Search

This paper investigates the practical prescribed time tracking for a class of uncertain nonlinear systems based on neural networks and event‐triggered control. Introducing a time‐varying constraint function transforms the original practical prescribed time‐tracking control issue into a tracking error constraint problem. An event‐triggered adaptive control has been proposed, which can effectively reduce the communication burden between the controller and the actuator. Using neural networks to approximate unknown nonlinear functions avoids the differentiation of virtual controllers, thereby reducing the computational burden. In addition, users can independently choose preset time and tracking accuracy without changing the control structure, which remains independent of the initial conditions and any design parameters. Finally, the effectiveness of this method is verified through simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, the model‐free robust control problem is investigated for nonlinear systems with a relaxed condition of initial admissible control. An advanced integral reinforcement learning method is developed, which merges the adaptive network‐based fuzzy inference system (ANFIS) and pre‐training of the initial weights. To loose the condition for choosing the initial control law, pre‐training of initial weights is established by utilizing the ANFIS to provide the information corresponding to the system model, which is applicable to the model‐free issue. Based on the actor‐critic structure, the approximate optimal control law is obtained by employing adaptive dynamic programming. Redesigning the obtained control law, the robust controller can be derived to stabilize the system with the uncertain term. Eventually, two examples are utilized to verify the effectiveness of the constructed algorithm. [ABSTRACT FROM AUTHOR]

The traditional Nussbaum‐type functions encounter challenges when extended to systems with multiple unknown control directions, as the coupling between the Nussbaum‐type function and Nussbaum‐type gain may lead to mutual elimination. To address this issue, a novel Nussbaum‐type function is introduced to handle multiple unknown control directions for stochastic systems. The stability of the proposed Nussbaum‐based design can be guaranteed using the Lyapunov analysis. To conserve computational resources, a static composite event‐triggered mechanism is integrated with intermittent feedback in the Nussbaum‐based design. In contrast to conventional event‐triggering mechanisms that depend solely on control signals, the presented design incorporates tracking errors into the event‐triggering conditions. Moreover, to further alleviate computational burdens, we further develop a dynamic composite event‐triggered mechanism. With the overall design scheme, bounded tracking errors and reduced computational burden can be ensured. Simulation examples validate the efficacy of the proposed adaptive Nussbaum composite event‐based robust control design. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the problem of adaptive robust safety‐critical control (ARSCC) for switched systems, where the safety of subsystems is not necessary. A novel ARSCC framework and an executable algorithm are presented to solve the ARSCC problem by finding a switching signal and controllers of subsystems. To estimate uncertainties, a novel switched piecewise‐constant adaptive law is presented, which guarantees a pre‐computable estimation error boundary. A single barrier function (SBF) method is proposed to ensure safety of switched systems with uncertainties, where the safety of subsystems is satisfied only in some subregion of a given safe set, instead of the whole safe set. Based on the SBF method, a novel state‐dependent switching law possessing different dwell times for different subsystems, is established to orchestrate the switching among potentially unsafe subsystems. As a special case of the SBF method, a common barrier function method is presented to achieve safety of switched systems with uncertainties under switching signals with given dwell times. In addition, some sufficient conditions are derived to obtain safety and asymptotic stability for switched systems with uncertainties by combining SBF and single Lyapunov function. Finally, a switched RLC circuit system is given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The consensus problem of a multi-agent system with nonlinear second-order underactuated agents is addressed. The essence of the approach can be outlined as follows: the output is redesigned first so that the agents attain the minimum-phase property. The second step is to apply the exact feedback linearization to the agents. This transformation divides their dynamics into a linear observable part and a non-observable part. It is shown that consensus of the linearizable parts of the agents implies consensus of the entire multi-agent system. To achieve the consensus of the original system, the inverse transformation of the exact feedback linearization is applied. However, its application causes changes in the dynamics of the multi-agent system; a way to mitigate this effect is proposed. Two examples are presented to illustrate the efficiency of the proposed synchronization algorithm. These examples demonstrate that the synchronization error decreases faster when the proposed method is applied. This holds not only for the states constituting the linearizable dynamics but also for the hidden internal dynamics. [ABSTRACT FROM AUTHOR]

Robust control of uncertain fully actuated systems (FASs) with nonlinear uncertainties and perturbed input matrices is considered. Motivated by the recent work on this issue, two novel robust controllers are further developed for two cases under different assumptions. For both cases, the assumption on the perturbation input matrix in the previous work is relaxed to a significant extent, which allows many typical perturbation input matrices, such as constant ones, to be handled, while the previous method cannot. Moreover, for the first case, the assumption on the system uncertainty is further relaxed, and the states of the closed-loop system are globally bounded and converge into an arbitrarily small spherical domain centered at the origin. For the second case, with another requirement on the system nonlinearity imposed, the global exponential stability of the closed-loop system is achieved. The successful application in an electromechanical system verifies the effectiveness of the method. • The nonlinear uncertainty and the uncertainty in the input matrix are considered. • A controller makes the states converge globally into an arbitrarily small region. • Another controller achieves the global exponential stability. • The assumptions on the perturbed input matrix in the previous work are relaxed. • A successful application in the control of electromechanical systems. [ABSTRACT FROM AUTHOR]

