The block regularised linear quadratic optimal controller

We have presented an LQ adaptive controller which has a data sample and control action generation interval of O(1), and the readjustment interval of control law of N * O(1), where N is the length of the horizon used for the LQ control computation, by using a pipelined parallel implementation. This controller has a number of important properties. The regularised identification procedure is robust because it prevents covariance of the estimates from becoming reduced-rank and causing the estimator to "blow up" and also limits the estimates from varying beyond a "safe" region. The identification is implemented on O(n²) processing cells and produces an estimate every O(n) time intervals. The computation of the LQ control law also uses O(n²) processing cells and has a speed of N * O(1), which is independent of the system order. This is an order of magnitude faster than that previously proposed and has the added advantage of no feedback loops on the systolic array. The computation of the control law allows for the setpoints to be nonzero and, also time-varying, which is important for practical applications. The penalties can also be time-varying. Lastly, the computation required to implement the control law is very simple and has a speed of O(1) on O(n) processing elements.