Linear time-invariant systems play significant role in the control field. A number of methods have been published for identification of the deterministic part of a process. However, identification of the stochastic part has had much less attention. This paper deals with estimation of covariance matrices of the noise entering a linear system. The process and measurement noise covariance matrices are tuning parameters of the Kalman filter, and they affect the quality of the state estimation. The noise covariance matrices are generally not known, and their estimation from the measured data is a challenging task. This paper introduces a method for estimation of the noise covariance matrices using Bayesian approach along with Monte Carlo numerical methods. Performance of the approach is tested on various systems and noise properties. The second part of the paper compares Monte Carlo approach with the recently published methods. The speed of convergence is compared with the Cramér-Rao bounds.
This paper proposes a method to approximate a dual controller by a computationally feasible algorithm. Dual control that optimally solves the problem of simultaneous control and identification of a system with uncertain parameters is known to be both analytically and computationally unsolvable. This paper proposes a multiple-step active control algorithm that gives a suboptimal but tractable solution to the original dual control problem. The algorithm is based on model predictive control (MPC) and approximates persistent system excitation in terms of the increase of the lowest eigenvalue of the parameter estimate information matrix.The problem is formulated as a two-phase optimization problem, where first an MPC solution is found and then the lowest eigenvalue of the information matrix is maximized in the next step within a given permitted input perturbation. Unlike similar methods, the proposed algorithm predicts the information matrix for more than one step of control, which makes it possible to uniformly excite the parameter space. The use of MPC in the first design phase instead of a cautious controller is justified by showing unfavorable properties of cautious control. The advantage of the multiple-step prediction over single-step prediction is shown by examples and simulations. The proposed algorithm is analyzed in terms of convergence and complexity, and stability issues are addressed. The formal proofs are included in the Appendix. Copyright
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