Stochastic adaptive control using multiple models for improved performance in the presence of random disturbances

Abstract

The use of multiple models for adaptively controlling an unknown continuous-time linear system was proposed in Narendra and Balakrishnan (IEEE ¹ransactions on Automatic Control 1994; 39(9):1861}1866). and discussed in detail in Narendra and Xiang (IEEE ¹ransactions on Automatic Control 2000, 45(9):(1669}1686) ¹echnical Reports 9801 and 9803, Centre for System Science, Yale University, 1998). Recently, the same concepts were extended to discrete-time systems, both for the noise free case as well as when a stochastic disturbance is present, and the convergence of the algorithms was established. In this paper we consider structurally di!erent estimation models, and use the multiple models approach to select, on-line, the one that results in the best performance of the overall system for the given disturbance characteristics. The principal objective of the paper is to demonstrate that the convergence of these schemes can be treated in a uni"ed manner. Simulations are included towards the end of the paper to indicate the improvement in performance that can be achieved using such schemes.

Multiple‐Model Adaptive Estimation with A New Weighting Algorithm

“…Suppose there is a model, say M j ∈ M, which is closest to the true plant in the following sense with probability one where d is an unknown limited time instant. Then, the weighting algorithm (13), (14), (15), (16), (17), and (18) guarantees…”

“…According to [25], we have the following convergence result of the weighting algorithm (13), (14), (15), (16), (17), and (18). For more details on the proof of the theorem, see Lemma A.2 in the appendix.…”

“…Then, the state estimates of MMAE with the weighting algorithm (13), (14), (15), (16), (17), and (18) will converge to the optimal estimates given by the jth KF corresponding to M j , that is,x k →x j k 28…”

“…Since the late 1990s, MMAC is an important research direction in the adaptive control area, including switching MMAC [9][10][11][12][13][14] and weighted MMAC [15][16][17][18][19][20]. With MMAC, it is expected that the limitations of classical adaptive control (mainly self-tuning control and model reference adaptive control), such as poor transient performance and stabilizability of an online estimated model, could be overcome.…”

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise

“…Recently a methodology known as multiple model (a.k.a mixture of experts) adaptive estimation and control has become highly appealing in the identification of unknown and arbitrarily random noise and in modelling the general pdfs of the system dynamics (Murray-Smith and , Eds. ; Narendra and Driolet, 2001;Karniel et al, 2001). In this framework, a weighted sum of local models is used to model the nonlinear dynamics of the system.…”