Uncertain Nonlinear Systems Research Articles

Multiple dynamic targets enclosing control for a class of nonlinear uncertain multiagent systems

The multiple dynamic targets enclosing control protocol is proposed in this paper for a class of nonlinear uncertain multiagent systems. To accomplish the mission of hunting multiple targets with double-integral nonlinear dynamics, a distributed estimator is established firstly for each agent by employing the signum function, leading to an estimation of the average position of multiple targets. Specifically, only partial information about the dynamic targets is utilized to construct the enclosing formation reference beacon. Furthermore, due to the existence of the system uncertainties, it is a challenging task to design the enclosing controller. To overcome this difficulty, an augmented system is constructed to compensate for the effect caused by the uncertainties, which is introduced afterwards into the control protocol design along with comprehensive theoretical analysis. Sufficient conditions are derived and proved under Lyapunov stability criterion to ensure the closed-loop stability of nonlinear multiagent systems. The effectiveness of the proposed control scheme is finally verified through the numerical simulations. More precisely, by appropriately picking control parameters α and β based on Lemma 3.1, the designed formation reference beacon estimator is validated by achieving convergence of errors between the actual state and estimated states to zero. Meanwhile, the feasibility of the proposed enclosing control protocol is demonstrated simultaneously as it enables the regulation of enclosing errors using a self-designed parameter γ0. Additionally, the sensitivity analysis of the control parameters is presented, which indicates that the proposed reference beacon estimator remains robust to the variation of its control parameters, while larger values for the control parameters in the designed controller result in faster error convergence rates.

Event-triggered prescribed-time control for a class of uncertain nonlinear systems using finite time-varying gain

This paper addresses the event-triggered prescribed-time control problem for a class of high-order nonlinear systems based on finite time-varying gain. Due to the existence of unknown gain functions and system uncertainties, the resultant control with prescribed-time convergence performance becomes nontrivial. The problem becomes even more complex due to the use of event-based communication instead of continuous communication. To tackle the aforementioned challenges, this paper proposes an event-triggered prescribed-time stabilization approach with the following key steps. Firstly, we establish a new prescribed-time stability lemma to overcome the technical difficulty arising from the prescribed-time controller design, and stability analysis. Secondly, we give the controller design procedure upon using the backstepping technique. Thirdly, we redesign the event-triggering threshold condition based on time-varying functions, which allows the controller terminal jitter to be mitigated and the controller to be implemented straightforwardly in practice. Furthermore, the proposed control scheme avoids Zeno behavior. The numerical simulation confirms the effectiveness of the proposed control scheme.

Neural network adaptive switched fault-tolerant control of uncertain nonlinear systems with full state constraints

This paper studies the neural network adaptive fault-tolerant control (NNAFTC) for a class of uncertain nonlinear systems with full state constraints. It is the first time to introduce switched adaptive fault compensation strategy for the controller design process. On the one hand, the proposed method overcomes the limitation needed to be given a prescribed local restriction region of the traditional state constraint schemes, such as log-type, tan-type and integral-type. On the other hand, the full-state constraint and switched fault-tolerant problem is effectively solved even if the existence of actuator failures. Concomitantly, the novel switched tuning functions, the NN approximation technique and the integral barrier Lyapunov functions (IBLF) are combined to construct the backstepping controllers and adaptation laws. It can be proved that all the closed-loop states are restricted in the proper compact sets for any given initial values. Finally, A simulation is shown to demonstrate the validity and advantages of the presented control approach.

A Practical Predefined-Time Stability Criterion and Its Application to Uncertain Nonlinear Systems

A Practical Predefined-Time Stability Criterion and Its Application to Uncertain Nonlinear Systems

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

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

Robust adaptive safety control of uncertain nonlinear systems and its application to differential robots

AbstractThis 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.

Online Adaptive Neural Observer for Prescribed Performance Hyper-Chaotic Systems

This paper proposes a new neural-based algorithm applied to online identifying, observing, and adaptively controlling of uncertain nonlinear systems via which the system transient and residual values independently regulated. The Lyapunov stability concept is used for enhancing the control performance. Especially, distinguished from recent related studies, not only identified model but the learning method and control rules are also innovatively implemented through which it independently separates the transient-time regulation from residual error adjustment.Sequentially, an advanced adaptive neural controller for an uncertain nonlinear plant with state feedback is implemented using the open-loop estimation result. The key contribution of the online estimator will be verified in this proposed control algorithm. Eventually, as to verify the prescribed performance and the flexibility of the suggested control approach, the estimation and control of an uncertain hyper-chaotic weld plant will be tested.

