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The problem of data-driven recursive computation of receding horizon LQRcontrol through a randomized combination of online/current andhistorical/recorded data is considered. It is assumed that large amounts ofhistorical input-output data from a system, which is similar but not identicalto the current system under consideration, is available. This (possibly large)data set is compressed through a novel randomized subspace algorithm todirectly synthesize an initial solution of the standard LQR problem, whichhowever is sub-optimal due to the inaccuracy of the historical model. The firstinstance of this input is used to actuate the current system and thecorresponding instantaneous output is used to iteratively re-solve the LQRproblem through a computationally inexpensive randomized rank-one update of theold compressed data. The first instance of the re-computed input is applied tothe system at the next instant, output recorded and the entire procedure isrepeated at each subsequent instant. As more current data becomes available,the algorithm learns automatically from the new data while simultaneouslycontrolling the system in near optimal manner. The proposed algorithm iscomputationally inexpensive due to the initial and repeated compression of oldand newly available data. Moreover, the simultaneous learning and control makesthis algorithm particularly suited for adapting to unknown, poorly modeled andtime-varying systems without any explicit exploration stage. Simulationsdemonstrate the effectiveness of the proposed algorithm vs popularexploration/exploitation approaches to LQR control.

Learning from similar systems and online data-driven LQR using iterative randomised data compression