This paper is devoted to the iterative interval estimation for nonlinear discrete-time systems. To reconstruct the system state, a sequence of iterative observers is established based on the iterative disturbance estimation and measured output. By means of the Lipschitz condition and H ∞ technique, sufficient conditions are built by the Lyapunov function method to make observation errors convergent. Resorting to the zonotope-based reachability analysis, the reachable set of nonlinear terms and observation errors are analyzed such that the state interval can be supplied. The presented approach is validated by a simulation comparison. [ABSTRACT FROM AUTHOR]

This article explores the problem of sampled‐data cooperative robust practical output regulation for nonlinear multi‐agent systems whose leader system is unknown. In this study, the nonlinearities of the follower systems are not constrained by the linear growth condition. Based on the robust control technology and the adaptive control technology, a distributed output‐based sampled‐data control protocol is developed to deal with the uncertainty of the exosystem which can belong to any large known compact set. We first perform the coordinate transformation of closed‐loop system to obtain the so‐called augmented system, and then perform the stability analysis for this system. As a result, it is proven that the steady‐state tracking errors are in any small given neighborhood of the origin. Finally, the performance of the proposed controller is validated by a numerical example. [ABSTRACT FROM AUTHOR]

ABSTRACT In this brief, an optimal active fuzzy fault‐tolerant control (OAFFTC) scheme is proposed for a class of unknown perturbed multi‐input multi‐output (MIMO) nonlinear systems with nonaffine nonlinear actuator faults and time‐varying sensor faults. The control strategy can handle automatically (online updating) with three additives (bias, drift, and loss of accuracy) along with one multiplicative (loss of effectiveness) sensor faults and nonlinear state‐dependent actuator faults. In order to deal with uncertain system dynamics, sensor and actuator faults, and external disturbances, fuzzy systems (FSs) and backstepping techniques were combined to provide the adaptive control term as well as a robust control term. Butterworth filter is used to get rid the algebraic loop problem. The suggested robust term, can deal with approximation errors of the fuzzy systems (FSs). To automatically optimize the adaptive parameters and the starting conditions, particle swarm optimization (PSO) approach is introduced. The Lyapunov approach is employed to demonstrate the closed‐loop system's stability. To assess the efficacy and correctness of the suggested scheme, quadrotor dynamic model is performed on the simulation part. [ABSTRACT FROM AUTHOR]

In this paper, the problem of output tracking control is considered for a class of uncertain strict-feedback nonlinear systems with virtual control coefficients and full state constraints. It is assumed only that the nonlinear uncertainties of the systems are some smooth functions enough to guarantee the existence of solutions to the differential equations which describe uncertain systems, and that the virtual control coefficients are unknown. Based on backstepping algorithm, by combining the barrier Lyapunov function with an integral inequality reported in the current control literature, a design method is presented whereby a simple adaptive robust output tracking control scheme can be synthesised. The presented design method can evade the repeated differentiation problem appearing in using backstepping algorithm, and need not know all the nonlinear upper bounds of uncertainties, which are repeatedly employed at each step of backstepping procedure. It is also shown that the output tracking error of the uncertain nonlinear systems with both unknown virtual control coefficients and full state constraints can converge uniformly exponentially towards a ball which can be as small as desired. Finally, a numerical example is given, and the corresponding simulations are also implemented to demonstrate the simplicity of the proposed method and the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

A methodology is presented for the design and implementation of robust controllers that optimise inter-sample performance for a broad range of nonlinear systems operated within a sampled-data environment. The methodology applies to nonlinear continuous-time systems described by state equations, and it allows for modelling uncertainties and constraints on maximal control effort. It is shown that there exist optimal robust state-feedback controllers that minimise inter-sample tracking errors for such systems, as long as an appropriate controllability requirement is met. A relatively simple design and implementation procedure for such controllers is described. [ABSTRACT FROM AUTHOR]

The problem of robust tracking and model following is reconsidered for a class of uncertain nonlinear systems with some uncertainties and dead-zone input constraints. In this paper, the system uncertainties are regarded as some nonlinear functions which are not required to must satisfy the matching conditions. That is, being different from traditional robust control theory, the matched structures of uncertainties are sufficient, but not necessary, for being able always to design some types of robust tracking control schemes. In addition, the external disturbances of dynamical systems are assumed to be any bounded functions which is not also required to satisfy the matching condition. By making use of the integral inequality, instead of Lyapunov function, a class of robust tracking control schemes is constructed to guarantee the uniform exponential boundedness of the model tracking errors. Moreover, the upper bounds of nonlinear uncertainties are not required to be known, and it is also unnecessary to know or estimate the characteristic parameters of dead-zone functions. Therefore, the resulting robust tracking control schemes have a simple structure. Actually, the resulting robust tracking control scheme is a linear feedback control one with a self-tuning control gain. Finally, an illustrative numerical example is provided to demonstrate the validity of the presented theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an output feedback controller using iterative learning algorithm is proposed for stabilising a class of uncertain nonlinear single-input single-output (SISO) systems with unknown bounded disturbances. By dividing the time interval into equal iteration periods, iterative learning algorithm is integrated into output feedback control and is carried out under alignment condition. Using the output signal, control input and estimates of uncertain parameters, adaptive state observers are established to generate state estimates which will be employed to design the control law. Based on the backstepping technique, the output feedback controller is developed consisting of the ILC part and robust control part. Different from the traditional ILC update laws of uncertain parameters with constant gains, a novel type of parameter update law is developed where the ILC gain is variable and determined by the real-time state estimates such that system stability can be guaranteed. By virtue of the composite energy function, it is proved that all the signals of the closed-loop system are bounded and the output will uniformly converge to zero along the iteration axis, which indicates the stabilisation of the output signal over the time domain. Simulation verification is conducted to apply the proposed controller to a one-degree-of-freedom suspension system to validate the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

