Exponential Convergence Of Tracking Error Research Articles

Universal Control for Both Rendezvous and Tracking of Multiple Nonholonomic Unicycles

This paper studies the universal control for multiple nonholonomic unicycles, i.e., finding a control law that allows for both rendezvous and tracking uses. The reduced-order approach and optimal technique are applied to design an exponential observer that estimates the leader's states. Using the observer signal, we convert the pose errors into the form of nonholonomic integrators and derive a local tracking control law. The obtained control law guarantees exponential convergence of tracking errors and maintains the solution trajectory of converted states in an invariant set. More importantly, the original pose error between each unicycle and the leader is proven exponentially convergent to zero, whether or not the leader satisfies persistency of excitation (PE) conditions. The extension of the proposed control algorithm to leader-following formation control is also illustrated. Numerical simulations validate the control design.

Automatic reinforcement for robust model‐free neurocontrol of robots without persistent excitation

SummaryModel‐based adaptive control suffers over parametrization from the many adaptive parameters compared to the order of system dynamics, leading to sluggish tracking with a poor adaptation transient without robustness. Likewise, adaptive model‐free neurocontrol that relies on the Stone–Weierstrass theorem also suffers from similar problems in addition to over‐fitting to approximate inverse dynamics. This article proposes a novel reinforced adaptive mechanism to guarantee a transient and robustness for the model‐free adaptive control of nonlinear Lagrangian systems. Inspired by the symbiosis of Actor‐Critic (AC) architecture and integral sliding modes, the reinforced stage neural network, analogous to the critic, injects excitation signals to reinforce the parametric learning of the adaptive stage neural network, analogous to the actor to improve the approximation of inverse dynamics. The underlying integral sliding surface error drives improved learning onto a low‐dimensional invariant manifold to guarantee local exponential convergence of tracking errors. Lyapunov stability substantiates the robustness with an improved transient response. Our proposal stands for a hybrid approach between AC and neurocontrol, where the reinforced stage does not require a value function nor reward to provide automatic reinforcement to the adaptive stage parametric adaptation. Dynamic simulations are presented for a nonlinear robot manipulator under different conditions.

A Novel Actor—Critic Motor Reinforcement Learning for Continuum Soft Robots

Reinforcement learning (RL) is explored for motor control of a novel pneumatic-driven soft robot modeled after continuum media with a varying density. This model complies with closed-form Lagrangian dynamics, which fulfills the fundamental structural property of passivity, among others. Then, the question arises of how to synthesize a passivity-based RL model to control the unknown continuum soft robot dynamics to exploit its input–output energy properties advantageously throughout a reward-based neural network controller. Thus, we propose a continuous-time Actor–Critic scheme for tracking tasks of the continuum 3D soft robot subject to Lipschitz disturbances. A reward-based temporal difference leads to learning with a novel discontinuous adaptive mechanism of Critic neural weights. Finally, the reward and integral of the Bellman error approximation reinforce the adaptive mechanism of Actor neural weights. Closed-loop stability is guaranteed in the sense of Lyapunov, which leads to local exponential convergence of tracking errors based on integral sliding modes. Notably, it is assumed that dynamics are unknown, yet the control is continuous and robust. A representative simulation study shows the effectiveness of our proposal for tracking tasks.

A composite adaptive robust control for nonlinear systems with model uncertainties

AbstractThis article is concerned with a composite adaptive robust control (CARC) for non‐strict feedback nonlinear systems with model uncertainties including parametric uncertainties and uncertain nonlinearities. It is assumed that the model uncertainties of the nonlinear system are bounded but unknown. Firstly, prescribed tracking performance is achieved by the CARC control law even the unknown parameters are time‐varying. This is accomplished firstly by designing a discontinuous projection that confines the unknown parameters in an estimated region. Then the robustness of the closed‐loop system is guaranteed by leveraging the deterministic robust control philosophy. Also, a command filter has been designed to avoid computing complex derivatives of virtual control law in the backstepping procedure. Secondly, a composite adaptation law that intelligently integrates information of both tracking error and prediction error is constructed for improving the performance of controllers. The high adaptation gain of CARC leads to higher parameter convergence speed and smaller tracking errors. Moreover, if the actual parameters are within the design range, asymptotic stability can be achieved in presence of parametric uncertainties only. In addition, exponential convergence of tracking errors and parameters can be shown under certain conditions. Finally, numerical examples are made to validate the superiority and effectiveness of the proposed control scheme.

