论文信息 - Optimal Adaptive Control Based on an ARX Model with Randomly Varying Coefficients

Optimal Adaptive Control Based on an ARX Model with Randomly Varying Coefficients

Adaptive control of systems described by an ARX (autoregressive system with exogenous input) model with randomly varying coefficients and d delays in the input is considered. The variation of each coefficient in the model is assumed to consist of white noise process and coloured noise process modelled as the output of a linear shaping filter. The optimal estimation of the state of the shaping filter is possible by using the Kalman filter algorithm. Two simple optimal adaptive control algorithms are derived. One is an algorithm obtained by determining the control input so that the d step ahead optimal prediction of the output coincides with a reference output, and the other is obtained by minimizing a quadratic cost function consisting of the d step ahead output error and the control input at each time step. It is shown that these optimal adaptive controls require the moments of the a posteriori probability distribution of the state of the shaping filter up to d and d+1 respectively. By omitting the higher moments from the optimal algorithms, suboptimal algorithms are obtained. Simulation results are presented to compare the performance of the optimal and the suboptimal algorithms with that of the self tuning regulator of Astrom and Wittenmark. Keyword: adaptive control, randomly varying coefficient, Bayesian approach

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