Abstract: The latest technological progress in sensors, actuators and energy storage devices enables the developments of miniature VTOL systems. In this paper we present the results of two nonlinear control techniques applied to an autonomous micro helicopter called Quadrotor. A backstepping and a sliding-mode techniques. We performed various simulations in open and closed loop and implemented several experiments on the test-bench to validate the control laws. Finally, we discuss the results of each approach. These developments are part of the OS4 project in our lab.

Abstract: The latest technological progress in sensors, actuators and energy storage devices enables the developments of miniature VTOL systems. In this paper we present the results of two nonlinear control techniques applied to an autonomous micro helicopter called Quadrotor. A backstepping and a sliding-mode techniques. We performed various simulations in open and closed loop and implemented several experiments on the test-bench to validate the control laws. Finally, we discuss the results of each approach. These developments are part of the OS4 project in our lab.

Abstract: The problem of stabilization for a class of feedback linearizable systems with multiple state constraints is addressed. The design procedure is constructive, and yields a continuous final control law which guarantees that all specified states remain within certain bounds for all time. The achieved bounds on the states are independent of the initial conditions. The procedure entails shaping the control Lyapunov function, and propagating hard-bounds imposed on the pertinent stabilising functions and associated error signals through the steps of the backstepping control design framework.

Abstract: The attitude tracking control problem of a rigid spacecraft with external disturbances and an uncertain inertia matrix is addressed using the adaptive control method. The adaptive control laws proposed in this paper are optimal with respect to a family of cost functionals. This is achieved by the inverse optimality approach, without solving the associated Hamilton-Jacobi-Isaacs partial differential (HJIPD) equation directly. The design of the optimal adaptive controllers is separated into two stages by means of integrator backstepping, and a control Lyapunov argument is constructed to show that the inverse optimal adaptive controllers achieve H/sub /spl infin// disturbance attenuation with respect to external disturbances and global asymptotic convergence of tracking errors to zero for disturbances with bounded energy. The convergence of adaptive parameters is also analyzed in terms of invariant manifold. Numerical simulations illustrate the performance of the proposed control algorithms.

Abstract: A command filtered backstepping approach is presented that uses adaptive function approximation to control unmanned air vehicles. The controller is designed using three feedback loops. The command inputs to the airspeed and flight-path angle controller are x c , γ c , V c and the bounded first derivatives of these signals. That loop generates comand inputs μ c , α c for a wind-axis angle loop. The sideslip angle command β c is always zero. The wind-axis angle loop generates rate commands P c , Q c , R c for an inner loop that generates surface position commands. The control approach includes adaptive approximation of the aerodynamic force and moment coefficient functions. The approach maintains the stability (in the sense of Lyapunov) of the adaptive function approximation process in the presence of magnitude, rate, and bandwidth limitations on the intermediate states and the surfaces.

Abstract: In this note, the problem of robust output feedback control for a class of nonlinear time delayed systems is considered. The systems considered are in strict-feedback form. State observer is first designed, then based on the observed states the controller is designed via backstepping method. Both the designed observer and controller are independent of the time delays. Based on Lyapunov stability theory, we prove that the constructed controller can render the closed-loop system asymptotically stable. Simulation results further verify the effectiveness of the proposed approach.

Abstract: A novel adaptive fuzzy controller with H/sub /spl infin// performance is proposed for a wide class of strict-feedback canonical nonlinear systems. The systems may possess a class of uncertainties referred to as unstructured uncertain functions, which are not linearly parameterized and have no prior knowledge of the bound. The Takagi-Sugeno-type fuzzy logic systems are used to approximate the uncertainties and a systematic design procedure is developed for synthesis of adaptive fuzzy control with H/sub /spl infin// performance, which combines the backstepping technique and generalized small gain approach. The method preserves the three advantages, those are, the semiglobal uniform ultimate bound of adaptive control in the presence of unstructured uncertainties can be guaranteed, the adaptive mechanism with only one learning parameter is obtained and the possible controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques can be removed. Performance and limitations of proposed method are discussed and illustrated with simulation results.

