Computation and Control

The problem of developing a systematic approach to the design of feed­ back strategies capable of shaping the response of complicated dynamical control systems illustrates the integration of a wide variety of mathemat­ ical disciplines typical of the modern theory of systems and control. As a concrete example, one may consider the control of fluid flow across an airfoil, for which recent experiments indicate the possibility of delaying the onset of turbulence by controlling viscosity through thermal actuators located on the airfoil. In general, there are two approaches to the con­ trol of such a complica. ted process, the development of extremely detailed models of the process followed by the derivation of a more "dedicated" feed­ back law or the development of a more simple model class followed by the derivation of control laws which are more robust to unmodelled dynamics and exogeneous disturbances. In either approach, the two twin themes of approximation and computation play a significant role in the derivation and implementation of resulting control laws. And there is no doubt that the cross-fertilization between these twin themes and control theory will increase unabated throughout the next decade, not just as an important component of design and implementation of control laws but also as a source of new problems in computational mathematics. In this volume, we present a collection of papers which were deliv­ ered at the first Bozeman Conference on Computation and Control, held at Montana State University on August 1-11, 1988.

Contenu

Simultaneous Stabilization of Linear Time Varying Systems by Linear Time Varying Compensation.- Robust Feedback Stabilization of Nonlinear Systems.- Feedback Design from the Zero Dynamics Point of View.- Two Examples of Stabilizable Second Order Systems.- Orthogonality - Conventional and Unconventional - in Numerical Analysis.- Discrete Observability of Parabolic Initial Boundary Value Problems.- Numerical Optimal Control via Smooth Penalty Functions.- Observability and Inverse Problems Arising in Electrocardiography.- Eigenvalue Approximations on the Entire Real Line.- Prediction Bands for Ill-Posed Problems.- Controllability, Approximations and Stabilization.- Interval Mathematics Techniques for Control Theory Computations.- Accuracy and Conditioning in the Inversion of the Heat Equation.- On the Recovery of Surface Temperature and Heat Flux via Convolutions.- Observability, Interpolation and Related Topics.- Constructing Polynomials over Finite Fields.- A Collocative Variation of the Sinc-Galerkin Method for Second Order Boundary Value Problems.- A Sinc-Collocation Method for Weakly Singular Volterra Integral Equations.- Tuning Natural Frequencies by Output Feedback.- Efficient Numerical Solution of Fourth-Order Problems in the Modeling of Flexible Structures.- Explicit Approximate Methods for Computational Control Theory.- Sinc Approximate Solution of Quasilinear Equations of Conservation Law Type.- Systems with Fast Chaotic Components.- Bifurcation and Persistance of Minima in Nonlinear Parametric Programming.- Numerical Solution of an Ill-Posed Coefficient Identification Problem.- Observability, Predictability and Chaos.- Geometric Inverse Eigenvalue Problem.- Observability and Group Representation Theory.- Highly-Accurate Difference Schemes for Solving Hyperbolic Problems.- A Finite Spectrum Unmixing Set for $$\mathcal{G}\mathcal{L}\left( {3,\mathcal{R}} \right)$$.