Decentralized tracking for a class of interconnected nonlinear systems using variable structure control

Abstract This paper presents a solution to the decentralized tracking or servomechanism problem for a class of nonlinear, multivariable systems. Decentralized variable structure control is used to decompose the solution into two parts: (1) the design of a set of decentralized, nonlinear controls that force each subsystem's state trajectory onto an interconnected manifold in the composite system state space; and (2) the construction of the manifold such that asymptotic tracking occurs when the subsystem state trajectories are restricted to the manifold. While numerical methods are not explicitly considered, manifold design is relatively straightforward, requiring only the use of known decentralized eigenvalue assignment techniques and the solution of linear algebraic equations. The structure of a simple, decentralized, nonlinear control law is proposed which requires little design effort beyond the construction of the manifold.

[1]  E. Davison,et al.  On the stabilization of decentralized control systems , 1973 .

[2]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[3]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[4]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

[5]  Harry G. Kwatny,et al.  On alternative methodologies for the design of robust linear multivariable regulators , 1978 .

[6]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[7]  A. Laub,et al.  Numerical linear algebra aspects of control design computations , 1985, IEEE Transactions on Automatic Control.

[8]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

[9]  B. Draenovi.  The invariance conditions in variable structure systems , 1969 .

[10]  Raymond A. DeCarlo,et al.  Decentralized variable structure control of interconnected multi-input/ multi-output nonlinear systems , 1987 .

[11]  R. Decarlo,et al.  A continuation algorithm for eigenvalue assignment by decentralized constant-output feedback , 1985 .

[12]  Harry G. Kwatny,et al.  Variable structure servomechanism design and applications to overspeed protection control , 1982, Autom..

[13]  Edward J. Davison.  The robust decentralized control of a general servomechanism problem , 1975 .

[14]  Ümit Özgüner,et al.  A decentralized variable structure control algorithm for robotic manipulators , 1985, IEEE J. Robotics Autom..

[15]  M. Corless,et al.  Ultimate Boundedness and Asymptotic Stability of a Class of Uncertain Dynamical Systems via Continuous and Discontinuous Feedback Control , 1984 .

[16]  Raymond A. DeCarlo,et al.  Interconnected Dynamical Systems , 1981 .

[17]  R. Decarlo,et al.  A homotopy-method for eigenvalue assignment using decentralized state feedback , 1984, 1982 21st IEEE Conference on Decision and Control.