Abstract: This note presents a new method to design adaptive feedback controller for nonlinear time-delay systems. First, by using the LaSalle-Razumikhin theorem, a sufficient condition is derived that ensures the convergence of a part of the solution with stability for a class of functional differential equations. Then, using this condition, the adaptive stabilization problem is solved for nonlinear time-delay systems. Moreover, it is shown that for a class of nonlinear time-delay systems with triangular structure the adaptive stabilizing controller can be obtained by recursively constructing the Lyapunov-Razumikhin function. It will be shown that the provided recursive design approach, which is obviously motivated by the typical backstepping method, is not a trivial extension of the existing design method.

Abstract: An image-based "eye-in-hand" visual servo-control design is proposed for underactuated rigid-body dynamics. The dynamic model considered is motivated by recent work on vertical takeoff and landing aerial robotic vehicles. The task considered is that of tracking parallel linear visual features. The proposed design exploits the geometry of the task considered and passivity-like properties of rigid-body dynamics to derive a control Lyapunov function using backstepping techniques.

Abstract: This study is concerned with the position control of an induction servomotor using a recurrent-neural-network (RNN)-based adaptive-backstepping control (RNABC) system. The adaptive-backstepping approach offers a choice of design tools for the accommodation of system uncertainties and nonlinearities. The RNABC system is comprised of a backstepping controller and a robust controller. The backstepping controller containing an RNN uncertainty observer is the principal controller, and the robust controller is designed to dispel the effect of approximation error introduced by the uncertainty observer. Since the RNN has superior capabilities compared to the feedforward NN for dynamic system identification, it is utilized as the uncertainty observer. In addition, the Taylor linearization technique is employed to increase the learning ability of the RNN. Meanwhile, the adaptation laws of the adaptive-backstepping approach are derived in the sense of the Lyapunov function, thus, the stability of the system can be guaranteed. Finally, simulation and experimental results verify that the proposed RNABC can achieve favorable tracking performance for the induction-servomotor system, even with regard to parameter variations and input-command frequency variation.

Abstract: In automatic guidance of agriculture vehicles, lateral control is not the only requirement. Lots of research works have been focused on trajectory tracking control which can provide high longitudinal-lateral control accuracy. Satisfactory results have been reported as soon as vehicles move without sliding. But unfortunately pure rolling constraints are not always satisfied especially in agriculture applications where working conditions are rough and not expectable. In this paper the problem of trajectory tracking control of autonomous farm vehicles in presence of sliding is addressed. To take sliding effects into account, two variables which characterize sliding effects are introduced into the kinematic model based on geometric and velocity constrains in presence of sliding. With linearization approximation a refined kinematic model is obtained in which sliding appears as additive unknown parameters to the ideal kinematic model. By integrating parameter adaptation technique with backstepping method, a stepwise procedure is proposed to design a robust adaptive controller. It is theoretically proven that for the farm vehicles subjected to sliding, the longitudinal-lateral deviations can be stabilized near zero and the orientation errors converge into a neighborhood near the origin. To be more realistic for agriculture applications, an adaptive controller with projection mapping is also proposed. Simulation results show that the proposed (robust) adaptive controllers can guarantee high trajectory tracking accuracy regardless of sliding.

Abstract: An adaptive compensation control scheme using output feedback is designed and analysed for a class of non-linear systems with state-dependent non-linearities in the presence of unknown actuator failures. For a linearly parameterized model of actuator failures with unknown failure values, time instants and pattern, a robust backstepping-based adaptive non-linear controller is employed to handle the system failure, parameter and dynamics uncertainties. Robust adaptive parameter update laws are derived to ensure closed-loop signal boundedness and small tracking errors, in general, and asymptotic regulation, in particular. An application to controlling the angle of attack of a non-linear hypersonic aircraft dynamic model in the presence of elevator segment failures is studied and simulation results show that the developed adaptive control scheme has desired actuator failure compensation performance. Copyright © 2004 John Wiley & Sons, Ltd.