Distributed Average Tracking for Linear Heterogeneous Multi-Agent Systems With External Disturbances

In this paper, we address the distributed average tracking (DAT) problem for linear multi-agent systems with heterogeneous dynamics and external disturbances. The objective is that each agent can accurately track the desired tracking signal by designing controllers without initialization. The desired tracking signal means the average of individual time-varying reference inputs (one per agent). The current problem setting is technically more challenging and more practical than existing works. Based on the feedforward method, a state feedback controller is first designed to solve the DAT problem, which can guarantee the exponential convergence of tracking errors in the case where the desired tracking signal and external disturbances are known. Then the DAT problem for linear heterogeneous multi-agent systems with unknown desired tracking signal and unknown external disturbances is also solved. A distributed observer is designed for each agent to estimate the desired tracking signal. In parallel, the output of each agent is driven to track the output of the observer. Since each agent cannot access the desired tracking signal and external disturbances, a dynamic compensator independent of the exogenous signal and a dynamic internal-model based component are introduced to overcome these challenges. Finally, a numerical example is included for illustration.

Intelligent wind farm control via deep reinforcement learning and high-fidelity simulations

Wind farms’ power-generation efficiency is constrained by the high system complexity. A novel deep reinforcement learning (RL)-based wind farm control scheme is proposed to handle this challenge and achieve power generation optimization. A reward regularization (RR) module is designed to estimate wind turbines’ normalized power outputs under different yaw settings and uncertain wind conditions, which brings strong robustness and adaptability to the proposed control scheme. The RR module is then combined with the deep deterministic policy gradient algorithm to evaluate the optimal yaw settings for all the wind turbines within the farm. The proposed wind farm control scheme is data-driven and model-free, which addresses the limitations of current approaches, including reliance on accurate analytical/parametric models and lack of adaptability to uncertain wind conditions. In addition, a novel composite learning-based controller for each turbine is designed to achieve closed-loop yaw tracking, which can guarantee the exponential convergence of tracking errors in the presence of uncertainties of yaw actuators. The whole control system can be pre-trained offline and fine-tuned online, providing an easy-to-apply solution with enhanced generality and flexibility for wind farms. High-fidelity simulations with SOWFA (simulator for offshore wind farm applications) and Tensorflow show that the proposed scheme can significantly improve the wind farm’s power generation by exploiting a sparse data set without requiring any wake model.

Adaptive Sliding Mode Control for Spacecraft Rendezvous With Unknown System Parameters and Input Saturation

In this study, we investigated the sliding mode control (SMC) for the spacecraft rendezvous maneuver under unknown system parameters and input saturations. On the basis of the attitude and position tracking subsystem, two anti-saturation sliding mode surfaces (SMSs) are constructed to guarantee the exponential convergence of tracking errors between the target spacecraft and the pursuer spacecraft. In connection with hyperbolic tangent, a modified auxiliary system is established to compensate the nonlinear constraint caused by the actuator saturation. Meanwhile, in order to enhance the practicability and reliability of the controller, unknown inertial information is taken into consideration. The resulting system uncertainties are estimated accurately via adaptive laws. Additionally, it is concluded that the designed controller is capable of ensuring the boundedness of the closed-loop signals with reasonable selection of control parameters. Finally, the effectiveness and advantages of the proposed methods are verified through numerical simulations.

Robust energy aware output controller for uncertain plant

Abstract Nowadays, safety guarantee during physical Human-Robot Interaction (pHRI) is important problem. Control over energy becomes very useful approach and provides possibility of safety conditions implementation but requires measurement of energy variables. In this paper we extend our previous results for discrete robust output control algorithm by insertion of energy aware mechanism in the structure of control system. It is proven earlier that this way make the controller aware of the energy that they inject into the plant. By combining this approaches we introduce here a robust discrete-time output controller for uncertain plant that provides exponential convergence of tracking error to the bounded area and passivity of the closed loop system. The proposed approach is validated through simulation and experiments using Ball-and-Plate setup.

A novel continuous fractional sliding mode control

ABSTRACTA new fractional-order controller is proposed, whose novelty is twofold: (i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodelled dynamics, and (ii) based on a principle of dynamic memory resetting of the differintegral operator, it is enforced an invariant sliding mode in finite time. Both (i) and (ii) account for exponential convergence of tracking errors, where such principle is instrumental to demonstrate the closed-loop stability, robustness and a sustained sliding motion, as well as that high frequencies are filtered out from the control signal. The proposed methodology is illustrated with a representative simulation study.

