Riemann-Stieltjes optimal control problems for uncertain dynamic systems
Ross, I. Michael
Proulx, Ronald J.
MetadataShow full item record
Motivated by uncertain parameters in nonlinear dynamic systems, we define a nonclassical optimal control problem where the cost functional is given by a Riemann–Stieltjes “functional of a functional.” Using the properties of Riemann–Stieltjes sums, a minimum principle is generated from the limit of a semidiscretization. The optimal control minimizes a Riemann–Stieltjes integral of the Pontryagin Hamiltonian. The challenges associated with addressing the noncommutative operations of integration and minimization are addressed via cubature techniques leading to the concept of hyper-pseudospectral points. These ideas are then applied to address the practical uncertainties in control moment gyroscopes that drive an agile spacecraft. Ground test results conducted at Honeywell demonstrate the new principles. The Riemann–Stieltjes optimal control problem is a generalization of the unscented optimal control problem. It can be connected to many independently developed ideas across several disciplines: search theory, viability theory, quantum control and many other applications involving tychastic differential equations.
The article of record as published may be found at http://dx.doi.org/10.2514/1.G000505
Showing items related by title, author, creator and subject.
Phelps, Chris; Royset, Johannes O.; Gong, Qi (Society for Industrial and Applied Mathematics, 2016);In this paper, we introduce the uncertain optimal control problem of determining a control that minimizes the expectation of an objective functional for a system with parameter uncertainty in both dynamics and objective. ...
Optimal Control of the Unsteady Euler Equations in 1D with Application to Ignition Overpressure Attenuation in Launch Vehicles Moshman, Nathan D.; Hobson, Garth V.; Sritharan, Sivaguru S. (2011-06);This paper presents a new formulation and computational solution of an optimal control problem concerning unsteady shock wave attenuation. The adjoint system of equations for the unsteady Euler system in 1D is derived ...
Royset, Johannes O.; Phelps, Chris; Gong, Qi (IEEE, 2013-12);This paper focuses on an optimal control problem in which the objective is to minimize the expectation of a cost functional with stochastic parameters. The inclusion of the stochastic parameters in the objective raises ...