Optimal Control with Information Pattern Constraints

Despite the abundance of available literature that starts with the seminal paper of Wang and Davison almost forty years ago, when dealing with the problem of decentralized control for linear dynamical systems, one faces a surprising lack of general design methods, implementable via computationally tractable algorithms. This is mainly due to the fact that for decentralized control configurations, the classical control theoretical framework falls short in providing a systematic analysis of the stabilization problem, let alone cope with additional optimality criteria. Recently, a significant leap occurred through the theoretical machinery developed in Rotkowitz and Lall, IEEE-TAC, vol. 51, 2006, pp. 274-286 which unifies and consolidates many previous results, pinpoints certain tractable decentralized control structures, and outlines the most general known class of convex problems in decentralized control. The decentralized setting is modeled via the structured sparsity constraints paradigm, which proves to be a simple and effective way to formalize many decentralized configurations where the controller feature a given sparsity pattern. Rotkowitz and Lall propose a computationally tractable algorithm for the design of H2 optimal, decentralized controllers for linear and time invariant systems, provided that the plant is strongly stabilizable. The method is built on the assumption that the sparsity constraints imposed on the controller satisfy a certain condition (named quadratic invariance) with respect to the plant and that some decentralized, strongly stablizable, stabilizing controller is available beforehand. For this class of decentralized feedback configurations modeled via sparsity constraints, so called quadratically invariant, we provided complete solutions to several open problems. Firstly, the strong stabilizability assumption was removed via the so called coordinate free parametrization of all, sparsity constrained controllers. Next we have addressed the unsolved problem of stabilizability/stabilization via sparse controllers, using a particular form of the celebrated Youla parametrization. Finally, a new result related to the optimal disturbance attenuation problem in the presence of stable plant perturbations is presented. This result is also valid for quadratically invariant, decentralized feedback configurations. Each result provides a computational, numerically tractable algorithm which is meaningful in the synthesis of sparsity constrained optimal controllers

A convex parameterization of all stabilizing controllers for non-strongly stabilizable plants, under quadratically invariant sparsity constraints

This paper addresses the design of controllers, subject to sparsity constraints, for linear and timeinvariant plants. Prior results have shown that a class of stabilizing controllers, satisfying a given sparsity constraint, admits a convex representation of the Youla–type, provided that the sparsity constraints imposed on the controller are quadratically invariant with respect to the plant and that the plant is strongly stabilizable. Another important aspect of the aforementioned results is that the sparsity constraints on the controller can be recast as convex constraints on the Youla parameter, which makes this approach suitable for optimization using norm-based costs. In this paper, we extend these previous results to non-strongly stabilizable plants. Our extension also leads to a Youla-type representation for the class of controllers, under quadratically invariant sparsity constraints. In our extension, the controller class also admits a representation of the Youla–type, where the Youla parameter is subject to only convex constraints

Sample Complexity of the Robust LQG Regulator with Coprime Factors Uncertainty

This paper addresses the end-to-end sample complexity bound for learning the H2 optimal controller (the Linear Quadratic Gaussian (LQG) problem) with unknown dynamics, for potentially unstable Linear Time Invariant (LTI) systems. The robust LQG synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant. The closed-loop identification of the nominal model of the true plant is performed by constructing a Hankel-like matrix from a single time-series of noisy finite length input-output data, using the ordinary least squares algorithm from Sarkar et al. (2020). Next, an H-infinity bound on the estimated model error is provided and the robust controller is designed via convex optimization, much in the spirit of Boczar et al. (2018) and Zheng et al. (2020a), while allowing for bounded additive uncertainty on the coprime factors of the model. Our conclusions are consistent with previous results on learning the LQG and LQR controllers.Comment: Minor Edits on closed loop identification, 30 pages, 2 figures, 3 algorithm

Outcomes of Diabetic Retinopathy Post-Bariatric Surgery in Patients with Type 2 Diabetes Mellitus

Bariatric surgery is an emerging therapeutic approach for obese type 2 diabetes mellitus (T2DM) patients, with proven benefits for achieving target glucose control and even remission of diabetes. However, the effect of bariatric surgery upon diabetic retinopathy is still a subject of debate as some studies show a positive effect while others raise concerns about potential early worsening effects. We performed a systematic review, on PubMed, Science Direct, and Web of Science databases regarding the onset and progression of diabetic retinopathy in obese T2DM patients who underwent weight-loss surgical procedures. A total of 6375 T2DM patients were analyzed. Most cases remained stable after bariatric surgery (89.6%). New onset of diabetic retinopathy (DR) was documented in 290 out of 5972 patients (4.8%). In cases with DR at baseline, progression was documented in 50 out of 403 (12.4%) and regression in 90 (22.3%). Preoperative careful preparation of hemoglobin A1c (HbA1c), blood pressure, and lipidemia should be provided to minimize the expectation of DR worsening. Ophthalmologic follow-up should be continued regularly in the postoperative period even in the case of diabetic remission. Further randomized trials are needed to better understand the organ-specific risk factors for progression and provide personalized counseling for T2DM patients planned for bariatric surgery