Nonlinear Attitude Control of Spacecraft with a Large Captured Object

This paper presents an attitude control strategy and a new nonlinear tracking controller for a spacecraft carrying a large object, such as an asteroid or a boulder. If the captured object is larger or comparable in size to the spacecraft and has significant modeling uncertainties, conventional nonlinear control laws that use exact feedforward cancellation are not suitable because they exhibit a large resultant disturbance torque. The proposed nonlinear tracking control law guarantees global exponential convergence of tracking errors with finite-gain stability in the presence of modeling uncertainties and disturbances, and it reduces the resultant disturbance torque. Furthermore, this control law permits the use of any attitude representation, and its integral control formulation eliminates any constant disturbance. Under small uncertainties, the best strategy for stabilizing the combined system is to track a fuel-optimal reference trajectory using this nonlinear control law because it consumes the least amount of fuel. In the presence of large uncertainties, the most effective strategy is to track the derivative plus proportional–derivative-based reference trajectory because it reduces the resultant disturbance torque. The effectiveness of the proposed attitude control methods is demonstrated by using results of numerical simulation based on an Asteroid Redirect Mission concept.

ADAPTIVE VISUAL SERVOING FOR CONSTRAINED ROBOTS UNDER JACOBIAN, JOINT DYNAMIC AND CONTACT VISCOUS FRICTION UNCERTAINTIES

Visual servoing of constrained robots has not yet met a formal treatment nor its friction compensation. This kind of robots moves slowly along the constrained surface due to technological limitations of the camera system, therefore important problems of friction at the joint and contact point arise. The problem turns very complicated when parametric uncertainty on robot, camera and friction is considered. In this paper, a new visual servoing scheme that satisfy this problem is presented. It induces sliding modes without chattering to guarantee locally exponential convergence of tracking errors. Simulations results are presented and discussed.

Dynamic sliding PID control for tracking of robot manipulators: theory and experiments

For a class of robot arms, a proportional-derivative (PD) controller plus gravity compensation yields the global asymptotic stability for regulation tasks, and some proportional-integral-derivative (PID) controllers guarantee local regulation without gravity cancellation. However, these controllers cannot render asymptotic stability for tracking tasks. In this paper, a simple decentralized continuous sliding PID controller for tracking tasks that yields semiglobal stability of all closed-loop signals with exponential convergence of tracking errors is proposed. A dynamic sliding mode without reaching phase is enforced, and terminal attractors, as well as saturated ones, are considered. A comparative experimental study versus PD control, PID control, and adaptive control for a rigid robot arm validates our design.

Chattering‐free sliding mode control for a class of nonlinear mechanical systems

AbstractSecond‐order sliding mode control (2‐smc) and dynamic sliding mode control (dsmc) eliminate the disturbing characteristic of chattering in static sliding mode control under the assumption that the derivative of the sliding surface is available or complex inequalities at the acceleration level can be constructed. In this paper, passivity‐based adaptive and non‐adaptive chattering‐free sliding mode controllers are proposed assuming that the upper bound of the norm of the derivative of the sliding surface is available, a weaker and easy to implement assumption in comparison to those of 2‐smc and dsmc. The closed‐loop system accounts explicitly for the invariance condition without reaching phase, and therefore for a desired transient response with global exponential convergence of tracking errors. Preliminary experiments are presented. Copyright © 2001 John Wiley & Sons, Ltd.

Sliding Modes with Continuous Controllers for Robot Manipulators: Theory and Experiments

Two passivity-based continuous controllers are proposed which guarantee desired transient response with global exponential convergence of tracking errors without any persistent excitation assumption on the regressor. The controllers ensure dynamic sliding modes without reaching phase, which gives rise to a robust performance. Robustness to a class of bounded disturbance and complex friction models are briefly addressed. A comparative experimental study validates the stability properties of the closed-loop system.

An exponentially convergent adaptive sliding mode control of robot manipulators

Abstract A new robust adaptive algorithm for control of robot manipulators is proposed to account for a desired transient response with global exponential convergence of tracking errors without any persistent excitating assumption on the regressor. Its novelty lies in a new dynamic sliding surface that allows a systematic combination of adaptive control and variable structure control to yield a sliding mode inside an adaptive control loop. During sliding mode, parameter uncertainty appears in terms of known variables in such a manner that a new robust parameter estimator with enhanced stability properties is established. On the other hand, if the regressor meets the persistent exciting condition, the global uniform exponential stability of the equilibrium concerning the adaptive closed-loop error equation is easily established. The proposed controller from the VSS viewpoint relaxes the longstanding condition on a priori knowledge of the size of the parametric uncertainty to induce a sliding mode. On the other hand, from the adaptive control viewpoint it relaxes the standard assumption of the persistent excitation on the regressor to obtain the exponential convergence of tracking errors. Also, the stability against time-varying parameters is briefly discussed. Concluding remarks concerning its structural behaviour are given, and computer simulation data show a robust performance.