The aim of the present article is to design a robust fractional-order (FO) finite-time (FnT) control able to tackle Hölder disturbances of second-order nonlinear systems. First, a novel sliding manifold with Arc-Tangent function is suggested for second nonlinear systems. It has been proven that the system states globally converge to the origin in FnT using the proposed sliding mode variable. To ensure a FnT stability of the sliding variable, a robust control is developed. By using fractional operators, a uniformly continuous control law is designed to tackle Hölder disturbances. Furthermore, the suggested approach is shown to be resistant to matched Hölder disturbances and uncertainties that are continuous but not necessarily differentiable. Moreover, the FnT stability of quadrotors using the proposed control, that is our second result. The quadrotor simulations analysis demonstrates the practicality of the proposed FnT controller in the presence of Hölder disturbances. • A simple nonlinear manifold design is proposed to ensure a finite-time convergence of quadrotors unlike the existing nonlinear sliding variables (Mousavi et al., 2021). • Hölder disturbances are addressed using fractional switching control law in the design of the proposed control scheme. • Compared to existing rejection disturbances (Ju et al., 2022; Labbadi and Cherkaoui, 2020; Razzaghian, 2022; Mousavi et al., 2021), the proposed FOFTC scheme has a faster convergence speed. [ABSTRACT FROM AUTHOR]

Motivated by the fully actuated system (FAS) approach, this paper proposes a direct robust control method for a type of uncertain multi‐order sub‐fully actuated systems (MOSFASs). Unlike numerous previous results, this paper broadens to a more general multi‐order model and the more challenging sub‐fully actuated case with the presence of singular problems. Firstly, a general uncertain MOSFAS model is presented, where the uncertainty merely needs to satisfy a common assumption. Secondly, a direct robust control method is proposed, giving a robust controller which only needs to satisfy very loose and basic requirements to ensure that the states ultimately converge into an arbitrarily small region. Simultaneously, by constraining the initial values of the states, it is perfectly guaranteed that the states always remain in a "safe" zone free of singular points, thus preserving the realizability of the controller. Finally, under certain conditions, a less conservative robust control scheme is introduced, which can relax the constraint of initial values easily. A simulation for a coarse‐fine angle system demonstrates the validity and value of the proposed robust control method. [ABSTRACT FROM AUTHOR]

This article investigates the stabilization problem of uncertain switched nonlinear systems. Uncertainty and saturated impulses are first considered together in switched nonlinear systems. It appears that the considered systems are robustly locally exponentially stable under the fast average dwell time method and the designed saturated impulsive controller even though subsystems are unstable. At the same time, our conclusions cover some previous results. A step‐by‐step strategy for optimizing multiple objectives is designed to estimate the basin of attraction of the systems as large as possible. At last, the efficacy of our conclusions is illustrated by two given examples. [ABSTRACT FROM AUTHOR]

This article focuses on the problem of robust adaptive safety control of a class of nonlinear systems with parametric uncertainties. Two novel definitions, that is, robust adaptive control Lyapunov function (RACLF) and robust adaptive control barrier function (RACBF) are introduced in this article. Also, an estimation of unknown parameters is obtained based on multiple identification models, state predictors and a logic switching mechanism. The switching mechanism plays a vital role in enhancing the transient properties of nonlinear systems. Meanwhile, a safe motion framework for differential robots is provided based on the existence of parametric uncertainties in RACLF and RACBF, and a safe and stable controller is obtained by solving quadratic programming. Finally, simulation results of differential robot capable of safe motion in space are presented to verify the validity of the design method. [ABSTRACT FROM AUTHOR]

The problem of fixed‐time formation control for a class of second‐order nonlinear multi‐agent systems is studied. For a class of such systems, a control algorithm is proposed to maintain the connections among the agents while avoiding collisions. Furthermore, a radial basis function neural network is used in the design to precisely approximate the nonlinear function for the nonlinear terms in the model. Then, a dynamic sliding mode control method is proposed to suppress the chattering phenomenon that may arise due to the sliding mode control. A sufficient condition for the system to achieve fixed‐time formation is obtained by using different methods, such as Lyapunov stability. Finally, the effectiveness of the proposed algorithm is verified by example. Simulation experiments reveal that the proposed method has faster error convergence and better robust control than conventional algorithms. [ABSTRACT FROM AUTHOR]