Abstract: The paper contains certain results concerning the finite-time global stabilization for triangular control systems described by retarded functional differential equations by means of time-varying distributed delay feedback. These results enable us to present solutions to feedback stabilization problems for systems with delayed input. The results are obtained by using the backstepping technique.

Abstract: This paper presents a novel active backstepping control approach for controlling hyperchaotic Rossler system to a steady state as well as tracking of any desire trajectory to be achieved in a systematic way. The proposed method is a systematic design approach and consists in a recursive procedure that interlaces the choice of a Lyapunov function with the design of active control. Numerical results show that the controller is singularity free and the closed-loop system is stable globally. Especially, the main feature of this technique is that it gives the flexibility to construct a control law. Finally, numerical experiments verify the feasibility and effectiveness of the proposed control technique.

Abstract: This paper investigates the problem of output-feedback adaptive stabilization control design for non-holonomic chained systems with strong non-linear drifts, including modelled non-linear dynamics, unmodelled dynamics, and those modelled but with unknown parameters. An observer and an estimator are introduced for state and parameter estimates, respectively. By using the integrator backstepping approach and based on the observer and parameter estimator, a constructive design procedure for output-feedback adaptive stabilization control is given. It is shown that, under some conditions, the control design ensures the closed-loop system is globally asymptotically stable when there is no non-linear drift in the first subsystem, and semiglobally asymptotically stable, otherwise. An example is given to show the effectiveness of the theory.

Abstract: In this paper, adaptive neural network (NN) control is investigated for a class of discrete-time multi-input-multi-output (MIMO) nonlinear systems with triangular form inputs. Each subsystem of the MIMO system is in strict feedback form. First, through two phases of coordinate transformation, the MIMO system is transformed into input-output representation with the triangular form input structure unchanged. By using high-order neural networks (HONNs) as the emulators of the desired controls, effective output feedback adaptive control is developed using backstepping. The closed-loop system is proved to be semiglobally uniformly ultimate bounded (SGUUB) by using Lyapunov method. The output tracking errors are guaranteed to converge into a compact set whose size is adjustable, and all the other signals in the closed-loop system are proved to be bounded. Simulation results show the effectiveness of the proposed control scheme.

Abstract: In this paper, we investigate the leader following based formation control of multiple nonholonomic mobile robots. We present a new kinematics model for the leader-follower system using Cartesian coordinates rather than the commonly used polar coordinates in literature. Based on this new model and the idea of integrator backstepping, a globally stable controller is derived for the whole system. Simulation results are included to verify the efficacy of the presented new model and controller.

Abstract: This paper is concerned with the problem of global stabilization by state feedback and output feedback for a class of time-delay nonlinear systems that are dominated by a triangular system satisfying linear growth conditions By solving the Lyapunov equation and constructing the appropriate Lyapunov-Krasovskii functionals (LKF), the linear and memoryless state feedback controller and output feedback controller making the closed-loop system globally asymptotically stable (GAS) are explicitly constructed respectively Comparing our design scheme with the backstepping method which has been widely used to deal with strictly feedback nonlinear systems, our design scheme is much simpler and more efficient An example is given to show that the proposed design procedures are very simple and efficient

Abstract: This paper describes a visual tracking control law of an Unmanned Aerial Vehicle (UAV) for monitoring of structures and maintenance of bridges. It presents a control law based on computer vision for quasi-stationary flights above a planar target. The first part of the UAV’s mission is the navigation from an initial position to a final position to define a desired trajectory in an unknown 3D environment. The proposed method uses the homography matrix computed from the visual information and derives, using backstepping techniques, an adaptive nonlinear tracking control law allowing the effective tracking and depth estimation. The depth represents the desired distance separating the camera from the target.

Abstract: A novel active backstepping control method is presented for synchronizing two identical Rossler hyperchaotic systems with each other and extended to achieve the generalized synchronization of the Chua chaotic system with the Rossler hyperchaotic system. It is a systematic design approach and consists of a recursive procedure interlacing the choice of a Lyapunov function with the design of active control. In particular, this technique gives flexibility in constructing a control law. Numerical experiments verify the feasibility and effectiveness of the proposed control technique.