AbstractApproximate solutions are suggested for receding horizon dual control to guarantee acceptable control performance of a plant with largea prioriparameter uncertainties under poor excitation by the output reference and to satisfy the requirement of very fast adaptation using knowledge available on sensor and performance in industrial applications of adaptive control. the aim of the paper is to present several levels of interaction between on‐line identification and control performance using parameter bounds. an interesting theorem shows that parameter bounding is a necessary part of the solution of the dual control problem. Starting from the complete separation of identification and control, various approximations are presented at different levels of optimality. Finally, the exact solution of the dual control problem is found for static gain adaptation, which implicitly involves a parameter‐bounding identification proced