The commonly accepted control theory for discrete event systems, due to Ramadge and Wonham , followed by several other [17,4], has been more recently extended to temporal logic specifications [8,2,14]. Control consists in supervising a plant to guarantee some desired behavior, called control objectives; the objectives are standard properties such as non-blocking, safety, temporal logic definable behaviors, etc. Concerning the nature of the supervision, it is natural and standard to suppose a partial observation of the plant, as information on it moves and states is incomplete; we then talk about control under partial observation (see ). In this paper, we adapt the logical approach of  to specify control under partial observation. This approach is based on quantification over atomic propositions of the mu-calculus of , called the quantified mu-calculus. We prove the decidability of controller synthesis when the specification is a nested observational formula: the construction of controllers relies on the generalizations of the automata quotient of  and the automata projection of . An immediate important corollary is the synthesis of maximally permissive controllers under partial observation for mu-calculus definable control objectives. To our knowledge, maximal permissiveness of controllers has never been properly answered before: permissiveness is manageable in the regular languages framework , but becomes intricate when branching-time objectives are considered. The few results of the literature are  which concern control problems with full observation, and [8,2] which do not take maximal permissiveness into account. The paper is organized as follows: Sec.1 introduces the quantified mu-calculus and show its adequacy to control specification ; Sec.2 is dedicated to the control synthesis for the decidable fragment of the logic.