Second-order Uncertain Nonlinear Systems Research Articles

Time-Varying Optimal Formation Control for Second-Order Multiagent Systems Based on Neural Network Observer and Reinforcement Learning.

This article addresses a distributed time-varying optimal formation protocol for a class of second-order uncertain nonlinear dynamic multiagent systems (MASs) based on an adaptive neural network (NN) state observer through the backstepping method and simplified reinforcement learning (RL). Each follower agent is subjected to only local information and measurable partial states due to actual sensor limitations. In view of the distributed optimized formation strategic needs, the uncertain nonlinear dynamics and undetectable states may jointly affect the stability of the time-varying cooperative formation control. Furthermore, focusing on Hamilton-Jacobi-Bellman optimization, it is almost incapable of directly dealing with unknown equations. Above uncertainty and immeasurability processed by adaptive state observer and NN simplified RL are further designed to achieve desired second-order formation configuration at the least cost. The optimization protocol can not only solve the undetectable states and realize the prescribed time-varying formation performance on the premise that all the errors are SGUUB, but also prove the stability and update the critics and actors easily. Through the above-mentioned approaches offer an optimal control scheme to address time-varying formation control. Finally, the validity of the theoretical method is proven by the Lyapunov stability theory and digital simulation.

Exponential Convergence of Distributed Optimal Coordination for Nonlinear Multiagent Systems Under Directed Graphs

In this article, the distributed optimal coordination problem of second-order uncertain nonlinear multiagent systems, which aims to satisfy a global constrained optimal objective, is formulated and investigated. To solve this problem, a couple of novel proportional–integral (PI)-type control laws are explored. Specifically, a gradient-descent-based PI control law is developed for the weight-balanced graph. Furthermore, by introducing the estimator of the left eigenvector of the Laplacian matrix, the proposed method is extended to the case of an unbalanced graph. Compared with the existing optimal coordination algorithms over nonlinear multiagent systems, our algorithm exhibits the favorable exponential convergence property, albeit employing relaxed balanced/unbalanced directed communication topologies. Two numerical simulations are provided to demonstrate the theoretical results.

A New Finite–Time Sliding–Mode Controller for a Class of Second–Order Non–Linear Systems

This paper contributes to the design of a new finite-time sliding-mode controller for a class of uncertain second-order non-linear systems. The proposed strategy takes into account the design of a family of sliding variables, which establishes a second-order sliding-mode and ensures the convergence of the trajectories of the system to the origin in a finite time and despite the effect of some uncertainties on the system. The straightforward structure of the controller is simple to tune and implement. The global, uniform and finite-time stability of the closed-loop dynamics is demonstrated by means of Lyapunov functions. Furthermore, the performance of the proposed approach is validated through some simulation results.

Fully distributed adaptive finite-time consensus over uncertain network topology

ABSTRACT Communication network could suffer uncertainties originating from link faults and network attacks. This situation, in multi-agent systems, can be featured by unknown weights of network topology. To impair the influence of the uncertain topology, typical compensation should be taken into account in distributed protocols to the workability of multi-agent systems. This paper, in the context of uncertain topology, addresses finite-time leader-following consensus for second-order uncertain nonlinear multi-agent systems. In addition to uncertainties in topology, the systems also allow unknown control coefficients, which together with the unknown weights renders the realisation of finite-time leader-following consensus nontrivial. Specifically, a fully distributed protocol based on distributed finite-time observer is designed via integrating the adaptive compensation scheme. Notably, in the designed protocol, dynamic high gains are introduced for the compensations of the network uncertainties and agents uncertainties. It turns out that the designed fully distributed protocol guarantees the global finite-time leader-following consensus. Simulation examples are provided to illustrate the validity of the proposed approach.

Prescribed Performance Adaptive Tracking Control With Small Overshoot for a Class of Uncertain Second-Order Nonlinear Systems

This brief investigates the problem of prescribed performance adaptive tracking control for a class of second-order nonlinear systems with uncertainties. First, a new performance function is defined to guarantee that the tracking error has small overshoot and converges to a predetermined region for a user-defined time. Then, to effectively diminish the control input energy consumption caused by the introduction of constraints, a novel coordinate transformation function is designed. Next, an improved fixed-time backstepping control framework is established to achieve the tracking control objective. According to the theoretical analysis, all signals of the closed-loop system are bounded, and the tracking error converges to a preset domain with small overshoot for a user-designed time. Finally, numerical simulations confirm the effectiveness of the presented control strategy.

