Gain scheduling via linear fractional transformations
Systems & Control Letters
Automatica (Journal of IFAC)
Bilinear separation of two sets in n-space
Computational Optimization and Applications
The Extended Linear Complementarity Problem
SIAM Journal on Matrix Analysis and Applications
Self-scheduled H∞ control of linear parameter-varying systems: a design example
Automatica (Journal of IFAC)
Low-order control design for LMI problems using alternating projection methods
Automatica (Journal of IFAC)
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We show in the present paper that many open and challenging problems in control theory belong the the class of concave minimization programs. More precisely, these problems can be recast as the minimization of a concave objective function over convex LMI (Linear Matrix Inequality) constraints. As concave programming is the best studied class of problems in global optimization, several concave programs such as simplicial and conical partitioning algorithms can be used for the resolution. Moreover, these global techniques can be combined with a local Frank and Wolfe feasible direction algorithm and improved by the use of specialized stopping criteria, hence reducing the overall computational overhead. In this respect, the proposed hybrid optimization scheme can be considered as a new line of attack for solving hard control problems.Computational experiments indicate the viability of our algorithms, and that in the worst case they require the solution of a few LMI programs. Power and efficiency of the algorithms are demonstrated for a realistic inverted-pendulum control problem.Overall, this dedication reflects the key role that concavity and LMIs play in difficult control problems.