Mixture‐based adaptive probabilistic control

Abstract

Quasi-Bayes algorithm, combined with stabilized forgetting, provides a tool for efficient recursive estimation of dynamic probabilistic mixture models. They can be interpreted either as models of closedloop with switching modes and controllers or as a universal approximation of a wide class of non-linear control loops.Fully probabilistic control design extended to mixture models makes basis of a powerful class of adaptive controllers based on the receding-horizon certainty equivalence strategy.Paper summarizes the basic elements mentioned above, classifies possible types of control problems and provides solution of the key one referred to as 'simultaneous' design. Results are illustrated on mixtures with components formed by normal auto-regression models with external variable (ARX).

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

“…Compared with the results presented in (Kárný et al, 2003) this article has three distinct features. Firstly, based on using the well developed probabilistic based MDN methods (Herzallah, 2012), the involved pdfs in the FPD method are estimated such that their parameters are dependent on the input values in the way reflecting the uncertainty of the network dynamics.…”

“…Depending on the problem being handled, a number of modeling techniques are employed to represent the local models including standard neural networks (Park and Sandberg, 1991), statistical mixture models (Titterington et al, 1985;Smídl et al, 2005), and regression type models (Wang et al, 2013) among others. The multiple model approach has been recently exploited in the FPD method for deriving a randomised controller for systems that operate in different operation modes (Kárný et al, 2003). The method proposed in (Kárný et al, 2003), however, is constrained by its high computational complexity.…”

“…The multiple model approach has been recently exploited in the FPD method for deriving a randomised controller for systems that operate in different operation modes (Kárný et al, 2003). The method proposed in (Kárný et al, 2003), however, is constrained by its high computational complexity. In principle, the optimal control law can be obtained by solving a recurrence equation analogical to the dynamic programming solution.…”

“…The implementation and exploitation of the available analytical results of FPD become even more arduous for the majority of practical systems, which are non-linear and non-Gaussian in nature. Most important, the parameters of the probabilistic models involved in the FPD are assumed in (Kárný et al, 2003) to be input and state independent, limiting the resulting control strategies to deterministic certainty-equivalent systems.…”

Variational stabilized linear forgetting in state-space models

“…A general characterization of SF is given by [6]. SF is discussed in the context of control by [7], and SF is justified in the context of recursive estimation by [5], [8]. In general terms, recursive Bayesian estimation distinguishes two stages: a time step that predicts a new state belief given previous measurements, and a data step that updates the predicted state belief with information from a new measurement, see e.g.…”