The efficiency of standalone photovoltaic (PV) systems heavily relies on the effectiveness of their maximum power point tracking (MPPT) controller. This study aims to improve the operational efficiency and reliability of standalone PV systems by introducing a novel control scheme, the Immersion and Invariance Neural Network (II-NN). This innovative system integrates a nonlinear estimator of solar irradiance with a neural network (NN) model, eliminating the need for direct irradiance measurements and associated costly sensors. The proposed methodology uses the Immersion and Invariance algorithm to design a nonlinear estimator that leverages the real-time measurements of PV current and voltage to estimate the incident irradiance. The NN then processes this estimated irradiance to determine the MPP voltage accurately. A robust nonlinear controller ensures the PV system operates at the MPP. This approach stands out by managing the nonlinearities, parametric uncertainties, and dynamic variations in PV systems without relying on direct irradiance measurements. The II-NN system was rigorously tested and validated under real climatic conditions, providing a realistic performance assessment. The principal results show that the II-NN system achieves a mean error of 0.0183V and a mean absolute percentage error of 0.3913%, with an overall MPPT efficiency of up to 99.84%. Comparisons with the existing methods, including perturb and observe, incremental conductance, and three other recent algorithms, reveal that the II-NN system outperforms these alternatives. The major conclusion is that the II-NN algorithm significantly enhances the operational efficiency of PV systems while simplifying their implementation, making them more cost-effective and accessible. This study substantially contributes to PV system control by advancing a robust, intelligent, and sensorless MPPT control scheme that maintains high performance even under varying and unpredictable climatic conditions. [ABSTRACT FROM AUTHOR]

This article investigates the robust consensus problem for nonlinear multiagent systems against time‐varying false data injection attacks on actuators and sensors. First, the root‐mean‐square (RMS) theory is used to extend the assumption of the slow‐varying or constant attack signals to the case of time‐varying attack signals. Second, a novel distributed multivariate observer (DMO) is designed to estimate the followers' system states and the time‐varying attack signals on actuators and sensors. With the help of the outputs of DMO, a distributed robust consensus control arithmetic is proposed, which can compensate for actuator attacks and isolate sensor attacks so that exponential consensus and robust consensus are achieved. In particular, the robust performance of estimation errors and consensus errors is ensured by establishing the RMS gain index via linear matrix inequality, in which the zero initial conditions of estimation errors and consensus errors are not required. Finally, two simulation examples, including a network of four aircraft longitudinal dynamic systems, are given to verify the effectiveness of the proposed arithmetic. [ABSTRACT FROM AUTHOR]

In this paper, a robust fault-tolerant control with a dynamic event-triggered mechanism based on the observer is proposed for a nonlinear switched system with faults, external disturbances, and uncertainties. A first-order filter is utilized to equate sensor faults to actuator faults, and the augmented system is constructed. An adaptive observer with H∞ performance is designed based on the augmented system. The condition that the state error and fault error of the adaptive observer are uniformly bounded is given. To save communication resources and reduce the transmission of unnecessary information, an improved dynamic event-triggered mechanism is designed by introducing a fixed threshold and defining a sampling error function based on the observed state and the actual state. This mechanism can further expand the triggering time interval and effectively avoid the Zeno behavior. According to the observed state and real-time fault estimation information at the triggering moment, a fault-tolerant controller for the switched system based on the dynamic event-triggered mechanism is proposed, and the conditions for asymptotic stability of the closed-loop system are provided. Finally, the validity of the proposed method is verified by application simulation for the variant aircraft switched system. [ABSTRACT FROM AUTHOR]

This study addresses the problem of fractional-order nonlinear containment control of heterogeneous multi-agent systems within a leader–follower framework, focusing on the impact of False Data Injection (FDI) attacks. By employing adaptive mechanisms and fuzzy logic, the suggested method enhances system resilience, ensuring reliable coordination and stability even in the presence of deceptive disturbances. To deal with these uncertainties, our controller makes use of interval type-II (IT2) fuzzy sets, and we create matrix equalities and inequalities to account for the asymmetry of Laplace matrices. Also, we use the Lyapunov functions for the stability analysis of our system. Lastly, we explain the numerical simulations for the effectiveness of our theoretical results, and these simulated examples are used to verify the effectiveness of our approach and designed model. [ABSTRACT FROM AUTHOR]

This paper proposes a second-order terminal sliding mode (2TSM) approach to the trajectory tracking of the differential drive mobile robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the innermost loop, tracks the robot's velocity quantities while a kinematic controller, at the outermost loop, regulates the robot's positions. In this manner, chattering is greatly attenuated, and finite-time convergence is guaranteed by the second-order TSM manifold, which involves higher-order derivatives of the state variables, resulting in an inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods. [ABSTRACT FROM AUTHOR]

This article addresses the issue of collaborative wildfire monitoring using a group mobile mecanum‐wheeled omnidirectional vehicles (MWOVs) affected by nonlinear uncertainties and external disturbances. By integrating finite‐time extended state observers (FTESO) and backstepping nonsingular fast terminal sliding mode (BNFTSM) control method, an observer‐based finite‐time time‐varying elliptical formation control scheme is proposed for a group of MWOVs tasked with monitoring the propagation of wildfires in an elliptical pattern. First, the FTESO is employed to estimate the unavailable velocity system states and the lumped disturbances. Then, a novel nonsingular fast terminal sliding surface, enhanced with an exponential term, is introduced to improve the convergence rate. Through the Lyapunov theorem, the convergence of position and velocity cooperative tracking errors to zero in fast finite‐time is demonstrated. To showcase the effectiveness of the proposed control scheme, comparative simulation results are presented. [ABSTRACT FROM AUTHOR]

