Abstract: A dynamical extension that makes possible the integration of a kinematic controller and a torque controller for nonholonomic mobile robots is presented. A combined kinematic/torque control law is developed using backstepping, and asymptotic stability is guaranteed by Lyapunov theory. Moreover, this control algorithm can be applied to the three basic nonholonomic navigation problems: tracking a reference trajectory, path following, and stabilization about a desired posture. The result is a general structure for controlling a mobile robot that can accommodate different control techniques, ranging from a conventional computed-torque controller, when all dynamics are known, to robust-adaptive controllers if this is not the case. A robust-adaptive controller based on neural networks (NNs) is proposed in this work. The NN controller can deal with unmodeled bounded disturbances and/or unstructured unmodeled dynamics in the vehicle. On-line NN weight tuning algorithms that do not require off-line learning yet guarantee small tracking errors and bounded control signals are utilized. © 1997 John Wiley & Sons, Inc.

Abstract: This article develops a new nonlinear backstepping design for the control of active suspension systems, which improves the inherent tradeoff between ride quality and suspension travel. The novelty is in the use of a nonlinear filter whose effective bandwidth depends on the magnitude of the suspension travel. This intentional introduction of nonlinearity, which is readily accommodated by backstepping, results in a design that is fundamentally different from previous ones: as the suspension travel changes, the controller smoothly shifts its focus between the conflicting objectives of ride comfort and rattlespace utilization, softening the suspension when suspension travel is small and stiffening it as it approaches the travel limits. Thus, our nonlinear design allows the closed-loop system to behave differently in different operating regions, thereby eliminating the dilemma of whether to use a soft or stiff suspension setting. The improvement achieved with our design is illustrated through comparative simulations.

Abstract: Develops a methodology for recursive construction of optimal and near-optimal controllers for strict-feedback stochastic nonlinear systems under a risk-sensitive cost function criterion. The design procedure follows the integrator backstepping methodology, and the controllers obtained guarantee any desired level of long-term average cost, for a given risk-sensitivity parameter /spl theta/. Furthermore, they lead to closed-loop system trajectories that are bounded in probability, and in some cases asymptotically stable in the large. These results also generalize to nonlinear systems with strongly stabilizable zero dynamics.

Abstract: A nonlinear vectorial backstepping control law for commercial ships is derived by using the concept of vectorial backstepping. Vectorial backstepping is done in 3 steps corresponding to the state vectors of the ship dynamics, kinematics and actuator dynamics. Emphasis is placed on compensation of the actuator dynamics since the bandwidth of the propellers, thrusters and rudders often is close to the bandwidth of the ship dynamics. Global exponential tracking is proven by applying Lyapunov stability analysis. The case study is simultaneously global exponential tracking of the surge and sway positions (x,y) and the yaw angle /spl psi/ of a surface ship. This can only be done by applying nonlinear control theory due to the nonlinear structure of the kinematic equations, Coriolis and centripetal forces, and hydrodynamic damping forces.

Abstract: We propose a simple sliding mode based controller for nonlinear systems with mismatched uncertainties. The design methodology is similar to backstepping and multiple surface control method but with the inclusion of sliding mode filters for estimating the derivatives of the plant output.

Abstract: The control of flexible joint robot manipulators by backstepping design approach is presented. In contrast with the other controllers for flexible joint robot manipulators, the proposed controller neither assumes weak joint flexibility nor requires joint acceleration measurements. With the proposed controller, the link position and velocity errors converge to zero exponentially fast. The simulation results prove that the proposed controller performs superior to the other controllers as the flexibility increases in the joints.

Abstract: An alternative adaptive scheme to achieve output tracking for a class of minimum-phase dynamically input–output linearizable nonlinear systems with parametric uncertainties is considered. The proposed approach is based upon a combination of the adaptive backstepping design method and a sliding mode control (SMC) scheme to design dynamical adaptive sliding mode controllers and provide robust output tracking even in the presence of unknown disturbances. The validity of the proposed approach, regarding tracking objectives and robustness with respect to bounded stochastic perturbation inputs, is tested through digital computer simulations. © 1997 by John Wiley & Sons, Ltd.

