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Lebesgue-Stieltjes Optimal Control for Uncertain Dynamical Systems

In recent years, we have advanced the notion of Lebesgue-Stieltjes optimal control that addresses uncertainty in a sharply different manner than stochastic optimal control. Results from these new ideas have spawned a small set of computationally viable approaches to manage uncertainties in nonlinear dynamical systems. For instance, unscented optimal control is a new technique to improve the robustness of standard optimal control. As our early results are extremely encouraging, we propose to advance these emerging ideas along the two interdependent tracks of theory and computation. Our past experience has shown that theory and computation arc not divorced, and that progress in one track can support the other. To this end, we intend to further our efforts to advance the notion of hyper-pseudospectral (HS) points. HS points are a multi-dimensional extension of pseudospectral (PS) points. They are based on the idea that Kronecker products of PS points arc not minimal; hence, there must exist a collection of pseudospectral-like points in higher dimensions that provide a minimal set for cubature. Although the principles can be applied to any dynamical system, we will focus largely on problems with aerospace applications. Aerospace technology is a key component of national security and military operations. In an era of severe budgetary constraints, there is a greater need to design high-performance aerospace systems at lower cost. In addition, there is a need for designing aerospace systems that degrade gracefully. This means that systems need to function even under failure modes. The new concepts introduced in this proposal have the potential to offer these benefits through the use of system operability in the presence of sensor failures or through the exploitation of exogenous inputs heretofore considered unwanted effects
Mechanical & Aerospace Engineering
Defense Advanced Research Projects Agency