An indirect adaptive nonlinear teleoperation control based on operator-environment impedance identification

1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

This paper focuses on an adaptive robust dynamic surface control (ARDSC) with composite adaptation laws (CAL) for a class of uncertain nonlinear systems in semi‐strict feedback form. A simple and effective controller has been obtained by introducing dynamic surface control (DSC) technique and designing novel adaptation laws. First, the ‘explosion of terms’ problem caused by backstepping method in the traditional adaptive robust control (ARC) is avoided. Meanwhile, through a new proof philosophy the asymptotical output tracking that the ARC possesses is theoretically preserved. Second, when persistent excitation (PE) condition satisfies, true parameter estimates could be acquired via designing CALs which integrate the information of estimation errors. Finally, simulation results are presented to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.

In recent years, robotic systems have been widely used in different applications, and this has motivated researchers to develop different control methods. A model-free, intelligent, robust control method for a nonlinear robotic manipulator system is proposed in this work. This paper presents a novel solution for the major drawbacks of the sliding mode control scheme, which are chattering. Prior knowledge is needed about the dynamic model of the controlled system and the upper bound of uncertainty. In this paper, a fuzzy-like PD controller with SMC (FLPDSM) is proposed. The fuzzy-like PD controller was designed according to fuzzy rules and membership functions based on the nominal model of the robot manipulator. A robust control term was added to the control signal to compensate for the system uncertainty, and external disturbances are compensated by adding an auxiliary robust term to the SMC control law. Two methods for designing robust control terms are proposed. The first proposed method assumes that the upper bound of system uncertainty is known although it cannot be exactly determined due to external disturbances and uncertainty. Hence, a second method was proposed that assumes this bound to be unknown, and an adaptive gain based on Lyapunov theory was used to derive the adaptation law. The Lyapunov second method was used to ensure the stability of the closed loop system. Performance tests on the proposed methods were implemented through simulation studies for the two-link robotic manipulator, and the test results were compared with the standard SMC to verify the effectiveness of the proposed method. A good trajectory tracking with a high robustness against parameter variations and external disturbances was observed under the presented control scheme.

In this paper, a quadrotor with two manipulators constrained on a straight path is modeled and a robust adaptive controller is proposed for it. Adding two manipulators to quadrotor increases its capabilities and applications in industry. Here, these two manipulators are used to place the robot on a constraint path so that the quadrotor can perform monitoring operations more accurately, because the under-actuated quadrotor becomes over-actuated by these constrained manipulators and one can use this feature to accurately control the position of the robot. Reduced form of motion equations are derived for the constrained quadrotor and based on this a robust adaptive controller is proposed. The nonlinear terms in the dynamic model are approximated by basic functions with constant weights and adaptive laws are designed by projection operator. Stability analysis is performed based on the Lyapunov theory. Evaluation of the presented controller is done by some numerical simulations. The simulation results showed that the robot tracks the reference path with bounded error in spite of dynamic uncertainties and wind force and satisfies the considered constraints.

For floating production storage and offloading (FPSO) vessels, a dynamic positioning controller is necessary because using only a mooring system is not possible to keep the ship within a predefined region. Position control of the FPSO vessel is extremely challenging due to model uncertainties and unknown control coefficients. This paper develops a new robust adaptive positioning controller consisting of several components: adaptive law, dynamic surface control (DSC) technology, sigmoid tracking differentiator (STD), Nussbaum gain function, and structural reliability index. Model uncertainties can be estimated by the adaptive law derived from the Lyapunov theory. The DSC technology is used to eliminate repeated differentiation by introducing first-order filtering of the virtual control. The chattering-free STD with the characteristics of global fast convergence can estimate the derivatives of model uncertainties that are difficult to calculate directly. Therefore, the DSC and STD techniques make the proposed controller simpler to compute and easier to implement in engineering practice. Most of the traditional controllers require the information about the control coefficients to guarantee the stability of the closed-loop system while the Nussbaum gain function can remove the requirement for a priori knowledge of the sign of control coefficients. The capacity of the mooring system can be fully utilized to position the FPSO vessel by adjusting the structural reliability index on the premise of ensuring the safety of mooring lines, and hence less control effort is needed for the positioning controller. Simulations using two sets of system parameters demonstrate the proposed controller’s effectiveness. In addition, a qualitative comparison with the adaptive backstepping controller shows that our proposed controller is computationally more efficient and does not require a priori knowledge of the sign of control coefficients. A quantitative comparison with robust adaptive controller without the structural reliability shows that less control effort is needed using our proposed controller.

This paper aims at introducing H2 and H∞ robustness into the well-known characteristic model-based golden-section adaptive control law, and applying the robust adaptive control scheme to the attitude control of hypersonic cruise vehicles that are subject to external disturbances and aerodynamic coefficients uncertainties. When maneuvering at ultra high speeds, the attitude system of the hypersonic cruise vehicle is extremely sensitive to external disturbances and aerodynamic coefficients variations, and therefore the adaptiveness and the robustness of the attitude system are crucial during the controller design. To enhance the robustness of the existing golden-section adaptive control law, a golden-section robust adaptive control law is proposed. Compared to the existing control law where the design of the parameter λ depends on experience and is carried out offline, linear matrix inequality-based synthesis of λ is proposed such that the closed-loop system is stable with guaranteed H2 and H∞ performance. It is suitable for online computing and provides a time-varying λ(k) that is adjusted towards the optimal H2 and H∞ performance. When being applied to the attitude control of hypersonic vehicles during re-entry, the adaptive nature of the proposed control law provides the attitude system the capability to accommodate large flight conditions, and its H2 and H∞ robustness brought by λ(k) guarantees satisfying tracking performance in the presence of disturbances including both external disturbance and absolute aerodynamic coefficients errors.