Abstract: This paper presents an adaptive partial state feedback controller for rigid-link flexible-joint (RLFJ) robots. The controller compensates for parametric uncertainty throughout the entire mechanical system while only requiring measurement of link position and actuator position. To eliminate the need for measuring link velocity and actuator velocity a set of filters is utilized as a surrogate for the unmeasurable quantities. Based on this set of filters, an adaptive integrator backstepping procedure is used to develop a torque input controller which guarantees semiglobal asymptotic link position tracking while also ensuring that all signals remain bounded during closed-loop operation. Simulation results for a two-link RLFJ robot are utilized to validate the performance of the proposed controller.

Abstract: We pose and solve an "inverse optimal" adaptive tracking problem for nonlinear systems with unknown parameters. A controller is said to be inverse optimal when it minimizes a meaningful cost functional that incorporates integral penalty on the tracking error state and the control, as well as a terminal penalty on the parameter estimation error. The basis of our method is an adaptive tracking control Lyapunov function whose existence guarantees the solvability of the inverse optimal problem. The controllers designed in this paper are not of certainty-equivalence type. Even in the linear case they would not be a result of solving a Riccati equation for a given value of the parameter estimate. Our abandoning of the CE approach is motivated by the fact that, in general, this approach does not lead to optimality of the controller with respect to the overall plant-estimator system, even though both the estimator and the controller may be optimal as separate entities. Our controllers, instead, compensate for the effect of parameter adaptation transients in order to achieve optimality of the overall system. We combine inverse optimality with backstepping to design a new class of adaptive controllers for strict-feedback systems. These controllers solve a problem left open in the previous adaptive backstepping designs-getting transient performance bounds that include an estimate of control effort.

Abstract: In this paper we propose anti surge controllers for a close coupled valve in a compression system. The valve modifies the characteristic of the compressor, and allows for stable operation beyond the original surge line. The design tool used is backstepping and global uniform asymptotic stability is proven. Damping terms are included in the controllers, and in the presence of both mass flow and pressure disturbances, global uniform boundedness and convergence to a set is ensured. Under the assumption of decaying disturbances the controller ensures convergence to the origin.

Abstract: By using the integrator backstepping technique, the control of rigid link, electrically driven robot manipulators is addressed in the presence of arbitrary uncertain manipulator inertia parameters and actuator parameters. The control scheme developed is computationally simple owing to the avoidance of the derivative computation of the regressor matrix. Semiglobal asymptotic stability of the controller is established in the Lyapunov sense. Simulation results are included to demonstrate the tracking performance.

Abstract: A smooth adaptive control methodology combining the results of a variable structure control scheme and backstepping is proposed for the class of systems in the special strict feedback form. The controller ensures the global asymptotic tracking and regulation of the first /spl kappa/ states which are in a chain of integrators form and globally uniformly bounded tracking for the remaining states. An application of this methodology for the case of friction compensation in drives containing a compliant transmission between the load and the actuator is presented. The friction model considered is a six parameter dynamic model. This problem is significant because the load side friction is mismatched with the control. The advocated controller does not require knowledge of any of the parameters of friction and is shown to give global asymptotic tracking of the load angle and velocity in the presence of dynamic uncertainties. Simulation results indicate the efficacy of the proposed approach.

Abstract: An adaptive output feedback dead-zone compensation scheme is designed for systems with an unknown dead-zone at the input of an n th-order smooth nonlinear dynamics in the output-feedback canonical form. The proposed adaptive controller employs an adaptive dead-zone inverse to cancel the dead-zone and uses a backstepping design for adaptive output feedback control. It has a new state observer parametrization that is needed to handle the dead-zone uncertainty and a new robust control law that is suitable for the parameter projection needed to implement an adaptive dead-zone inverse. The adaptive dead-zone compensation design ensures closed-loop signal boundedness and improves system tracking performance.

Abstract: Brief Reports are accounts of completed research which do not warrant regular articles or the priority handling given to Communications; however, the same standards of scientific quality apply. (Addenda are included in Brief Reports.) A Brief Repor no longer than four printed pages and must be accompanied by an abstract. The same publication schedule as for regular a followed, and page proofs are sent to authors.