This paper proposes a systematic approach for optimizing the distribution of local models in multi-model control systems (MMCS) to enhance overall robustness. While existing literature discusses this method for linear parameter varying (LPV) and uncertain linear time-invariant (LTI) systems, significant limitations persist in addressing nonlinear dynamic systems. Robust control tools like the gap metric and generalized stability margin (GSM) have limited effectiveness in analyzing the robustness of nonlinear feedback systems. To address these challenges, novel concepts of the gap metric and GSM are introduced to determine central operating points (COPs) within local operating areas (LOAs) across the total operating area (TOA). These COPs guide the extraction of affine disturbance local models (ADLMs). Additionally, an optimization problem based on the s-gap metric and GSM is presented to optimize COPs placement and LOAs boundaries. Challenges such as non-monotonic behavior of the cost function and complexity arising from the s-gap metric formulation necessitate novel solution methods. To address these, constraints are applied to the cost function, and a novel discrete optimization approach is introduced. Finally, theoretical findings are applied to the Duffing system, pH neutralization process, and continuous stirred tank reactor (CSTR) plant to evaluate the proposed method's effectiveness. This comprehensive validation across different systems underscores the versatility and practical utility of the proposed approach. • We provide a systematic solution for addressing multi-model control systems (MMCS) for nonlinear dynamic systems. • Our approach stands out for its versatility, extending its applicability to a broad spectrum of nonlinear dynamical systems. • The solution is achieved through the utilization of s-gap metric concepts. • We tackle the optimization problem in a discrete form, introducing a novel clustering-based optimization approach. • The non-monotonic behavior of the s-gap metric is addressed by incorporating constraints into the problem formulation. [ABSTRACT FROM AUTHOR]

This article presents an extremum‐seeking control (ESC) algorithm for unmodeled nonlinear systems with known steady‐state gain and generally non‐convex cost functions with bounded curvature. The main contribution of this article is a novel gradient estimator, which uses a polyhedral set that characterizes all gradient estimates consistent with the collected data. The gradient estimator is posed as a quadratic program, which selects the gradient estimate that provides the best worst‐case convergence of the closed‐loop Lyapunov function. We show that the polyhedral‐based gradient estimator ensures the stability of the closed‐loop system formed by the plant and optimization algorithm. Furthermore, the estimated gradient provably produces the optimal robust convergence. We demonstrate our ESC controller through three benchmark examples and one practical example, which shows our ESC has fast and robust convergence to the optimal equilibrium. [ABSTRACT FROM AUTHOR]

The control of quadrotor vehicles under state and parameter uncertainty is a well studied problem that is vitally important to the deployment of these systems under real world conditions. In this article, we propose a linearization‐based extension to nonlinear systems of the existing scenario model predictive control (MPC) framework, which quantifies the impact of uncertainty on the vehicle dynamics through repeated sampling of the uncertainty space. Given the computational costs of such an approach, we also propose two simplifications of the scenario MPC algorithm that are significantly more tractable. In order to evaluate the performance of the algorithms, the specific problem of the control of a bidirectionally actuated quadrotor vehicle is considered. Simulations are carried out for each scenario MPC scheme as well as for a reference deterministic MPC scheme. When a sufficiently large sample count is considered, each of the scenario MPC algorithms achieves safer performance than the deterministic formulation without sacrificing any optimality. Additionally, the approximate solution techniques conclusively outperform the original nonlinear scenario MPC formulation for the same computational cost. [ABSTRACT FROM AUTHOR]

This article investigates the problem of monitoring wildfires using a quadcopter uncrewed aerial vehicle (UAV) subject to external perturbations and nonlinear uncertainties. A finite‐time control scheme is designed for the quadcopter UAV to monitor the elliptical propagation of a wildfire. The control scheme is composed of an improved nonsingular fast terminal sliding mode control (NFTSMC) and a higher order sliding mode observer (HOSMO). The HOSMO is constructed first to estimate external perturbations, nonlinear uncertainties, and incomplete system states resulting from the system's uncertainties. Then, a novel NFTSMC is developed that utilizes the estimated system states. The Lyapunov theorem is used to demonstrate that the quadcopter UAV can elliptically monitor a wildfire, and the tracking error can rapidly converge to zero within a finite time. Comparative simulation results are presented to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This article focuses on establishing a general robust actor‐critic online learning control structure for disturbed nonlinear continuous systems with input constraints. It enriches the existing studies for the robustness of input constraint systems. First, the problem of robust controller design is successfully transformed into optimal controller design, and this process is proven, in which a particular nonquadratic discount cost function is defined. Then, build two neural networks (NNs) to estimate the cost function together and update each other. In the update process of actor NN, a robust term related to the state is introduced, which can guarantee the system's stability during the online learning process, and the state information is more fully utilized. Furthermore, using Lyapunov's direct method, it is proved that the estimated weights of the closed‐loop optimal control system and the actor‐critic NNs are uniformly ultimately bounded (UUB). It also provides extended discussions and a simulation example to demonstrate the robustness verification results of the novel algorithm. [ABSTRACT FROM AUTHOR]

In many engineering problems, modelling the state and output derivative variables in reciprocal state space form can be generated more easily than in standard state space one. The formulation of a robust H ∞ control problem using feedback principle for continuous Lipschitz nonlinear systems with uncertainties in reciprocal state space is presented in this article. In contrast to the existing approaches, the considered model is affected by unknown disturbances, parameter uncertainties and derivative Lipschitz nonlinearities. The asymptotic stability based on the proper Lyapunov functions of the closed-loop system is guaranteed. The H ∞ control design resolution problem is ensured through the linear matrix inequality technique, the lemmas and the use of new variables with S-procedure. The performance of the proposed approach is shown through the experimental results using real-time implementation with a digital signal processing device (DSpace DS 1104). [ABSTRACT FROM AUTHOR]

