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We analyze the performance of receding horizon controllers for the problem of keeping the state of a system within a given admissible set while minimizing an averaged functional. This problem does not satisfy the usual conditions needed for the analysis of receding horizon schemes. We give conditions under which approximate optimal performance can be guaranteed without imposing terminal constraints and illustrate our results by means of two numerical examples.doi:10.15495/epub_ubt_00005625 fatcat:ipwqi5amt5gqvhx6pbr7kpmm2y