SGER: Nonlinear Robust Control: A Stochastic Programming Approach

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The objective of this research is to develop stochastic approaches to robust analysis and control design, particularly for nonlinear control of uncertain systems. The stochastic robust control is an effective combination of control design methodologies with stochastic modeling of parametric uncertainties and robustness characterization. The proposed research aims to 1) formulate the control of a class of nonlinear uncertain systems into a computational tractable stochastic programming problem, which allows systematic robust control design methodologies; 2) provide design flexibility and different tradeoff for control designers in terms of performance, robustness and computational/controller complexity. First, the project will study algebraic recasting of a nonlinear model into low-order polynomial vector fields at the expense of increase in system dimensionality, where balance between system nonlinear complexity and system dimensionality will be investigated. Second, will be to investigate different formulations of stochastic robustness cost function in terms of design specifications. Third, the robust control design of nonlinear uncertain systems will be formulated into a stochastic programming problem, where the sum of squares technique will be combined with statistical tools and stochastic optimization algorithms. This project will advance the state of the art for robust control theory, in particular for nonlinear uncertain systems. The proposed stochastic characterization of uncertainties and robust control has the advantage of computational tractability, compared to several deterministic worst-case robustness problems. In addition, by designing controllers with provable probabilistic robustness, the proposed research offers systematic design of low-complexity controllers with significant improvement in nominal performance and reduction in control effort. It also allows the control designers to explicitly tradeoff between performance, robustness and reliability. The sum of squares technique has mainly been used for nonlinear stability analysis for polynomial vector fields; the proposed research extends this tool to the design of stochastic robust nonlinear control, where a stochastic programming problem is formulated to allow systematic parameterization and search of nonlinear controllers. This research is expected to impact both theory and applications. By directly evaluating and optimizing the probability of violating design specifications, the proposed stochastic robust control design addresses practical concerns and helps bridge the gap between theory and practice. The education plan includes developing a cross-disciplinary controls course that will help popularize control theory among those with primary interest in control implementation. The collaboration with Penn State Women in Engineering Program will help recruit underrepresented groups and facilitate their education and research in engineering.