This paper studies the robust adaptive control of fractional-order chaotic systems with system uncertainties and bounded external disturbances. Based on a proposed lemma, quadratic Lyapunov functions are used in the stability analysis and fractional-order adaptation laws are designed to update the controller parameters. By employing the fractional-order expansion of classical Lyapunov stability method, a robust controller is designed for fractional-order chaotic systems. The system states asymptotically converge to the origin and all signals in the closed-loop system remain bounded. A counterexample is constructed to show that the fractional-order derivative of a function is less than zero does not mean that the function monotonically decreases (this property appears in many references). Finally, simulation results are presented to confirm our theoretical results.

Modified robust optimal adaptive control for flight environment simulation system with heat transfer uncertainty

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

The problem of controlling bilateral teleoperation systems in the presence of uncertain kinematics and dynamics is studied in this paper. Control algorithms and adaptive laws are developed to address the impediment of imprecise measurement resulting from when the slave robot grips a tool with unknown grasping point and orientation. We first demonstrate that with the utilization of the proposed adaptive laws, the teleoperation system is stable and the position tracking is guaranteed even if there are dynamic and kinematic uncertainties. Due to the end-effector velocity being difficult to obtain, an alternative control algorithm that does not incorporate task-space velocity information is developed. The issue of asymmetric constant communication delays in the teleoperation system is studied by Lyapunov–Krasovskii theorem. In the presence of external forces, we prove that all signals in the proposed teleoperation systems are bounded, and that force feedback is proportional to the tracking errors. Numerical simulations and experiments are performed to demonstrate the efficacy of the developed teleoperation systems.

In this paper, an adaptive robust control is investigated in order to deal with the unmatched and matched uncertainties in the manipulator dynamics and the actuator dynamics, respectively. Because these uncertainties usually include smooth and unsmooth functions, two adaptive mechanisms were investigated. First, an adaptive mechanism based on radial basis function neural network (RBFNN) was used to estimate the smooth functions. Based on the Taylor series expansion, adaptive laws derive for not only the weighting vector of the RBFNN, but also for the means and standard derivatives of the RBFs. The second one was the adaptive robust laws, which is designed to estimate the boundary of the unsmooth function. The robust gains will increase when the sliding variable leave the predefined region. Conversely, they will significantly decrease when the variable approaches the region. So, when these adaptive mechanisms are derived with the backstepping technique and sliding mode control, the proposed controller will compensate the uncertainties to improve the accuracy. In order to prove stability and robustness of the controlled system, the Lyapunov approach, based on backstepping technique, was used. Some simulation and experimental results of the proposed methodology in the electrohydraulic manipulator were presented and compared to other control to show the effectiveness of the proposed control.

To keep the attitude control of maneuvering reentry vehicle in reentry phase, the strict feedback attitude model of reentry vehicle with time-varying parameters is built. An adaptive robust controller is designed based on backstepping, which consists of backstepping adaptive control and robust control. The controller design method uses adaptive strategies to estimate the unknown parameters, introduces robust control to avoid the singularity in parameters estimation of gain matrix phase. Theoretical analysis shows that all signals of the closed-loop system are proved intimately uniform bounded. Simulation results of six-degree-of-freedom demonstrate that the proposed control method has strong robust performance.

Uncertainties are prevalent in real-world applications of bipedal walking robots, which may deteriorate the robot’s locomotion performance and even cause instability. However, designing controllers to address uncertainties for bipedal robotic walking is challenging mainly due to the high complexity of the hybrid walking dynamics under uncertainties. In this paper, an adaptive robust control strategy is proposed by combining control Lyapunov functions and the construction of multiple Lyapunov functions for provably guaranteeing the stability and trajectory tracking performance of fully actuated bipedal robots in the presence of uncertainties such as modeling errors and unmodeled disturbances. Simulation results on a three-dimensional bipedal robot with nine revolute joints were conducted to illustrate that the proposed adaptive robust control law can ensure stability and satisfactory tracking performance in the presence of parametric modeling uncertainties and unmodeled nonlinearities.

On reduced-complexity robust adaptive control of switched Euler–Lagrange systems

In this paper, a 3-axis motion simulator is proposed to provide a laboratory environment for testing spacecraft instruments. A mathematical model of the simulator mechanical structure is developed by means of calculating angular momentum of each rotating part with respect to relevant reference frames. Motion simulator actuators are permanent magnet synchronous motor (PMSM) drives. A compact mathematical model of the whole electromechanical system is obtained by representing the PMSM drives in their field orientation. By using Lyapunov stability theory and linearization techniques, a novel robust adaptive nonlinear control law, which is not only adaptable to constant unknown parameters but also robust to unknown but bounded fast varying disturbances, is developed for the tracking task of this PMSM direct driven system. The efficiency and correctness of the proposed control system are verified by simulation and experimental results.