem is formulated in terms of the tradeoff between the ultimate domain and the communication burden. The optimized STA gains are obtained by solving the above-formulated optimization problem via a particle swarm optimization algorithm. Finally, the applicability of the proposed self-triggered STA for PMSM is verified by simulation and experiment results.

Approximation-Based Nussbaum Gain Adaptive Control of Nonlinear Systems With Periodic Disturbances

Abstract: This article considers the Nussbaum gain adaptive control issue for a type of nonlinear systems, in which some sophisticated and challenging problems, such as periodic disturbances, dead zone output, and unknown control direction are addressed. The Fourier series expansion and radial basis function neural network are incorporated into a function approximator to model time-varying-disturbed function with a known period in nonlinear systems. To deal with the problems of the dead zone output and unknown control direction, the Nussbaum-type function is recommended in the design of the control algorithm. Applying the Lyapunov stability theory and backstepping technique, the proposed control strategy ensures that the tracking error is pulled back to a small neighborhood of origin and all closed-loop signals are bounded. Finally, simulation results are presented to show the availability and validity of the analysis approach.

Finite-Time Synchronization of Markovian Coupled Neural Networks With Delays via Intermittent Quantized Control: Linear Programming Approach

Abstract: This article is devoted to investigating finite-time synchronization (FTS) for coupled neural networks (CNNs) with time-varying delays and Markovian jumping topologies by using an intermittent quantized controller. Due to the intermittent property, it is very hard to surmount the effects of time delays and ascertain the settling time. A new lemma with novel finite-time stability inequality is developed first. Then, by constructing a new Lyapunov functional and utilizing linear programming (LP) method, several sufficient conditions are obtained to assure that the Markovian CNNs achieve synchronization with an isolated node in a settling time that relies on the initial values of considered systems, the width of control and rest intervals, and the time delays. The control gains are designed by solving the LP. Moreover, an optimal algorithm is given to enhance the accuracy in estimating the settling time. Finally, a numerical example is provided to show the merits and correctness of the theoretical analysis.

Prescribed-Time Event-Triggered Bipartite Consensus of Multiagent Systems

Abstract: This article studies event-triggered control for the prescribed-time bipartite consensus of first-order multiagent systems. For each agent, the new event-triggered control law and triggering condition are constructed without continuous interneighboring communication. Based on the Lyapunov stability theory and the algebraic graph theory, permissible value ranges of the designed parameters are established to guarantee that all agents reach bipartite consensus in a completely prespecified time. Moreover, a comprehensive theoretical discussion is provided to show that the Zeno behavior can be excluded during the whole time span except the prespecified settling time T . The simulation results demonstrate the feasibility of the provided methods.

Consensus of second-order heterogeneous multi-agent systems with and without input saturation

Abstract: This paper seeks to investigate the consensus issue of heterogeneous multi-agent system formed by second-order linear and nonlinear agents. An input saturated algorithm and an input unsaturated algorithm are proposed respectively for the heterogeneous system. Through applications of graph theory, Lyapunov technique, Lasalle's invariance principle as well as other mathematical methods, it turns out that every agent of the heterogeneous system will be guaranteed to achieve consensus if some conditions are satisfied. Finally, some detailed simulation examples are utilized to verify our conclusion.

Adaptive Neural Network Control of a Flexible Spacecraft Subject to Input Nonlinearity and Asymmetric Output Constraint

Abstract: This article focuses on the vibration reducing and angle tracking problems of a flexible unmanned spacecraft system subject to input nonlinearity, asymmetric output constraint, and system parameter uncertainties. Using the backstepping technique, a boundary control scheme is designed to suppress the vibration and regulate the angle of the spacecraft. A modified asymmetric barrier Lyapunov function is utilized to ensure that the output constraint is never transgressed. Considering the system robustness, neural networks are used to handle the system parameter uncertainties and compensate for the effect of input nonlinearity. With the proposed adaptive neural network control law, the stability of the closed-loop system is proved based on the Lyapunov analysis, and numerical simulations are carried out to show the validity of the developed control scheme.

Intelligent Event-Based Fuzzy Dynamic Positioning Control of Nonlinear Unmanned Marine Vehicles Under DoS Attack

Abstract: This article addresses the dynamic positioning control problem of a nonlinear unmanned marine vehicle (UMV) system subject to network communication constraints and deny-of-service (DoS) attack, where the dynamics of UMV are described by a Takagi-Sugeno (T-S) fuzzy system (TSFS). In order to save limited communication resource, a new intelligent event-triggering mechanism is proposed, in which the event triggering threshold is optimized by a Q -learning algorithm. Then, a switched system approach is proposed to deal with the aperiodic DoS attack occurring in the communication channels. With a proper piecewise Lyapunov function, some sufficient conditions for global exponential stability (GES) of the closed-loop nonlinear UMV system are derived, and the corresponding observer and controller gains are designed via solving a set of matrix inequalities. A benchmark nonlinear UMV system is adopted as an example in simulation, and the simulation results validate the effectiveness of the proposed control method.

