Decentralized adaptive control schemes are presented for a class of large-scale interconnected systems. These schemes have the advantage that in addition to the standard assumption about the uncertainty of the subsystems, the strength of interconnection is assumed unknown. Provided certain structural constraints are satisfied, the adaptation gains automatically adjust to levels that assure stability of the overall system. Simulations of a spring-coupled dual pendulum showed that for high interconnection strengths, the proposed algorithm exhibits better tracking performance than existing algorithms. >

Decentralized adaptive control: structural conditions for stability

The results obtained in studies of robust stability and stabilizability of control systems with parametric (structured) uncertainties are reviewed. Both the algebraic methods based upon characteristic equations and the methods using Lyapunov functions and Riccati equations are discussed and compared. In the context of algebraic methods, most promising are the Kharitonov-type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space, maximizing its size using minimax or some other mathematical programming technique. In the framework of Lyapunov's direct method, the dominant approach has been a quadratic function estimation of stability regions in the parameter space. In large-sale systems, the concept of vector Lyapunov functions has been used with the possibility of choosing quadratic forms, norm-like functions, and their combinations. >

Parameter space methods for robust control design: a guided tour

Decentralized robust adaptive controller designs for large-scale interconnected systems are investigated. Motivated by real mechanical systems, the authors consider a general representation of interconnections when the strength of the interconnections is bounded by a pth-order polynomial in states. This is in contrast to other studies which have made simpler assumptions about the strength of the interconnections. The authors investigate several scenarios as the control computations become more distributed until the controllers are completely decentralized. The possible bound of the interconnections is assumed to be known for the decentralized semiadaptive controller. Without the knowledge of these bounds, two adaptive controllers are designed: a decentralized adaptive controller with partially centralized compensation and a fully adaptive decentralized controller. >

Decentralized adaptive controller design for large-scale systems with higher order interconnections

Decentralized adaptive control design for a class of large-scale interconnected nonlinear systems with unknown interconnections is considered. The motivation behind this work is to develop decentralized control for a class of large-scale systems which do not satisfy the matching condition requirement. To this end, large-scale nonlinear systems transformable to the decentralized strict feedback form are considered. Coordinate-free geometric conditions under which any general interconnected nonlinear system can be transformed to this form are obtained. The interconnections are assumed to be bounded by polynomial-type nonlinearities. Global stability and asymptotic regulation are established using classical Lyapunov techniques. The controller is shown to maintain robustness for a wide class of systems obtained by perturbation in the dynamics of the original system. Furthermore, appending additional subsystems does not require controller redesign for the original subsystems. Finally, the scheme is extended to the model reference tracking problem when global uniform boundedness of the tracking error to a compact set is established.

Decentralized adaptive control of a class of large-scale interconnected nonlinear systems

The author presents a simple decentralized adaptive control scheme for multijoint robot manipulators based on the independent joint control concept. The control objective is to achieve accurate tracking of desired joint trajectories. The proposed control scheme does not use the complex manipulator dynamic model, and each joint is controlled simply by a PID (proportional-integral-derivative) feedback controller and a position-velocity-acceleration feedforward controller, both with adjustable gains. Simulation results are given for a two-link direct-drive manipulator under adaptive independent joint control. The results illustrate trajectory tracking under coupled dynamics and varying payload. The proposed scheme is implemented on a MicroVAX II computer for motion control of the three major joints of a PUMA 560 arm. Experimental results are presented to demonstrate that trajectory tracking is achieved despite coupled nonlinear joint dynamics. >

Decentralized adaptive control of manipulators: theory, simulation, and experimentation

A decentralized adaptive control scheme is presented for multilink robot arms. The structure of dynamic and force interactions in the robot arm allows local high gain feedback control to stabilize the overall system, and cause the arm to track reference trajectories to any accuracy desired. The adaptive law is locally stable with an attractive set that is adjustable a-priori using minimal knowledge of robot parameters. Robot manipulators control using decentralized approach is highly desirable in that it facilitates real-time implementation.

Decentralized adaptive control of robot manipulators

Decentralized control has the advantages of low demand on computer resources and high-speed operation, since the subsystem controllers are implemented in parallel with one another. The authors introduce adaptation to counter the effects of nonlinear and trajectory dependent coupling among the robot joints which cause the independent joint dynamics to vary. They present the results of experimentation with a PUMA 560 arm using a decentralized adaptive control law. The experiments were specially selected for a high degree of intercoupling so that they could investigate how the adaptation mechanism responds. >

D.T. Gavel

Papers

Decentralized adaptive control of robot manipulators

Decentralized adaptive control experiments with the PUMA robot arm