Ryan Feeley

Some controls applications of sum of squares programming

We consider nonlinear systems with polynomial vector fields and present two algorithms based on sum of squares programming, that may answer system theoretic questions. The first algorithm provides a bound for the reachable set of a system driven by a unit-energy disturbance, while the second synthesizes a polynomial state feedback controller to enlarge the provable region of attraction. We also outline a variant of the second algorithm for handling systems with input saturation. Both algorithms are demonstrated using two-state nonlinear systems.

Control Applications of Sum of Squares Programming

We consider nonlinear systems with polynomial vector fields and pose two classes of system theoretic problems that may be solved by sum of squares programming. The first is disturbance analysis using three different norms to bound the reachable set. The second is the synthesis of a polynomial state feedback controller to enlarge the provable region of attraction. We also outline a variant of the state feedback synthesis for handling systems with input saturation. Both classes of problems are demonstrated using two-state nonlinear systems.

Sensitivity analysis of uncertainty in model prediction.

Data Collaboration is a framework designed to make inferences from experimental observations in the context of an underlying model. In the prior studies, the methodology was applied to prediction on chemical kinetics models, consistency of a reaction system, and discrimination among competing reaction models. The present work advances Data Collaboration by developing sensitivity analysis of uncertainty in model prediction with respect to uncertainty in experimental observations and model parameters. Evaluation of sensitivity coefficients is performed alongside the solution of the general optimization ansatz of Data Collaboration. The obtained sensitivity coefficients allow one to determine which experiment/parameter uncertainty contributes the most to the uncertainty in model prediction, rank such effects, consider new or even hypothetical experiments to perform, and combine the uncertainty analysis with the cost of uncertainty reduction, thereby providing guidance in selecting an experimental/theoretical strategy for community action.

Chapter 6 Optimization of Reaction Models with Solution Mapping

Publisher Summary Chemical reaction models are built for several reasons, such as exploratory modeling with the purpose of identifying possible reaction pathways, analyzing ones own experimental data, testing possible experimental trends, or making predictions for the purpose of design and policy assessment. Chemical reaction models are composed from individual reaction steps, either elementary or global. Each reaction step has a prescribed rate law, which is characterized by a set of parameters. The parameter values are collected from the literature, evaluated using theoretical machinery, estimated by empirical rules, or simply guessed. The predictive power of a reaction model is determined by two factors: the authenticity of the reaction steps and the correctness of the rate parameters. The chapter focuses on the identification and determination of the “correct” parameter values of a chemical kinetics model given a set of experimental measurements and on the development of predictive reaction models. The chapter introduces the chemical kinetics with the subject matter and terminology, exposing the specific difficulties and problems associated with optimization of chemical kinetic models and provides guidance to get practical results.

A system analysis approach for atmospheric observations and models: Mesospheric HOx dilemma

[1] A systematic consistency analysis and optimization procedure is applied to models of representative ozone, OH, and HO 2 observations in the mesosphere and upper stratosphere. The approach considers both measurement and rate parameter uncertainties. The results show some data point inconsistencies and the inability of the accepted photochemical mechanism to predict observations without unfavored large alterations of many rate constants from their consensus values. Optimization results do favor larger rate constants for OH + O and photolytic ozone and OH production.