Command filtering‐based adaptive neural network control for uncertain switched nonlinear systems using event‐triggered communication

Abstract: In this article, a command filtering‐based adaptive event‐triggered neural network control scheme is proposed for a class of uncertain switched nonlinear systems with unknown control coefficient and input saturation. First, radial basis function neural networks are used as function approximators to estimate unknown nonlinear functions. Then, an event‐triggering mechanism based on the tracking error is introduced to avoid the over‐consumption of communication resources. Furthermore, command filters are employed to solve the problem of complexity explosion that exists in conventional backstepping control design, and the error compensation signals are designed to reduce the errors caused by the filters. Considering that the unknown control gain and input saturation exist in many practical applications, a Nussbaum‐type function is thus introduced into the controller design to address these challenging issues. Finally, stability of the closed‐loop system is strictly proven under a standard Lyapunov stability analysis framework. The effectiveness of the proposed control scheme is illustrated by a simulation example.

Cooperative Fault-Tolerant Control for Networks of Stochastic Nonlinear Systems With Nondifferential Saturation Nonlinearity

Abstract: This article addresses the cooperative fault-tolerant control problem for networks of stochastic nonlinear systems with actuator faults and input saturation. The fuzzy neural networks (FNNs) are employed to estimate the unknown functions and stochastic disturbance terms. To analyze the nondifferential saturation nonlinearity, a smooth nonlinear function of the control input signal is constructed to estimate the saturation function. A novel adaptive fault-tolerant control protocol is proposed by using backstepping design technique. By using the stochastic Lyapunov functional strategy, it is proved that all the followers’ outputs eventually converge to a small neighborhood of the leader’s output, and all the signals in the closed-loop systems are bounded in probability. Finally, the performance of the proposed control strategy is illustrated through simulation.

Event-Triggered Guaranteed Cost Leader-Following Consensus Control of Second-Order Nonlinear Multiagent Systems

Abstract: This article deals with the event-triggered leader-following guaranteed cost consensus control problem for second-order nonlinear multiagent systems, in which the guaranteed cost function is proposed to facilitate to enhance the consensus tracking regulation performance. To reduce the frequency of information transmission, a distributed event-triggered mechanism, which broadcasts the triggered states to its neighbours for each agent, is designed, and the triggering condition is then constructed for leader-following second-order nonlinear multiagent systems. By employing Lyapunov–Krasovskii method and Barbalat’s lemma, some sufficient conditions are derived to ensure the leader-following consensus and guaranteed cost performance for second-order nonlinear multiagent systems. It is also exhibited that the constructed triggering condition can efficaciously exclude the Zeno behavior. To testify the efficacy of the proposed theoretical methodology, a simulation example is offered.

Resilient Distributed Fuzzy Load Frequency Regulation for Power Systems Under Cross-Layer Random Denial-of-Service Attacks

Abstract: In this article, a novel distributed fuzzy load frequency control (LFC) approach is investigated for multiarea power systems under cross-layer attacks. The nonlinear factors existing in turbine dynamics and governor dynamics as well as the uncertain parameters therein are modeled and analyzed under the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. The cross-layer attacks threatening the stability of power systems are considered and modeled as an independent Bernoulli process, including denial-of-service (DoS) attacks in the cyber layer and phasor measurement unit (PMU) attacks in the physical layer. By using the Lyapunov theory, an area-dependent Lyapunov function is proposed and the sufficient conditions guaranteeing the system's asymptotically stability with the area control error (ACE) signals satisfying H∞ performance are deduced. In simulations, we adopt a four-area power system to verify the resiliency enhancement of the presented distributed fuzzy control strategy against random cross-layer DoS attacks. Results show that the designed resilient controller can effectively regulate the load frequency under different cross-layer DoS attack probabilities.

Distributed Optimization of Multiagent Systems Against Unmatched Disturbances: A Hierarchical Integral Control Framework

Abstract: This article investigates a distributed optimization problem of double-integrator multiagent systems with unmatched constant disturbances. Instead of involving an internal model or a disturbance observer to deal with the disturbances as in existing works, a two-layer control framework is presented based on state-integral feedback control (SIFC) and adaptive control techniques. The upper layer uses a virtual system to generate a global optimal consensus trajectory which is shared by the agents via a communication network. The lower layer includes an SIFC controller to guarantee asymptotic tracking of the given trajectory. Also in this layer, a model reference adaptive controller is introduced to enhance the dynamic tracking performance of the SIFC controller. This framework enables distributed optimization with time-triggered communication and mild requirements on the team objective. The method yields an interesting co-design algorithm of the control parameters and the communication intervals, which is proved to be convergent using Lyapunov stability theory. The effectiveness and advantages of the method are illustrated by numerical simulations.