A Numerical Algorithm for Optimal Control of Systems with Parameter Uncertainty

The application of ‘optimal search’ to marine mapping

“…Formulated during WWII, this tool has only reached computational feasibility for nonlinear dynamics and irregular target spaces in the last few years, thanks to contributions such as [6], [10], [22], [25], and [29]. It now provides a foundation which can be leveraged to provide both guidance and insight.…”

“…In the last few years, distinct progress has been made in numerical algorithms for generating solutions to optimal control problems of this type. Beginning with the work of [6] and [10], and reaching greater generality with [22], [25], and [29], efficient algorithms are now available for use. Informally, the approaches to solving problems of this form have focused on discretization of the parameter space ⌦.…”

“…In the last decade, optimal search has experienced a computational maturation, progressing from an abstract framework solvable in mostly idealized cases to a practical framework which can provide global path planning for multiple, heterogeneous vehicles and sensors [22], [29], [30]. This development has opened wider applicability of optimal search's latent potential as a well-studied tool for refining mobile sensor performance.…”

Sensor-based motion planning for autonomous vehicle teams

“…Recent developments in numerical methods have made it possible to explicitly incorporate parameter uncertainty into the objective function of an an optimal control problem [1], [2], [3], [4]. Moreover, these generalized optimal control problems can incorporate sensor performance models to produce optimal vehicle trajectories for a given sensor configuration.…”

Optimal motion planning in rapid‐fire combat situations with attacker uncertainty

“…These parameters are considered to have uncertain values, with a prior probability density function attached to them denoted by φ : Ω → R. Recently, multiple algorithms for obtaining numerical solutions to high-dimensional optimal control problems with parameter uncertainty have been developed. These algorithms address parameter dependent costs (Foraker, 2011;Chung, Polak, Royset, & Sastry, 2011;Phelps, Gong, Royset, Walton, & Kaminer, 2014), parameter dependent dynamics (Ross, Proulx, Karpenko, & Gong, 2015;Walton, Phelps, Gong, & Kaminer, 2016), and a variety of state and control constraints (Walton et al, 2016). These developments enable the consideration of a multitude of new optimal control scenarios incorporating parameter uncertainty.…”