Continuous Adaptive Controller Research Articles

Global Adaptive Stabilization of High-order Nonlinear Systems with Zero Dynamics

This paper investigates the global adaptive stabilization for a class of high-order nonlinear systems with uncertain control coefficients and unmeasurable zero dynamics. Compared with the existing works, restriction on zero dynamics is further relaxed, and the dynamic order of a continuous adaptive state-feedback controller is reduced to be minimum (only one dimensional) through delicately defining an appropriate unknown parameter. The design procedures of the controller are provided by flexibly incorporating the method of adding a power integrator with the related adaptive technique and the idea of changing supply functions. Finally, a simple example is given to demonstrate the effectiveness of the control scheme.

Adaptive Control Design of High-order Nonlinear Systems with Unknown Control Coefficients and Zero Dynamics

This paper focuses on the adaptive stabilization problem for a class of high-order nonlinear systems with uncertain control coefficients and unmeasurable zero dynamics.Restriction on zero dynamics is further relaxed,and the dynamic order of a continuous adaptive state-feedback controller reduces to the minimum(only one dimension) through delicately defining an appropriate unknown parameter.The design procedures of the controller are provided by flexibly incorporating the method of adding a power integrator with the related adaptive technique and the idea of changing supply functions.The designed controller guarantees that all the closed-loop system states are globally uniformly bounded,and that the original state converges to zero.

Global Practical Tracking for High-Order Uncertain Nonlinear Systems with Unknown Control Directions

This paper addresses the global practical tracking problem for a class of high-order uncertain nonlinear systems with unknown control directions under fairly weak conditions. Although the stabilization problem has been studied for the systems, the tracking problem remains unsolved up to now mainly because of the essential differences between stabilization and tracking problems when control directions are unknown. In this paper, by introducing a novel coordinate transformation and new updating laws, an approach is presented for the first time to design a continuous adaptive controller to make the tracking error prescribed arbitrarily small after a finite time and simultaneously to keep all the closed-loop states bounded. It is worth emphasizing that the proposed adaptive tracking control design scheme is motivated by the recent tracking works, inspired by the ideas of universal control and dead zone and obtained by the approaches of Nussbaum-gain and adding a power integrator. Most importantly, this paper removes the basic assumption that the control directions are precisely known in the related tracking works, without additional conditions imposed on the systems and the reference signal.

ADAPTIVE ROBUST CONTROL OF UNCERTAIN SYSTEMS WITH TIME-VARYING STATE DELAY

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time-varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time-delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.

Exponential stabilization controller design for interconnected time delay systems

Decentralized robust control problem is investigated for a class of large scale systems with time varying delays. The considered systems have mismatches in time delay functions. A state coordinate transformation is first employed to change the original system into a cascade system. Then the virtual linear state feedback controller is developed to stabilize the first subsystem. Based on the virtual controller, a memoryless state feedback controller is constructed for the second subsystem. By choosing new Lyapunov Krasovskii functional, we show that the designed decentralized continuous adaptive controller makes the solutions of the closed-loop system exponentially convergent to a ball, which can be rendered arbitrary small by adjusting design parameters. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed design techniques.

Adaptive Practical Output Tracking Control for High-order Nonlinear Uncertain Systems

The problem of adaptive practical output tracking control is studied for a class of high-order nonlinear uncertain systems, which has been investigated under the assumption that the lower bounds of the unknown control coefficients are exactly known. Based on the idea of the new robust adaptive control and the continuous stabilization, this assumption is successfully removed. By means of adding a power integrator, a systematic approach is developed to construct a continuous adaptive practical output tracking controller, which guarantees that all the states of the closed-loop system are globally stable, while the tracking error can be bounded by any given positive number after a finite time. Finally, a simulation example is given to illustrate the correctness of the theoretical results.

Adaptive Lyapunov-Based Control of a Robot and Mass–Spring System Undergoing an Impact Collision

The control of dynamic systems that undergo an impact collision is both theoretically challenging and of practical importance. An appeal of studying systems that undergo an impact is that short-duration effects such as high stresses, rapid dissipation of energy, and fast acceleration and deceleration may be achieved from low-energy sources. However, colliding systems present a difficult control challenge because the equations of motion are different when the system suddenly transitions from a noncontact state to a contact state. In this paper, an adaptive nonlinear controller is designed to regulate the states of two dynamic systems that collide. The academic example of a planar robot colliding with an unactuated mass-spring system is used to represent a broader class of such systems. The control objective is defined as the desire to command a robot to collide with an unactuated system and regulate the mass to a desired compressed state while compensating for the unknown constant system parameters. Lyapunov-based methods are used to develop a continuous adaptive controller that yields asymptotic regulation of the mass and robot links. It is interesting to note that one controller is responsible for achieving the control objective when the robot is in free motion (i.e., decoupled from the mass-spring system), when the systems collide, and when the system dynamics are coupled.

Robust Attitude Tracking Control of Spacecraft in the Presence of Disturbances

I T IS well known that spacecraft usually operate in the presence of various disturbances and that their control input usually is limited because of actuator saturation. Therefore, two problems, disturbance rejection and saturation constraint accommodation, should be addressed in attitude control. Both problems have attracted considerable research interest in the existing literature. However, only limited results explicitly dealt with them simultaneously [1–5]. Di Gennaro [1] designed a dynamic controller that can globally asymptotically stabilize the spacecraft in the presence of saturation constraint and gravity gradient torque. However, the rejection of other disturbances is not guaranteed. Boskovic et al. [2,3] designed sliding-mode controllers, which are discontinuous and can cause chattering [6]. To avoid chattering, the boundary layer method was used in [2,3]. However, this method can only guarantee bounded attitude and angular velocity errors. To achieve global asymptotic stability with a smooth controller, Boskovic et al. [4] designed a continuous adaptive tracking controller with a condition necessary for guaranteeing the convergence of the attitude error to zero. However, it is difficult to know in what cases that condition can be satisfied. Moreover, according to [7], there do exist some disturbances in the presence of which that condition cannot be satisfied. Wallsgrove and Akella [5] designed a smooth controller using a hyperbolic tangent function. Although the angular velocity error converges to zero, the convergence of the attitude error to zero is not proved in [5]. Moreover, this controller gives rise to numerical problems in simulations of long duration. This paper proposes a controller without the aforementioned drawbacks. II. Spacecraft Attitude Dynamics

Adaptive global tracking for robots with unknown link and actuator dynamics

We present a continuous adaptive controller for the robot adaptive tracking problem with unknown robot parameters, unknown actuator parameters, and unavailable joint acceleration measurement. We prove that the proposed controller has global convergence to zero tracking error for any non-zero gains. This is a distinction compared to existing approaches, so far as applied to robots, such as the adaptive controller of Bridges et al. (Conference on Decision and Control, 1993; 159–165) whose global-convergence proof depended upon the controller gains being larger than certain bounding functions containing bounds on the system parameter estimates. The present work solves the same problem in a different way, where the main difference is that the global convergence does not impose a requirement of a gain size proportionate to the parameters' uncertainty sizes. Copyright © 2006 John Wiley & Sons, Ltd.

Adaptive robust control of uncertain systems with time-varying state delay

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time-varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time-delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.