JuliaCon 2026

In this talk we will present how DyadModelOptimizer is solving free final time problems using ModelingToolkit, BoundaryValueDiffEq and OptimizationMadNLP, showing the full julia stack that powers the Dyad analyses. Specifically we examine the solution in the context of minimum lap time optimization for a race car. The solution assumes a continuous lap optimizing throttle and braking under dynamical constraints.  We formulate the problem as a nonlinear optimal control problem with free terminal time, where the objective is to minimize total lap time subject to coupled vehicle dynamics, tire force limits, and path constraints along a prescribed track centerline. The vehicle model captures longitudinal and lateral dynamics, load transfer effects, and tire saturation through nonlinear algebraic relationships, resulting in a differential-algebraic system expressed symbolically. The talk walks through the entire process end to end: building the symbolic model, converting it into a boundary value formulation, choosing a discretization strategy, assembling the nonlinear program, and configuring the solver. We will also share practical lessons on mesh refinement, scaling for numerical stability, and what solve times and convergence actually look like in practice.

We aim to illustrate the initialization features of Dyad by trimming the Nonlinear F-16 model dynamics using NLSQ for desired altitude and cruise speed. We will then use the analysis features of Dyad by designing an LQR for longitudinal stabilization under trim and demonstrate a dashboard that enables real time tuning and response behavior visualization.

The plant model is written in Dyad, a new declarative acausal modeling language. The F-16 model encodes full six-degree-of-freedom rigid-body dynamics: translational and rotational equations of motion with coupled aerodynamic force and moment coefficients, ISA atmosphere density, and Euler angle kinematics. Dyad's RealInput/RealOutput connectors and analysis_point annotations expose the model's control and measurement interfaces for downstream analysis without modifying the physics..

Controller design uses DyadControlSystems' LQGAnalysis, which automatically linearizes the closed-loop Dyad model at the trim operating point and solves the dual Riccati equations. The 12-measurement, 5-control, 8-controlled-output problem yields a 12-state observer-based feedback controller. An interactive GLMakie GUI with a plugin architecture (Gang of Four, Nyquist, step response, pole-zero map) allows real-time tuning of LQR weights and Kalman filter covariances. A GLMakie animation engine renders the 3D trajectory alongside user-selected state and control variable time histories.

The key contribution is demonstrating that Dyad's declarative syntax unifies what are traditionally separate modeling, analysis, and design stages into a single reproducible project. The same .dyad files that define the physics also declare the trim analysis, the LQG synthesis problem, and the simulation scenarios. Julia's composability: ModelingToolkit for symbolic-numeric transformations, DyadControlSystems for control theory and GLMakie for visualization eliminates the toolchain fragmentation typical of aerospace control workflows.