A receding horizon generalization of pointwise min-norm controllers

Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a CLF based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuous-time receding horizon control law. The issue of implementation under discrete-time sampling is then discussed as a modification. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem. Finally, stronger connections to both optimal and pointwise min-norm control are proved

System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

Nucleation at the DNA supercoiling transition

Twisting DNA under a constant applied force reveals a thermally activated transition into a state with a supercoiled structure known as a plectoneme. Using transition state theory, we predict the rate of this plectoneme nucleation to be of order 10^4 Hz. We reconcile this with experiments that have measured hopping rates of order 10 Hz by noting that the viscosity of the bead used to manipulate the DNA limits the measured rate. We find that the intrinsic bending caused by disorder in the base-pair sequence is important for understanding the free energy barrier that governs the transition. Both analytic and numerical methods are used in the calculations. We provide extensive details on the numerical methods for simulating the elastic rod model with and without disorder.Comment: 18 pages, 15 figure

System level synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty – such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies

On receding horizon extensions and control Lyapunov functions

Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control (RHC) to develop a new class of control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a control Lyapunov function based receding horizon scheme, of which a special case provides an appropriate extension of a variation on Sontag's formula. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem

N 6 -Formyllysine as a Biomarker of Formaldehyde Exposure: Formation and Loss of N 6 -Formyllysine in Nasal Epithelium in Long-Term, Low-Dose Inhalation Studies in Rats

Exposure to both endogenous and exogenous formaldehyde has been established to be carcinogenic, likely by virtue of forming nucleic acid and proteins adducts such as N6-formyllysine. To better assess N6-formyllysine as a biomarker of formaldehyde exposure, we studied accumulation of N6-formyllysine adducts in tissues of rats exposed by inhalation to 2 ppm [13C2H2]-formaldehyde for 7, 14, 21, and 28 days (6 h/day) and investigated adduct loss over a 7-day postexposure period using liquid chromatography-coupled tandem mass spectrometry. Our results showed formation of exogenous adducts in nasal epithelium and to some extent in trachea but not in distant tissues of lung, bone marrow, or white blood cells, with a 2-fold increase over endogenous N6-formyllysine over a 3-week exposure period. Postexposure analyses indicated a biexponential decay of N6-formyllysine in proteins extracted from different cellular compartments, with half-lives of ∼25 and ∼182 h for the fast and slow phases, respectively, in cytoplasmic proteins. These results parallel the behavior of DNA adducts and DNA-protein cross-links, with protein adducts cleared faster than DNA-protein cross-links, and point to the potential utility of N6-formyllysine protein adducts as biomarkers of formaldehyde