Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

A switched system is a dynamic system that operates by switching between different subsystems or modes. Such systems exhibit both continuous and discrete characteristics—a dual nature that makes designing effective control policies a challenging task. The purpose of this paper is to review some of the latest computational techniques for generating optimal control laws for switched systems with nonlinear dynamics and continuous inequality constraints. We discuss computational strategiesfor optimizing both the times at which a switched system switches from one mode to another (the so-called switching times) and the sequence in which a switched system operates its various possible modes (the so-called switching sequence). These strategies involve novel combinations of the control parameterization method, the timescaling transformation, and bilevel programming and binary relaxation techniques. We conclude the paper by discussing a number of switched system optimal control models arising in practical applications

Targeted Metabolomics Reveals a Protective Role for Basal PPARα in Cholestasis Induced by α‑Naphthylisothiocyanate

α-Naphthylisothiocyanate (ANIT) is an experimental agent used to induce intrahepatic cholestasis. The <i>Ppara</i>-null mouse line is widely employed to explore the physiological and pathological roles of PPARα. However, little is known about how PPARα influences the hepatotoxicity of ANIT. In the present study, wild-type and <i>Ppara</i>-null mice were orally treated with ANIT to induce cholestasis. The serum metabolome of wild-type mice segregated from that of the <i>Ppara</i>-null mice, driven by changes of bile acid (BA) metabolites. Alkaline phosphatase and total BAs were elevated preferentially in <i>Ppara</i>-null mice, which correlated with changes in <i>Cyp7a1</i>, <i>Cyp8b1</i>, <i>Mrp3</i>, <i>Cyp3a11</i>, <i>Cyp2b10</i>, <i>Ugt1a2</i>, and <i>Ugt1a5</i> genes and showed cross-talk between basal PPARα and potentially adaptive pathways. <i>Il6</i>, <i>Tnfa</i>, and target genes in the STAT3 pathway (<i>Socs3</i>, <i>Fga</i>, <i>Fgb</i>, and <i>Fgg</i>) were up-regulated in <i>Ppara</i>-null mice but not in wild-type mice. The JNK pathway was activated in both mouse lines, while NF-κB and STAT3 were activated only in <i>Ppara</i>-null mice. These data suggest protection against cholestasis by basal PPARα involves regulation of BA metabolism and inhibition of NF-κB/STAT3 signaling. Considering studies on the protective effects of both basal and activated PPARα, caution should be exercised when one attempts to draw conclusions in which the PPARα is modified by genetic manipulation, fasting, or activation in pharmacological and toxicological studies