We present a proportional–integral–derivative-based controller plus an adaptive slide surface to solve the trajectory tracking control problem for a fully actuated vessel with unknown parameters perturbed by slowly varying external unknown dynamics. The controller design assumes that the vessel moves at low speed and frequency, its physical parameters are unknown, and its state is measurable. The control approach ensures error tracking convergence toward a small vicinity at the origin. We conduct the corresponding stability analysis using the Lyapunov theory and saturation functions. We tested the controller through two numerical experiments—a turning ellipse maneuver and a rest-to-rest maneuver—where the vessel parameters were unknown, and we obtained satisfactory results. [ABSTRACT FROM AUTHOR]

Sampled‐data control problems via memoryless state and output feedback are studied, respectively, for a class of strongly nonlinear systems with state and input delays. Under sample and hold, both state and output feedback control schemes are developed by virtue of the emulation method, the adding a power integrator technique, and the recursive design of nonlinear observers. With the aid of Lyapunov–Krasovskii functional theorem, together with the idea of robust control, we prove that the proposed sampled‐data state and output feedback controllers make the hybrid closed‐loop systems with delays and uncertainty globally asymptotically stable, if the input delay and sampling period are limited. The class of time‐delay uncertain systems under consideration goes beyond the Lipschitz or linear growth condition and is genuinely nonlinear in the sense that it contains uncontrollable/unobservable linearization and is not stabilizable, even locally, by any linear or smooth feedback. Applications of the sampled‐data robust control schemes presented in this article are illustrated by examples with simulations. [ABSTRACT FROM AUTHOR]

In this paper, a novel robust finite-time control scheme is specifically designed for a class of under-actuated nonlinear systems. The proposed scheme integrates a reaching phase-free integral backstepping method with an integral terminal fractional-order sliding mode to ensure finite-time stability at the desired equilibria. The core of the algorithm is built around proportional-integral-based nonlinear virtual control laws that are systematically designed in a backstepping manner. A fractional-order integral terminal sliding mode is introduced in the final step of the design, enhancing the robustness of the overall system. The robust nonlinear control algorithm developed in this study guarantees zero steady-state errors at each step while also providing robustness against matched uncertain disturbances. The stability of the control scheme at each step is rigorously proven using the Lyapunov candidate function to ensure theoretical soundness. To demonstrate the practicality and benefits of the proposed control strategy, simulation results are provided for two systems: a cart–pendulum system and quadcopter UAV. These simulations illustrate the effectiveness of the proposed control scheme in real-world scenarios. Additionally, the results are compared with those from the standard literature to highlight the superior performance and appealing nature of the proposed approach for underactuated nonlinear systems. This comparison underscores the advantages of the proposed method in terms of achieving robust and stable control in complex systems. [ABSTRACT FROM AUTHOR]

In practice, there exist systems with high nonlinearity and time-varying functions. Time-varying nonlinear systems (TVNS) present inherent challenges due to their high nonlinearity and time-varying nature, especially when unknown input disturbance and model uncertainties occur. In this work, a class of single input single output (SISO) uncertain affine TVNS is considered for tracking controller design in the presence of unknown disturbance, in which both the disturbance and model uncertainties are assumed to be bounded. Based on these bounds, a tracking controller will be proposed for first-order uncertain TVNS with unknown input disturbance, and then it is extended for second-order uncertain affine TVNS with unknown input disturbance. Unlike other existing works, the proposed controller does not use fuzzy systems, neural networks or any adaptive mechanism to cope with uncertainties and disturbances. It only uses the bounds of disturbance and model uncertainties, the information of tracking error to compute the control signal, and Lyapunov stability theory is applied to analyze stability of the closed-loop system. In addition, the convergence rate of tracking error can be adjusted by tuning parameters. Some numerical simulations with a first-order system and a model of inverted pendulum are given to verify the developed controller. These systems are uncertain and disturbed by unknown external signals and the proposed controller does not know this information but the tracking error still converges to a small circle containing the origin. The proposed controller can be extended for higher-order systems or MIMO systems such as robotic manipulators. [ABSTRACT FROM AUTHOR]

Parallel robot systems have become increasingly applied due to significant advantages such as fast operating speed and high accuracy. Researchers are currently focusing on developing advanced control methods to increase the accuracy of this system. However, these advances face many challenges, including system dynamics and uncertain components in impact factors. Therefore, achieving a high level of accuracy remains a challenging problem and requires continued effort and careful research. This study proposes to use the Cerebellar Model Articulation Controller (CMAC) to estimate the nonlinear components of the system. By applying Lyapunov theory, this method focuses on adapting CMAC's online learning rules while ensuring stability and convergence. Besides using CMAC, the paper proposes a new signed distance method instead of sliding mode control (SMC) to handle input errors. This method aims to increase flexibility and adaptability and overcome the chattering of SMC in nonlinear systems. In particular, the research also adds a robust controller to ensure stability using Lyapunov to improve the system's accuracy. These recommendations increase the flexibility and accuracy of the control system, helping the system respond more quickly to changes and uncertainties in the operating environment. Finally, to demonstrate the effectiveness of the proposed controller, a five-bar parallel robot was chosen to conduct experiments in case situations. The results show that the proposed controller combined with signed distance achieves higher accuracy than other algorithms and is more stable in all cases mentioned in the research. [ABSTRACT FROM AUTHOR]

