Output-input stability and minimum-phase nonlinear systems

This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of output-input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. As an application, we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control.Comment: Revised version, to appear in IEEE Transactions on Automatic Control. See related work in http://www.math.rutgers.edu/~sontag and http://black.csl.uiuc.edu/~liberzo

Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Performance-based control system design automation via evolutionary computing

This paper develops an evolutionary algorithm (EA) based methodology for computer-aided control system design (CACSD) automation in both the time and frequency domains under performance satisfactions. The approach is automated by efficient evolution from plant step response data, bypassing the system identification or linearization stage as required by conventional designs. Intelligently guided by the evolutionary optimization, control engineers are able to obtain a near-optimal ‘‘off-thecomputer’’ controller by feeding the developed CACSD system with plant I/O data and customer specifications without the need of a differentiable performance index. A speedup of near-linear pipelineability is also observed for the EA parallelism implemented on a network of transputers of Parsytec SuperCluster. Validation results against linear and nonlinear physical plants are convincing, with good closed-loop performance and robustness in the presence of practical constraints and perturbations