Asymptotic Tracking Control for Uncertain MIMO Nonlinear Systems With Guaranteed Performance and Enhanced Controllability

Asymptotic Tracking Control for Uncertain MIMO Nonlinear Systems With Guaranteed Performance and Enhanced Controllability

Distributed Adaptive Formation Tracking for a Class of Uncertain Nonlinear Multiagent Systems: Guaranteed Connectivity Under Moving Obstacles.

This article explores a guaranteed network connectivity problem during moving obstacle avoidance within a distributed formation tracking framework for uncertain nonlinear multiagent systems with range constraints. We investigate this problem based on a new adaptive distributed design using nonlinear errors and auxiliary signals. Within the detection range, each agent regards other agents and static or dynamic objects as obstacles. The nonlinear error variables for formation tracking and collision avoidance are presented, and the auxiliary signals in formation tracking errors are introduced to maintain network connectivity under the avoidance mechanism. The adaptive formation controllers using command-filtered backstepping are constructed to ensure closed-loop stability with collision avoidance and preserved connectivity. Compared with the previous formation results, the resulting features are as follows: 1) the nonlinear error function for the avoidance mechanism is considered an error variable, and an adaptive tuning mechanism for estimating the dynamic obstacle velocity is derived in a Lyapunov-based control design procedure; 2) network connectivity during dynamic obstacle avoidance is preserved by constructing the auxiliary signals; and 3) owing to neural networks-based compensating variables, the bounding conditions of time derivatives of virtual controllers are not required in the stability analysis.

Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Unknown Control Directions

Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Unknown Control Directions

Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback

Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback

Event-Triggered Adaptive Neural Network Tracking Control for Uncertain Systems With Unknown Input Saturation Based on Command Filters.

This brief presents a modified event-triggered command filter backstepping tracking control scheme for a class of uncertain nonlinear systems with unknown input saturation based on the adaptive neural network (NN) technique. First, the virtual control functions are reconstructed to address the uncertainties in subsystems by using command filters. A piecewise continuous function is employed to deal with the unknown input saturation problem. Next, an event-triggered tracking controller is developed by utilizing the adaptive NN technique. Compared with standard NN control schemes based on multiple-function-approximators, our controller only requires a single NN. The closed-loop system stability is analyzed based on the Lyapunov stability theorem, and it is shown that the Zeno behavior is also avoided under the designed event-triggering mechanism. Simulation studies are performed to validate the effectiveness of our controller.

Distributed Feedback Optimization of Nonlinear Uncertain Systems Subject to Inequality Constraints

Distributed Feedback Optimization of Nonlinear Uncertain Systems Subject to Inequality Constraints

Asymptotic tracking control for a class of uncertain nonlinear systems with output constraint

In this paper, we investigate the asymptotic tracking control for a class of strict-feedback nonlinear systems with unknown nonlinear functions and output constraint. The nonlinear transformation function-based system transformation approach is employed to convert the initial constrained system into an unconstrained one. To achieve the objective of asymptotic tracking, the tracking error is scaled by an exponential proportional function. Furthermore, to address the challenge of repetitive derivation of virtual control laws that occurs in the traditional design process of high-order backstepping methods, a first-order filter is applied. The designed control scheme guarantees that the system output will asymptotically track a predefined reference tracking trajectory while ensuring that the output constraint is not violated. Moreover, it is shown that the filter error will converge asymptotically to the origin. The effectiveness of the developed control strategy is verified through simulation results.

Adaptive event-triggered optimal [formula omitted] tracking control for uncertain nonlinear systems: Comparative analysis applied to autonomic tractor-trailer system

In this paper, an event-triggered tracking optimization control method is proposed for nonlinear uncertain systems with H∞ discounted cost. First, the linearization method using the infinite series expansion theorem is given. And the tracking control design problem is solved by appropriate state augment. Secondly, the zero sum differential game strategy is introduced to address the control design problem of uncertain systems with event-triggered inputs. The actor-critic-disturbance networks framework is used to approximate the optimization of event- triggered controller strategy, optimization costs, and the disturbance strategy, respectively. Due to the consideration of discrete time and continuous time dynamics, we put the impulsive system method to use and choose appropriate Lyapunov functions to prove stability and boundedness, at the same time, there will be no infinite triggering situation. Finally, the effectiveness of the proposed scheme is demonstrated by an example of a practical tractor system with n trailers through simulation compared with another typical design method.

Adaptive fixed-time PID-based control of uncertain nonlinear systems and its application to unmanned surface vehicles

This article shows that the PID control, applied in linear systems, is introduced to handle the adaptive fixed-time PID-based control issue of uncertain nonlinear systems. For handling smooth complex unknown nonlinearities existing in the considered system, neural networks will be introduced to estimate these functions. Furthermore, by integrating the self-tuning gain PID controller, an actual controller is proposed. The stability analysis and the simulations all demonstrate the utilisability of the given scheme.