This paper aims to address the problem of event‐based adaptive robust control for a class of nonaffine nonlinear systems against actuator faults and unknown deception attacks. Firstly, different from the widely used relative threshold triggering mechanism, an improved event‐triggered mechanism with the time‐varying function threshold is devised for effectively saving more communication costs between controller and actuator. Then, based on a class of modified filter‐based coordinate transformations and the improved event‐triggered mechanism, the intermediate virtual control laws are devised to construct actual controllers, which not only guarantees robust stabilization of the system but also relaxes the universal assumptions on control coefficients and attack weights. Besides, the design challenges resulting from the presence of coupling terms in the nonaffine nonlinear system are successfully overcome by virtue of mean value theorem and the property of fuzzy basis function. Theoretical analysis proves that all signals of the closed‐loop system are semiglobally uniformly ultimately bounded (SUUB) and the Zeno behavior can be averted. Finally, the effectiveness of the proposed strategy is verified via comprehensive simulation results. [ABSTRACT FROM AUTHOR]

This study focuses on the problem of perturbation suppression and tracking control of nonlinear fractional order systems with time‐varying delay. To simplify the control process for such systems, the Takagi–Sugeno fuzzy model is used to describe the nonlinear fractional order delayed systems. Additionally, a modified repetitive controller is applied to develop an output feedback technique for the proposed systems. To ensure system stability, the study establishes new delay‐dependent stabilization conditions using a novel Lyapunov–Krasovskii functional (LKF). These stability conditions are expressed in formation of linear matrix inequalities (LMIs) by adopting a frequency‐distributed model transformation and some slack matrices. The proposed method demonstrates that the system output can track the desired input with ignorable error, while effectively rejecting disturbances. Finally, the efficacy of the proposed method is evaluated through simulations of the modified Chua circuit and the hydraulic turbine governing system (HTGS). [ABSTRACT FROM AUTHOR]

In this paper, we develop an improved data-based integral policy iteration method to address the robust control issue for nonlinear systems. Combining multi-step neural networks with pre-training, the condition of selecting the initial admissible control policy is relaxed even though the information of system dynamics is unknown. Based on adaptive critic learning, the established algorithm is conducted to attain the optimal controller. Then, the robust control strategy is derived by adding the feedback gain. Furthermore, the computing error is considered during the process of implementing matrix inverse operation. Finally, two examples are presented to verify the effectiveness of the constructed algorithm. [ABSTRACT FROM AUTHOR]

In this article an optimal control scheme is proposed to solve robust control problem for matched and unmatched system. In the proposed optimal approach the value functions are designed such that the obtained optimal control law guarantees asymptotic stability of the uncertain nonlinear system. Since the proposed robust optimal control problem is not straightforward to solve, an off‐policy reinforcement‐learning algorithm based on neural networks approximation is developed to obtain robust optimal control law iteratively. The robust control law for matched uncertain systems can be achieved via proposed off‐policy learning algorithm without requiring exact knowledge of system's dynamics. The advantages of the proposed robust optimal controller are verified by comparative simulations on an uncertain model of a car suspension system and a mathematical nonlinear model. [ABSTRACT FROM AUTHOR]

This article addresses the problem of robust output regulation for uncertain switched systems. A general result is first proposed for the case of uncertain and nonlinear systems. In order to cope with model uncertainties, the proposed approach implements the internal model principle. Local asymptotic stability of the closed‐loop system as well as zero steady state error on the controlled output are proven using Lur'e Lyapunov functions. Then, this result is specialized to the linear case. Sufficient conditions ensuring global or local stability of the closed loop system are provided. Furthermore, a constructive method based on LMI is presented. When only local stability is achieved, outcomes of this procedure are not only the controller gains, but also an estimation of the robust domain of attraction. Finally, illustrative examples are proposed, showing the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

For uncertain multiple‐inputs multi‐outputs nonlinear systems, it is nontrivial to achieve asymptotic tracking due to the intrinsic coupling among inputs, while the controllability conditions in most existing methods are rather restrictive or even impractical especially when unexpected actuator faults are involved. In this article, we focus on extending such controllability condition by resorting to the existence (instead of a priori knowledge) of some feasible auxiliary matrix, upon which a robust adaptive control scheme is first presented in the absence of actuator faults that is not only able to achieve asymptotic tracking even in the presence of non‐parametric uncertainties with all the closed‐loop signals globally ultimately uniformly bounded, but also able to deal with a larger class of system models. Furthermore, for the case with intermittent actuator faults, we develop a fault‐tolerant control scheme with extended condition for controllability that is able to accommodate such faults automatically without using any fault detection or fault diagnosis unit. The effectiveness and benefits of the proposed method are verified via simulation on robotic systems. [ABSTRACT FROM AUTHOR]

This paper proposes an enhanced and robust tracking control method for the class of uncertain and disturbed affine nonlinear systems. The approach is based on predictive sliding mode control (PSMC) to combine the advantages of sliding mode control (SMC) with those of model predictive control (MPC). The resulting controller offers numerous benefits, including high robustness, quick transient response, finite-time convergence, and robustness against uncertainties and external disturbances. However, a significant limitation of the proposed PSMC is its reliance on prior knowledge of the disturbance and uncertainty bounds. To address this drawback, a sliding mode observer (SMO) is synthesised to identify uncertainties and disturbances. The proposed controller successfully eliminates the chattering effect without compromising robustness and precision. The Lyapunov theory is used to prove the stability of the closed-loop system. The effectiveness of the proposed approach is validated through simulations on a well-known benchmark. [ABSTRACT FROM AUTHOR]