Active Disturbance Rejection Control of Second-Order Nonlinear Uncertain Systems with Guaranteed Transient and Steady State Tracking Error Bounds

Active Disturbance Rejection Control of Second-Order Nonlinear Uncertain Systems with Guaranteed Transient and Steady State Tracking Error Bounds

Fixed‐time non‐singular terminal sliding mode control with globally fast convergence

This paper investigates a fixed-time terminal sliding mode (TSM) control scheme of second-order non-linear uncertain systems. A globally fast fixed-time stable system is proposed, and the convergence time is established with the Lyapunov method. Then, a novel non-singular TSM utilising the proposed fixed-time stable system and an auxiliary polynomial function is constructed. Meanwhile, a fixed-time disturbance observer technique is employed to estimate the matched lumped perturbation. Globally fast fixed-time convergence of the closed-loop system is guaranteed with the phase plane analysis and Lyapunov tools, and the upper bound of the settling time independent of the initial conditions can be predefined by the controller parameters. Finally, the simulation results of a single inverted pendulum system are included to confirm the validity of the proposed methodology while comparing with some popular TSM control strategies.

Control of Nonlinear Uncertain Systems by Extended PID

Since the classical proportional-integral-derivative (PID) controller is the most widely and successfully used ones in industrial processes, it is of vital importance to investigate theoretically the rationale of this ubiquitous controller in dealing with nonlinearity and uncertainty. Recently, we have investigated the capability of the classical PID control for second-order nonlinear uncertain systems, and provided some analytic design methods for the choices of PID parameters, where the system is assumed to be in the form of cascade integrators. In this article, we will consider the natural extension of the classical PID control for high-order affine-nonlinear uncertain systems. In contrast to most of the literature on controller design of nonlinear systems, we do not require such special system structures as normal or triangular forms, thanks to the strong robustness of the extend PID controller. To be specific, we will show that under some suitable conditions on nonlinearity, and uncertainty of the systems, the extended PID controller can semiglobally stabilize the nonlinear uncertain systems, and at the same time the regulation error converges to zero exponentially fast, as long as the control parameters are chosen from an open unbounded parameter manifold constructed in this article.

Robust Fixed-Time Stability: Application to Sliding-Mode Control

This article deals with robust fixed-time stability and stabilization. First, new global robust fixed-time stability results are proposed for scalar systems by using constant and variable exponent coefficients. Then, they are applied to global robust fixed-time stabilization of a class of uncertain nonlinear second-order systems by using sliding-mode control. All the results are illustrated in simulation.

Novel Nonsingular Fast Terminal Sliding Mode Control for a Class of Second-Order Uncertain Nonlinear Systems

This paper presents a novel nonsingular fast terminal sliding mode control scheme for a class of second-order uncertain nonlinear systems. First, a novel nonsingular fast terminal sliding mode manifold (NNFTSM) with adaptive coefficients is put forward, and a novel double power reaching law (NDP) with dynamic exponential power terms is presented. Afterwards, a novel nonsingular fast terminal sliding mode (NNFTSMNDP) controller is designed by employing NNFTSM and NDP, which can improve the convergence rate and the robustness of the system. Due to the existence of external disturbances and parameter uncertainties, the system states under controller NNFTSMNDP cannot converge to the equilibrium but only to the neighborhood of the equilibrium in finite time. Considering the unsatisfying performance of controller NNFTSMNDP, an adaptive disturbance observer (ADO) is employed to estimate the lumped disturbance that is compensated in the controller in real-time. A novel composite controller is presented by combining the NNFTSMNDP method with the ADO technique. The finite-time stability of the closed-loop system under the proposed control method is proven by virtue of the Lyapunov stability theory. Both simulation results and theoretical analysis illustrate that the proposed method shows excellent control performance in the existence of disturbances and uncertainties.

