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The paper presents the design of reference governors for systems with state and control constraints in which unmeasured disturbances/uncertainties are estimated using a disturbance input observer (DIO) and compensated in the nominal controller. The disturbance can be state and time-dependent and is assumed to satisfy continuous differentiability assumptions. The reference governor modifies reference commands if these commands have a potential to induce state and control constraint violations. The reference governor design procedure is presented, and simulation results are reported to illustrate it. The integration of reference governor facilitates the implementation of DIO-based compensation as no a priori boundedness of the disturbance time rate of change needs to be assumed; furthermore, control constraints are enforced thereby facilitating the application of DIO-based schemes to systems in which the control authority is limited. 

The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much larger than the sample size. The standard EM algorithm, which attempts to find the maximum likelihood estimator, becomes infeasible for such model. We devise a group lasso penalized EM algorithm and study its statistical properties. Existing theoretical results of regularized EM algorithms often rely on dividing the sample into many independent batches and employing a fresh batch of sample in each iteration of the algorithm. Our algorithm and theoretical analysis do not require sample-splitting, and can be extended to multivariate response cases. The proposed methods also have encouraging performances in numerical studies.