Event-triggered adaptive tracking for constrained multi-agent systems with saturated inputs and actuator faults

An fault-tolerant tracking control of uncertain nonlinear multi-agent systems with state constraints and input saturation is investigated. A saturated controller is processed by converting the saturation function into a linear form of the control input. The uncertain nonlinear dynamics are approximated by fuzzy logic systems and the unknown parameters are estimated by adaptive laws. By utilizing the nonlinear state-dependent function, the constrained system is converted into the unconstrained one. An adaptive distributed event-triggered control mechanism for consensus tracking is developed utilizing the backstepping approach. By stability analysis, it is ensured that all system signals are bounded, consensus tracking can be achieved with bounded errors, and no Zeno behavior happens. Finally, simulation is done to validate the theoretical results.

Integral reinforcement learning‐based optimal tracking control for uncertain nonlinear systems under input constraint and specified performance constraints

AbstractThis article addresses the optimal tracking control problem with prescribed performance for uncertain nonlinear systems subject to input constraint and unknown disturbances. First, a fixed‐time monotonic convergence function is introduced to restrain tracking error, and a nonlinear mapping technique is employed to transform the constrained error into an unconstrained variable, then the fixed‐time output tracking issue is boiled down to the boundedness problem of the transformed variable. With the aid of a nonquadratic cost function, the input constraint is encoded into the optimization problem. To solve the unknown disturbances, an auxiliary system and an auxiliary disturbance policy are constructed, and the optimal control problem is formulated as a two‐player zero‐sum game. Moreover, a Hamilton–Jacobi–Isaacs (HJI) equation associated with this nonquadratic zero‐sum game is established to give the optimal control and the worst‐case disturbance policy solution. Subsequently, to avoid using knowledge of the system dynamics, three neural network approximators, namely, actor, critic, and disturbance, which are tuned online and simultaneously for approximating the solution of HJI, are constructed based on the integral reinforcement learning algorithm. Theoretical analysis shows that the reconstructed error system states and the weight estimation errors are semi‐globally uniformly ultimately bounded. Finally, the simulation study further tests the availability of the proposed control strategy.

Self-Organizing Type-2 Fuzzy Double Loop Recurrent Neural Network for Uncertain Nonlinear System Control.

Nonlinear systems, such as robotic systems, play an increasingly important role in our modern daily life and have become more dominant in many industries; however, robotic control still faces various challenges due to diverse and unstructured work environments. This article proposes a double-loop recurrent neural network (DLRNN) with the support of a Type-2 fuzzy system and a self-organizing mechanism for improved performance in nonlinear dynamic robot control. The proposed network has a double-loop recurrent structure, which enables better dynamic mapping. In addition, the network combines a Type-2 fuzzy system with a double-loop recurrent structure to improve the ability to deal with uncertain environments. To achieve an efficient system response, a self-organizing mechanism is proposed to adaptively adjust the number of layers in a DLRNN. This work integrates the proposed network into a conventional sliding mode control (SMC) system to theoretically and empirically prove its stability. The proposed system is applied to a three-joint robot manipulator, leading to a comparative study that considers several existing control approaches. The experimental results confirm the superiority of the proposed system and its effectiveness and robustness in response to various external system disturbances.

Adaptive Neural Control for a Class of Random Fractional-Order Multi-Agent Systems with Markov Jump Parameters and Full State Constraints

Based on an adaptive neural control scheme, this paper investigates the consensus problem of random Markov jump multi-agent systems with full state constraints. Each agent is described by the fractional-order random nonlinear uncertain system driven by random differential equations, where the random noise is the second-order stationary stochastic process. First, in order to deal with the unknown functions with Markov jump parameters, a radial basis function neural network (RBFNN) structure is introduced to achieve approximation. Second, for the purpose of keeping the agents’ states from violating the constraint boundary, the tan-type barrier Lyapunov function is employed. By using the stochastic stability theory and adopting the backstepping technique, a novel adaptive neural control design method is presented. Furthermore, to cope with the differential explosion problem in the design course, the extended state observer (ESO) is developed instead of neural network (NN) approximation or command filtering techniques. Finally, the exponentially noise-to-state stability in the mean square is analyzed rigorously by the Lyapunov method, which guarantees the consensus of the considered multi-agent systems and all the agents’ outputs are bounded in probability. Two simulation examples are provided to verify the effectiveness of the suggested control strategy.