Ensemble Control for Stochastic Systems with Asymmetric Laplace Noises

This paper presents an adaptive ensemble control for stochastic systems subject to asymmetric noises and outliers. Asymmetric noises skew system observations, and outliers with large amplitude deteriorate the observations even further. Such disturbances induce poor system estimation and degraded stochastic system control. In this work, we model the asymmetric noises and outliers by mixed asymmetric Laplace distributions (ALDs), and propose an optimal control for stochastic systems with mixed ALD noises. Particularly, we segregate the system disturbed by mixed ALD noises into subsystems, each of which is subject to a specific ALD noise. For each subsystem, we design an iterative quantile filter (IQF) to estimate the system parameters using system observations. With the estimated parameters by IQF, we derive the certainty equivalence (CE) control law for each subsystem. Then we use the Bayesian approach to ensemble the subsystem CE controllers, with each of the controllers weighted by their posterior probability. We finalize our control law as the weighted sum of the control signals by the sub-system CE controllers. To demonstrate our approach, we conduct numerical simulations and Monte Carlo analyses. The results show improved tracking performance by our approach for skew noises and its robustness to outliers, compared with single ALD based and RLS-based control policy.