Abstract: In recent years, the wind energy has been reconsidered because it is clean and the many studies for the effective use of the wind energy have been done. The generation of electric power using wind turbine generators is distinguished from conventional methods of generation by the variability of the prime source of power. A matter of concern is the effect of the varing wind on the generated power of wind turbine generators. This problem is very important to the power systems with small capacity in remote areas or islands. The purpose of this paper is to keep the generated power of wind turbine generators at a rated value under the varing wind, by changing the blade pitch angle. Here the backstepping algorithm is used to design the pitch angle controller in order to consider the non-linearity for wind turbine generator systems. The proposed controller not only locally asymptotically stabilizes the plants, but also effectively keep the gererated power of wind turbine generators at a rated value under the varing wind. Digital computer simulations using parameters of the actual windmill generator system also give good results.

Abstract: Using integrator backstepping we present a robust optimal control design method for nonlinear strict-feedback systems with disturbances also in strict-feedback form. We globally stabilize such systems while obtaining local optimality and global inverse optimality. An analytic example is presented which is used to compare the performance of the robust nonlinear optimal design to that of a robust linear optimal design.

Abstract: A nonlinear backstepping scheme is developed for adaptive control of linear plants with multiple inputs and multiple outputs. Solutions to plant parametrization, state observer, and adaptive control law for the multivariable backstepping design are proposed. The developed adaptive controller has the desired properties for ensuring closed-loop signal boundedness and asymptotical tracking.

Abstract: This paper introduces the concept of outer flatness, a derivative of differential flatness. Outer flatness describes a system that can be split in 2 subsytems, a non-flat inner system and a flat outer system. The outputs of the outer system are the tracking outputs of interest. The inputs of the outer system are the outputs of the inner system, and not subject to our direct control. The inputs of the inner system are the real actuator inputs. This system structure is also present in backstepping and dynamic inversion. We present two theorems on exponential and bounded tracking for outer flat systems, based on Lyapunoff arguments. We validate the approach with simulations and experiments on a model helicopter.

Abstract: Model reference robust control (M RRC) of single-input single-output (SISO) systems was introduced as a new means of designing I/O robust control (Qu et al. 1994). This I/O design is an extension of the recursive backstepping design in the sense that a nonlinear dynamic control (not static) is generated recursively. Backstepping entails the design of fictitious controls starting with the output state-space equation and backstepping until one arrives at the input state-space equation where the actual control can be designed. At each step the system is transformed and a fictitious control is designed to stabilize the transformed state (Naik and Kumar 1992). It is shown in this paper that M RRC of multiple input multiple output (MIMO) systems is an extension of model reference control (M RC) of MIMO systems and M RRC of SISO systems. Unwanted coupling exists in many physical MIMO systems. It is shown that M RRC decouples MIMO systems using only input and output measurements rather than state feedback. This i...

Abstract: In order to achieve robust output tracking for a class of uncertain triangular systems, a combination of a robust sliding observer and a backstepping procedure is introduced.

Abstract: This paper presents a new systematic way, based on the backstepping approach, to design discontinuous time-invariant state feedback controllers for exponential stabilization of nonholonomic systems in chained form. The enclosed simulation results show the effectiveness of the proposed controller.

Abstract: Model reference robust control (MRRC) is derived for MIMO systems that have a right Hermite normal form which is SPR and diagonal, and then for systems whose right Hermite normal form is diagonal but not SPR. It is shown that MRRC of multiple input multiple output (MIMO) systems is an extension of model reference control (MRC) of MIMO systems and MRRC of SISO systems. Unwanted coupling exists in many physical MIMO systems. The recursive backstepping procedure used in non-SPR SISO systems cannot be directly applied to diagonal MIMO non-SPR systems without the introduction of the augmented matrix or a precompensator. It is shown that MRRC decouples MIMO systems using only input and output measurements rather than state feedback.

Abstract: We address the worst-case adaptive controller design problem for uncertain single-input single-output linear systems with noisy output measurements, under the assumption that the (parametrically) unknown system is minimum phase with a known relative degree and unknown high-frequency gain of known sign. We first formulate this adaptive control problem as a nonlinear H∞ control problem with imperfect state measurements, which then directly addresses transient performance and robustness of adaptive control systems. Then, by utilizing cost-to-come function analysis and integrator backstepping methodology, we derive explicit expressions for the worst-case adaptive controllers. Using a soft projection technique, we guarantee the bounded-input bounded-output property of the closed-loop system with respect to exogenous disturbance inputs without any assumption of persistency of excitation of the reference signal.