A significant fraction of industrial MPC schemes employs linear prediction models. Closed loop performance of a linear model based MPC scheme can deteriorate over a period of time if the prediction model is not updated to account for the changing operating conditions. An effective way of handling this problem is to employ dual control, which directs the plant output towards a reference setpoint and simultaneously injects probing signals into the plant to get information-rich data which can be used for model identification under closed loop conditions. In this work, two multivariable adaptive dual MPC (ADMPC) schemes are developed based on MISO output error models that are parameterized using generalized orthonormal basis filters (GOBF). A nominal model is initially developed using offline identification exercise. The Fourier coefficients of the GOBF models are subsequently updated online using recursive parameter estimators. Also, to deal with large magnitude changes in the operating conditions, a shifting time window based approach is developed that can track variations of the GOBF poles online. To begin with, starting from a stochastic infinite horizon constrained optimal control problem, a computationally tractable finite horizon surrogate of the optimal control problem is derived. The surrogate problem includes terms that are sensitive to the parameter covariance. Based on the surrogate optimal control problem, two variants of ADMPC are proposed, viz. one that uses a fixed Fourier basis and another that uses a time varying Fourier basis. The effectiveness of the ADMPC schemes is evaluated by conducting stochastic simulations and experimental studies on the benchmark quadruple tank process. Analysis of the simulation results reveals that the proposed ADMPC schemes are able to achieve better tracking and regulatory performances when compared to the conventional adaptive MPC (AMPC). The simulation exercise also reveals that the proposed approach provides sufficient degrees of freedom to excite the plant in the closed loop for generating information-rich data for online model update. Experimental validation demonstrates that the proposed ADMPC is able to inject higher levels of input excitation throughout servo and regulatory responses with excitation levels similar to excitation levels used in the open loop identification experiments. (C) 2019 Elsevier Ltd. All rights reserved.