dymos: A Python package for optimal control of multidisciplinary systems

Abstract

Dymos is a library for optimizing control schedules for dynamic systems -sometimes referred to as optimal control or trajectory optimization. There are a number of other optimal control libraries that tackle similar kinds of problems, such as OTIS4 (Paris et al., 2006), GPOPS-II (Patterson & Rao, 2014),and CASADI (Andersson et al., 2019. These tools all rely on gradient-based optimization to solve optimal control problems, though their methods of computing the gradients vary. Dymos is built on top of the OpenMDAO framework (Gray et al., 2019) and supports its modular derivative system which allows users to mix-and-match from finite-differencing, complex-step, hand-differentiated, and algorithmic differentiation. This flexibility allows Dymos to efficiently solve optimal control problems constructed with both ordinary differential equations (ODE) and differential-algebraic equations (DAE).Dymos can also help solve more general optimization problems where dynamics are only one part in a larger system-level model with additional -potentially computationally expensivecalculations that come before and after the dynamic calculations. These broader problems are commonly referred to as co-design, controls-co-design, and multidisciplinary design optimization. Dymos provides specific APIs and features that make it possible to integrate traditional optimal-control models into a co-design context, while still supporting analytic derivatives that are necessary for computational efficiency in these complex use cases. An example of a co-design problem that was solved with Dymos is the coupled trajectory-thermal design of an electric vertical takeoff and landing aircraft where the thermal management and propulsion systems were designed simultaneously with the flight trajectories to ensure no components overheated (Hendricks et al., 2020). Difference between optimal-control and co-designOptimal-control and co-design problems deal with dynamic systems. The evolution of the states over time is governed by an ordinary differential equation (ODE) or differential-algebraic equation (DAE):ẋ = f ode (x, t,ū,d) Here,x is a vector of time-varying state variables whose behavior is affected by time (t), a vector of dynamic controls (ū), and a vector of static design parameters (d).To optimize a dynamic system we also need to account for the objective function (J):

Control Co-design of a Hydrokinetic Turbine with Open-loop Optimal Control

“…In this study, an open-loop optimal torque control [16] is employed, assuming that the generator torque can be controlled directly for optimal power production and the inflow velocity profile is known with sensors. The continuous optimal control load trajectory is discretized in time using third-order Legendre-Gauss-Lobatto collocation method and then solved numerically as a nonlinear programming problem in Dymos [11]. Generator torque at each time instant is treated as an optimization variable.…”

“…Open-loop optimal torque control is applied for maximum HKT power production. The control variable and other time-varying trajectories are simulated and optimized using open-source software Dymos [11]. CCD under different control constraints is investigated together with sensitivity analysis to different flow profiles and initial geometries.…”

Framework of a Power Management System for a Hybrid Electric VTOL Aircraft using Optimal Control

“…Many optimization packages rely on the parameterization of hardware models, for example, an approximation of an engine's mass as a function of its thrust level. Rather, Dymos allows users to impose higher-fidelity design considerations and apply the resulting subsystem designs to the trajectory profile [5]. Dymos is built upon the OpenMDAO framework, which enables highly effective/efficient computation of accurate derivatives.…”

“…In general, optimal-control and co-design problems will have both a very large number of design variables and a very large number of constraints. Both issues make gradient-based methods the strongly preferred choice [5].…”

“…The objective may be any output within the phase, as with constraints. Phases can also be incorporated into larger models wherein the objective is defined in some subsystem outside of the phase [5].…”