Optimal control problems

CTModels defines and builds optimal control problems (OCPs) through four focused modules: CTModels.Components, CTModels.Models, CTModels.Building, and CTModels.Solutions. An OCP is assembled incrementally into a mutable PreModel, then frozen into an immutable Model by build.

The model is built through a three-stage pipeline:

PreModel  →  declare components  →  build  →  Model
(mutable)    state!/control!/...           (immutable)

The OCP layer is organised by responsibility across four modules:

Module	Directory	What it provides
CTModels.Components	src/Components/	Component types (StateModel, TimeDependence, …) and their accessors
CTModels.Models	src/Models/	Immutable Model type and all model accessor methods
CTModels.Building	src/Building/	PreModel, declaration verbs (state!, control!, …), name validation, build
CTModels.Solutions	src/Solutions/	build_solution, solution types, dual model, interpolation

Reading order

Page	Topic	Key symbols
Types and traits	The noun/trait architecture	TimeDependence, AbstractStateModel, Empty*
Components	Declaring the spaces	state!, control!, variable!, time!
Dynamics and objective	The equations of motion and cost	dynamics!, objective!
Constraints	Path, boundary and box constraints	constraint!
Building a model	Freezing the PreModel	build, Model
Displaying models	Base.show and mathematical rendering	Model, PreModel display

The pipeline on an example

Getting started builds the complete beam problem through this pipeline: declaration of the spaces, in-place dynamics, Lagrange cost, boundary and box constraints, then build. The pages listed above take each step in turn. build_model is an alias of build; see Building a model for what build checks and guarantees.

Mathematical setting

CTModels represents a continuous-time OCP in Bolza form. With state   , control    and an optimisation variable   (free final time, design parameters, …):

Two orthogonal axes shape the representation:

• Time dependence — whether , depend explicitly on (Autonomous vs NonAutonomous).

• Time structure — whether / are fixed or free (FixedTimeModel vs FreeTimeModel).

How these axes become traits rather than separate types is the subject of Types and traits.