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger's inequality for the integral terms instead of the traditional and more conservative Jensen's condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates. [ABSTRACT FROM AUTHOR]

Summary: This work proposes a reinforcement learning control scheme for systems affected by persistent external perturbations. This scheme relies on ℋ∞$$ {\mathscr{H}}_{\infty } $$ and high‐order sliding mode control techniques combined to estimate the parameters with a certain degree of precision and simultaneously attenuate persistent and state‐dependent perturbations. The proposed solution is a novel design technique based on the minimization method via Discontinuous Gradient. The stability of the proposed scheme is proved via the Lyapunov approach. [ABSTRACT FROM AUTHOR]

This article discusses a quantiser-based stabilisation problem for uncertain nonlinear systems with the aid of robust $ \mathcal {[K, KL]} $ [ K , KL ] sector. We confirmed that the quantised-feedback control steers the state trajectories of the uncertain nonlinear systems within the robust $ \mathcal {[K, KL]} $ [ K , KL ] sector in finite time by adjusting the quantisation parameters. Furthermore, control-Lyapunov functions are helpful to obtain sufficient conditions for ensuring the closed-loop system's asymptotic stability and the reachability of the robust $ \mathcal {[K, KL]} $ [ K , KL ] sector. Finally, a nonlinear electronic circuit is provided to test the effectiveness of the designed control law. [ABSTRACT FROM AUTHOR]

Using the Hamiltonian function method with different powers, this paper studies the observer-based finite-time robust control problem of general nonlinear uncertain systems with time delay and presents some new results on this issue. First, by applying Hamiltonian realization method, the paper develops an equivalent Hamiltonian form of original system and designs its observer system. Then, based on the observer system, we study finite-time control problem and present several finite-time stabilization and finite-time robust stabilization results by using the augmented technology and the Lyapunov method. Finally, a real unmanned vehicle is used to verify the performance of the observer-based finite-time robust stabilization controller. Different from the existing literature on Hamiltonian method, the Hamiltonian function in the paper has different powers, which implies that the results developed in the paper have a wider range of application. [ABSTRACT FROM AUTHOR]

Considering overshoot and chatter caused by the unknown interference, this article studies the adaptive robust optimal controls of continuous‐time (CT) multi‐input systems with an approximate dynamic programming (ADP) based Q‐function scheme. An adaptive integral reinforcement learning (IRL) scheme is proposed to study the optimal solutions of Q‐functions. First, multi‐input value functions are presented, and Nash equilibrium is analyzed. A complex Hamilton–Jacobi–Issacs (HJI) equation is constructed with the multi‐input system and the zero‐sum‐game‐based value function. It is a challenging task to solve the HJI equation for nonlinear system. Thus, A transformation of the HJI equation is constructed as a Q‐function. The neural network (NN) is applied to learn the solution of the transformed Q‐functions based on the adaptive IRL scheme. Moreover, an error information is added to the Q‐function for the issue of insufficient initial incentives to relax the persistent excitation (PE) condition. Simultaneously, an IRL signal of the critic networks is introduced to study the saddle‐point intractable solution, such that the system drift and NN derivatives in the HJI equation are relaxed. The convergence of weight parameters is proved, and the closed‐loop stability of the multi‐system with the proposed IRL Q‐function scheme is analyzed. Finally, a two‐engine driven F‐16 aircraft plant and a nonlinear system are presented to verify the effectiveness of the proposed adaptive IRL Q‐function scheme. [ABSTRACT FROM AUTHOR]

This paper presents a joint synthesis algorithm of trajectory and controlled invariant funnel (CIF) for locally Lipschitz nonlinear systems subject to bounded disturbances. The CIF synthesis refers to a procedure of computing controlled invariance sets and corresponding feedback gains. In contrast to existing CIF synthesis methods that compute the CIF with a predefined nominal trajectory, our work aims to optimize the nominal trajectory and the CIF jointly to satisfy feasibility conditions without the relaxation of constraints and obtain a more cost‐optimal nominal trajectory. The proposed work has a recursive scheme that mainly optimize trajectory update and funnel update. The trajectory update step optimizes the nominal trajectory while ensuring the feasibility of the CIF. Then, the funnel update step computes the funnel around the nominal trajectory so that the CIF guarantees an invariance property. As a result, with the optimized trajectory and CIF, any resulting trajectory propagated from an initial set by the control law with the computed feedback gain remains within the feasible region around the nominal trajectory under the presence of bounded disturbances. We validate the proposed method via two applications from robotics. [ABSTRACT FROM AUTHOR]

This article addresses the event‐triggered adaptive consensus control of nonlinear multi‐agent systems with unknown control direction and actuator saturation. A new robust adaptive control algorithm based on an event‐triggered mechanism is designed. The smooth Lipschitz function approximates the saturated nonlinear function, while the Nussbaum function handles unknown control directions and residual terms. The event‐triggered mechanism is designed to determine the time of communication, significantly reducing the communication burden. An additional estimator is utilized to deal with unknown parameters involved in neighbor dynamics and prevent information exchange to consistency errors between connected subsystems. The results show that all the signals of the closed‐loop system are uniformly bounded, and the consensus tracking error converges to a bounded set. Meanwhile, Zeno's behavior is eliminated. Simulation results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]