Optimal Output Regulation for Square, Over-Actuated and Under-Actuated Linear Systems

This paper considers two different problems in trajectory tracking control for linear systems. First, if the control is not unique which is most input energy efficient. Second, if exact tracking is infeasible which control performs most accurately. These are typical challenges for over-actuated systems and for under-actuated systems, respectively. We formulate both goals as optimal output regulation problems. Then we contribute two new sets of regulator equations to output regulation theory that provide the desired solutions. A thorough study indicates solvability and uniqueness under weak assumptions. E.g., we can always determine the solution of the classical regulator equations that is most input energy efficient. This is of great value if there are infinitely many solutions. We derive our results by a linear quadratic tracking approach and establish a useful link to output regulation theory.Comment: 8 pages, 0 figures, final version to appear in IEEE Transactions on Automatic Contro

International trade and social standards

The agreements setting up the new World Trade Organisation (WTO) which were signed in Marrakesh have met with widespread approval. The accompanying controversy over the question of social clauses has made the latter an issue of national and international importance which has since been under discussion in many international bodies, such as the International Labour Organisation (ILO), the OECD and the EU. The following two articles present differing views on this issue

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