Ronald J. Proulx

Riemann-Stieltjes optimal control problems for uncertain dynamic systems

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...

A Lebesgue-Stieltjes framework for optimal control and allocation

A Lebesgue-Stieltjes optimal control framework is used as the basis for constructing deterministic controls for uncertain systems. The framework is motivated by large uncertainties that occur in the next generation of aerospace systems. Instead of designing new feedback controls that may be expensive to implement, this paper addresses the problem at the outer-loop level by reshaping the input subject to the constraints of the inner loop. Computations based on the combination of a hyper-pseudospectral method verified by Monte Carlo simulations demonstrate the efficacy of the ideas. Ground test results at Honeywell validate the operational readiness of the proposed concepts.

Path constraints in tychastic and unscented optimal control: Theory, application and experimental results

In recent papers, we have shown that a Lebesgue-Stieltjes optimal control theory forms the foundations for unscented optimal control. In this paper, we further our results by incorporating uncertain mixed state-control constraints in the problem formulation. We show that the integrated Hamiltonian minimization condition resembles a semi-infinite type mathematical programming problem. The resulting computational difficulties are mitigated through the use of the unscented transform; however, the price of this approximation is a solution to a chance-constrained optimal control problem whose risk level is determined a posteriori. Experimental results conducted at Honeywell are presented to demonstrate the success of the theory. An order of magnitude reduction in the failure rate in obtained through the use of an unscented optimal control that steers a spacecraft testbed driven by control-moment gyros.

Monte Rey Methods for Unscented Optimization

Unscented optimization offers a simple approach for solving stochastic programming problems. Optimization problems with uncertainty appear in nearly all aspects of guidance and control: air-traffic control, missile guidance, mission planning, pilot modeling etc. The uncertain parameters in many of these problems have a boundary defined by the laws of physics. Some of the strategies used in the selection of sigma points for unscented optimization may not lie in the support of the distribution. The alternative of using cubature points with nonnegative weights is limited by the curse of dimensionality. Monte Carlo sampling is very simple, but it generates a large scale optimization problem. The new idea of Monte Rey sampling provides a balance between simplicity, accuracy and scalability. These ideas are used in this paper to develop an unscented approach for risk-cost management. Results for a sample chance-constrained problem demonstrate a reduction in risk by over a factor of three when compared to deterministic optimization.