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Abstract

This paper extends a regulatory controller synthesis technique that was previously introduced for first-order processes to higher-order processes. The target of the design is to find a feedback control law such that the multivariate stationary probability density function (PDF) for the closed-loop process reasonably approximates a preselected target PDF. With the idea already motivated and introduced in previous work, the focus of this paper is on dealing with the various complications that arise when the process dimension is greater than one. As in the previous case, the main idea of multivariate PDF-shaping is to reduce the integral equation that governs the relationship between process dynamics and stationary PDF to a set of algebraic equations. The proposed approach relies on parameterization of the feedback control law to simplify manipulation of the integral equation. Numerical simulations with an example process are used to demonstrate application of the technique.

Keywords

discrete-time control feedback control methods non-Gaussian processes nonlinear processes probability density function stationarity stochastic control

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Control design to shape the stationary probability density function

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