Improved Function Augmented Sliding Mode Control of Uncertain Nonlinear Systems with Preassigned Settling Time

This paper investigates the robust tracking control of second-order uncertain nonlinear systems by adopting the function augmented sliding mode control approach. An improved version of this approach is proposed such that the exact information of the initial tracking error is not required when generating the desired trajectory of the tracking error. This evidently enlarges the application scope of the function augmented sliding mode control approach. Performance functions are introduced to form the performance envelopes for the sliding mode variables. A robust sliding mode controller is constructed such that the sliding mode variables are confined within their performance envelopes. This further guarantees that the tracking error converges to the given neighbourhood of zero within the preassigned settling time provided that proper control parameters are selected. An application example on the rendezvous control of spacecraft is also employed to illustrate the effectiveness of the proposed control approach.

Completely distributed neuro-learning consensus with position constraints and partially unknown control directions

In this paper, we propose a new neural network-based iterative learning leader-less consensus control algorithm for the second-order uncertain time-varying nonlinear multi-agent systems, where the position of each agent is constrained in an open interval which can be pre-selected and the control direction can be non-identical and partially unknown. With the help of a novel barrier composite energy function and multiple piece-wise Nussbaum functions, the designed completely distributed learning protocols can make the positions and velocities of the agents achieve the exact consensus on a finite time interval as the iteration number increases to infinity. Meanwhile, the position trajectories of the agents at each iteration do not exceed the constraints bounds. Besides, to testify the feasibility and utility of the presented algorithm, two simulation examples are given in the end.

Optimal adaptive neural PI full-order sliding mode control for robust fault tolerant control of uncertain nonlinear system

This paper proposes a robust fault tolerant control scheme for a class of second-order uncertain nonlinear systems. First, a novel PI full-order sliding mode (PI-FOSM) control, which integrates a new PI-FOSM sliding surface and a continuous control law, is developed. The crucial parameters of the controller are optimally selected by Bat algorithm so that the nearly optimal performance of the controller can be achieved. In addition, the unknown system dynamics is approximated by using a radial basic function neural network (RBFNN) so that the proposed controller does not require an exact model of the system. Compared with other existing sliding mode controllers for fault tolerant control system, the proposed method provides very strong robustness, low oscillation, fast convergence and high precision. The superior performance of the proposed robust fault tolerant controller is proved through simulation results for attitude control of a spacecraft.

A Novel Approach to Fixed-Time Stabilization for a Class of Uncertain Second-Order Nonlinear Systems

This paper is concerned with the problem of fixed-time stabilization for a class of uncertain second-order nonlinear systems. By delicately introducing extra manipulations in the feedback domination and revamping the technique of adding a power integrator, a new approach is developed, by which a state feedback controller, together with a suitable Lyapunov function, which is critical for verifying fixed-time convergence, can be explicitly organized to render the closed-loop system fixed-time stable. The major novelty of this paper is attributed to a subtle strategy that offers a distinct perspective in controller design as well as stability analysis in the problem of fixed-time stabilization for nonlinear systems. Finally, the proposed approach is applied to the attitude stabilization of a spacecraft to demonstrate its merits and effectiveness.

Adaptive Fast Finite-Time Consensus for Second-Order Uncertain Nonlinear Multi-Agent Systems With Unknown Dead-Zone

This paper presents an adaptive fast finite-time consensus (FTC) for second-order uncertain nonlinear (UN) multi-agent systems (MASs) with unknown nonsymmetric dead-zone and external disturbances. In the process of control protocols design, based on the estimation of the dead-zone width that is obtained by using adaptive method, a fuzzy logic dead-zone compensator is adopted to deal with the nonsymmetric dead-zone input phenomenon. Combining finite-time control technique and Lyapunov's relevant theory, a new fast FTC protocol is developed. Based on the basis of radial basis function neural networks (RBFNNs) theories, the unknown nonlinear functions are approximated. Under the presented consensus protocols and adaptive laws, it can be proved that the position errors of arbitrary two agents can reach a small region of zero in finite time as well as the velocity errors. Ultimately, the effectiveness of the designed method is tested via two numerical examples.

