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

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.

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.

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 presents a robust adaptive control strategy for nonlinear teleoperation systems. The controller is based on estimation of the impedance of human hand as well as that of the environment. The mentioned system is subjected to unmodeled dynamics, time-varying parameters and external force disturbances. The upper bound for the norm of disturbances and system uncertainties are not used in the presented control scheme. Furthermore, there is no constraint on the rate of changes and the amount of unknown parameters and perturbations. Given a robust adaptive control action and adaptation laws, the transparency and stability in teleoperation systems are mathematically proved using Lyapunov's direct method. Finally, simulation results obtained from a teleoperation system with two-link rotary robots are presented to show the effectiveness of the proposed control scheme.

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.

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

Robust adaptive control for nonlinear uncertain systems

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.

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.

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.

Using dynamic positioning (DP) ship maintains its position and heading by active thrusters. Several challenges exist with regard to the DP controller design, such as uncertain system model, actuator with saturation hard limitations, state or output (ship position or orientation) constraints. A robust receding horizon dual-mode control method is introduced into the design of DP controller using the property of the invariant ellipsoid. Outside the ellipsoid, the receding horizon control is employed .Once the state enters the ellipsoid, the control is switched to a linear state feedback control, which makes the state stay in the ellipsoid forever and stabilizes the system while satisfying the input, the state and the output constraints. The DP control is obtained by using semi-definite programming (SDP) which can be easily solved by means of linear matrix inequalities (LMI). At last, the simulation study is carried out to verify the feasibility and efficiency of the application of robust receding horizon dual-mode control for dynamic positioning ship.

This paper investigates the vibration control of geometrically nonlinear beam with Macro Fiber Composite (MFC) actuators using two different adaptive control algorithms. A complete mathematical modeling is presented in order to find the dynamic equation of motion. Then, a robust adaptive fuzzy control algorithm for controlling the proposed mechanical structure is introduced. This controller includes a fuzzy scheme and a robust controller. Based on sliding mode controller a fuzzy system is introduced to mimic an ideal controller. The robust controller is designed based on compensation of the difference between the fuzzy controller and the ideal controller. The parameters of the fuzzy system and uncertainty bound of the robust controller are adjusted adaptively. The adaptive laws are designed based on the Lyapunov stability theorem to reach the stability of the closed-loop system. Meanwhile, for comparison purposes the presented controller is compared with self tuning Ziegler-Nichols PID controller for both robustness and vibration suppression performance aspects. Effectiveness of these two control strategies is evaluated by numerical simulations. Detailed analysis for the closed-loop system is carried out to evaluate the vibration controlling performance under different output excitation, robustness of the closed-loop system under sudden loading and the effect of initial condition on vibration characteristic.

The design of a new hybrid controller for fractional-order uncertain chaotic systems with unknown time-varying delays

In this paper, we investigate the trajectory tracking control problem of surface ships subject to unknown parameters, unknown time-varying disturbances, and input saturation. The input saturation is approximated using a Gaussian error function. The compounded uncertain term caused by the unknown parameters and disturbances is transformed into a linear parametric form with a single parameter called virtual parameter. Then, a novel robust adaptive ship trajectory tracking control law is designed using the adaptive vector-backstepping design method, where the adaptive law online provides the estimation of the virtual parameter. Further, a finite-time control scheme is developed injecting a power function vector of the position and velocity errors into the proposed control scheme such that the control performance is improved. Both our control schemes are simple to compute and easy to implement in engineering applications. Theoretical analysis indicates that the designed control laws can force the surface ship to track the desired trajectory while guaranteeing the global uniform ultimate boundedness of all the signals in the closed-loop trajectory tracking control system of surface ships. Simulation results and comparison verify the effectiveness of our novel robust adaptive trajectory tracking control schemes.

In the paper, based on a combination of the robust control approach and an adaptive control technique, a design procedure of a new robust adaptive controller is proposed for power system load-frequency control with system parametric uncertainties. The system parametric uncertainties are obtained by changing parameters by 30% to 50% simultaneously from their typical values. In the design of the proposed controller, only the bounds of system parameters are required. The motivation of combining the robust control with an adaptive control is to use the robust control approach to deal with the small parametric uncertainties and to use the adaptive control for large parametric uncertainties so that stability of the overall system and good performance can both be achieved for all admissible uncertainties. The simulation results demonstrate that for the example system the proposed load-frequency controller can achieve good performance even in the presence of the generation rate constraint (GRC).