Dual Control for Stochastic Linear MIMO Systems With Parameter Uncertainty

This paper considers a dual control problem for stochastic linear MIMO (Multiple Input Multiple Output) systems with parameter uncertainty. A novel dual adaptive control law for MIMO systems is proposed. The design is based on the innovation of the dual control cost function, which was originally developed for conventional adaptive control of linear systems. However, the design process is modified and developed to cater to the stochastic MIMO case. This is a more challenging problem because the superposition of parameter uncertainty and the MIMO property makes the problem more intractable. As in all dual adaptive strategies, it leads to a control law that balances out the need for caution, due to parameter uncertainty, with the conflicting requirement of probing that acts to quickly reduce parameter uncertainty, which is the nature of dual control. The proposed control law has two parts. One reflects the goal of regulating the output, and the second reflects the ability to handle uncertain parameters. A learning factor is introduced to balance these two parts to obtain a control law that can be applied to the original system. In the simulation examples, the uncertain parameters can be estimated quickly and accurately for the unknown but constant case and the abrupt parameter case. Furthermore, it is shown that the novel dual control law is superior to other control strategies by comparing the performance of the cost function in a statistical sense.