Novel Fixed-Time Nonsingular Fast Terminal Sliding Mode Control for Second-Order Uncertain Systems Based on Adaptive Disturbance Observer

In this paper, a novel fixed-time nonsingular fast terminal sliding mode control incorporating with an adaptive disturbance observer is proposed for second-order uncertain nonlinear systems to achieve fast stabilization and robust control. Based on the theory of fixed-time convergence, a novel fixed-time stable system is first investigated. Using this system, a novel fixed-time nonsingular fast terminal sliding mode controller is developed, which can achieve system stabilization within bounded convergence time regardless of initial states and provide nonsingularity and fast convergence. Moreover, an adaptive disturbance observer is designed to improve the control performance and compensate for uncertain disturbances. The fixed-time stability of the sliding surface and the system states under the proposed composite control scheme are demonstrated by the Lyapunov stability theory. Both theoretical analysis and simulation results are presented to verify the feasibility and superiority of the proposed method.

A Non-Singular Fast Terminal Sliding Mode Control Based on Third-Order Sliding Mode Observer for a Class of Second-Order Uncertain Nonlinear Systems and its Application to Robot Manipulators

This paper proposes a controller-observer strategy for a class of second-order uncertain nonlinear systems with only available position measurement. The third-order sliding mode observer is first introduced to estimate both velocities and the lumped uncertain terms of system with high accuracy, less chattering, and finite time convergency of estimation errors. Then, the proposed controller-observer strategy is designed based on non-singular fast terminal sliding mode sliding control and proposed observer. Thanks to this combination, the proposed strategy has some superior properties such as high tracking accuracy, chattering phenomenon reduction, robustness against the effects of the lumped uncertain terms, velocity measurement elimination, finite time convergence, and faster reaching sliding motion. Especially, two period times, before and after the convergence of the velocity estimation takes place, are considered. The finite time stability of proposed controller-observer method is proved by using the Lyapunov stability theory. Final, the proposed strategy is applied to robot manipulator system and its effectiveness is verified by simulation results, in which a PUMA560 robot manipulator is employed.

A novel nonsingular terminal sliding mode control combined with global sliding surface for uncertain nonlinear second-order systems

This paper proposes a novel nonsingular terminal sliding mode control combined with global sliding surface for a class of uncertain nonlinear second-order systems. The suggested control approach is developed based on the Lyapunov theory. The sliding mode reaching the sliding surface in finite time can be guaranteed. Furthermore, chattering phenomenon caused by the switching control action can be eliminated theoretically, and desirable control performance is realized. The simulation and tank test results for heave control of a remotely operated vehicle are presented to verify the effectiveness of the proposed method.

Improved UDE and LSO for a Class of Uncertain Second-Order Nonlinear Systems Without Velocity Measurements

In recent years, the uncertainty and disturbance estimator (UDE) technique has been widely used for robustness improvement in state-feedback control systems. This article extends the design of the UDE to output feedback scenarios by considering the robust control problem of a class of Euler–Lagrange systems with a nonlinear velocity term but having no velocity measurements. We propose a simple feedback-control scheme that includes a modified Luenberger state observer (LSO) to estimate the velocity and a modified UDE to estimate exogenous disturbances. The novel feature of the scheme is that a mutual coupling between LSO and UDE is introduced to improve the estimation and control precision. To analyze the performance of the fifth-order nonlinear closed-loop system, we decompose it into a second-order tracking-error subsystem and a third-order estimation-error subsystem and propose a linear nonsingular state transformation and an ingenious parameter mapping for the estimation-error subsystem. Finally, by the singular perturbation theory, we derive a simple stability condition and a single-parameter tuning approach to reduce the steady-state estimation errors and tracking errors. The performance improvement resulting from the mutual coupling effect and the effectiveness of the tuning approach are demonstrated by numerical simulations and experimental verifications on a 3-DOF helicopter platform.

Adaptive Learning Control for Second-Order Nonlinear Multi-Agent Systems with Iteration-Switching Topologies

This paper investigates the consensus tracking problem for the leader-follower second-order uncertain nonlinear multi-agent systems with nonrepeatable mismatched input disturbance. The main structure of the proposed adaptive iterative learning controller contains a neural networks learning component and a robust learning component. The effect of the neural networks learning component is to estimate the system’s nonlinearity and the robust learning component is to suppress the nonlinear input gain and disturbance. An adaptive law combining time- and iteration- domain is used to tune the controller parameters. We use the composite energy function method to prove the consensus convergence and give a numerical simulation to illustrate the effectiveness of the proposed scheme.