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{"documenter":{"julia_version":"1.12.1","generation_timestamp":"2025-10-29T04:55:55","documenter_version":"1.15.0"}}

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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>CTBase.jl · OptimalControl.jl</title><meta name="title" content="CTBase.jl · OptimalControl.jl"/><meta property="og:title" content="CTBase.jl · OptimalControl.jl"/><meta property="twitter:title" content="CTBase.jl · OptimalControl.jl"/><meta name="description" content="Documentation for OptimalControl.jl."/><meta property="og:description" content="Documentation for OptimalControl.jl."/><meta property="twitter:description" content="Documentation for OptimalControl.jl."/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="search_index.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script><link href="https://control-toolbox.org/assets/css/documentation.css" rel="stylesheet" type="text/css"/><script src="https://control-toolbox.org/assets/js/documentation.js"></script><link href="assets/custom.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="index.html">OptimalControl.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="index.html">Getting Started</a></li><li><span class="tocitem">Basic Examples</span><ul><li><a class="tocitem" href="example-double-integrator-energy.html">Energy minimisation</a></li><li><a class="tocitem" href="example-double-integrator-time.html">Time mininimisation</a></li></ul></li><li><span class="tocitem">Manual</span><ul><li><a class="tocitem" href="manual-abstract.html">Define a problem</a></li><li><a class="tocitem" href="manual-ai-llm.html">Use AI</a></li><li><a class="tocitem" href="manual-model.html">Problem characteristics</a></li><li><a class="tocitem" href="manual-initial-guess.html">Set an initial guess</a></li><li><a class="tocitem" href="manual-solve.html">Solve a problem</a></li><li><a class="tocitem" href="manual-solve-gpu.html">Solve on GPU</a></li><li><a class="tocitem" href="manual-solution.html">Solution characteristics</a></li><li><a class="tocitem" href="manual-plot.html">Plot a solution</a></li><li><input class="collapse-toggle" id="menuitem-3-9" type="checkbox"/><label class="tocitem" for="menuitem-3-9"><span class="docs-label">Compute flows</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="manual-flow-api.html">Flow API</a></li><li><a class="tocitem" href="manual-flow-ocp.html">From optimal control problems</a></li><li><a class="tocitem" href="manual-flow-others.html">From Hamiltonians and others</a></li></ul></li></ul></li><li><span class="tocitem">API</span><ul><li><a class="tocitem" href="api-optimalcontrol-user.html">OptimalControl.jl - User</a></li><li><input class="collapse-toggle" id="menuitem-4-2" type="checkbox" checked/><label class="tocitem" for="menuitem-4-2"><span class="docs-label">Subpackages - Developers</span><i class="docs-chevron"></i></label><ul class="collapsed"><li class="is-active"><a class="tocitem" href="api-ctbase.html">CTBase.jl</a></li><li><a class="tocitem" href="api-ctdirect.html">CTDirect.jl</a></li><li><a class="tocitem" href="api-ctflows.html">CTFlows.jl</a></li><li><a class="tocitem" href="api-ctmodels.html">CTModels.jl</a></li><li><a class="tocitem" href="api-ctparser.html">CTParser.jl</a></li><li><a class="tocitem" href="api-optimalcontrol-dev.html">OptimalControl.jl</a></li></ul></li></ul></li><li><a class="tocitem" href="rdnopa-2025.html">RDNOPA 2025</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">API</a></li><li><a class="is-disabled">Subpackages - Developers</a></li><li class="is-active"><a href="api-ctbase.html">CTBase.jl</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="api-ctbase.html">CTBase.jl</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/control-toolbox/OptimalControl.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/control-toolbox/OptimalControl.jl/blob/main/docs/src/api-ctbase.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="CTBase.jl"><a class="docs-heading-anchor" href="#CTBase.jl">CTBase.jl</a><a id="CTBase.jl-1"></a><a class="docs-heading-anchor-permalink" href="#CTBase.jl" title="Permalink"></a></h1><p>The <a href="https://github.com/control-toolbox/CTBase.jl/">CTBase.jl</a> package is part of the <a href="https://github.com/control-toolbox">control-toolbox ecosystem</a>.</p><div class="mermaid">flowchart TD
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P(&lt;a href=&#39;api-ctparser.html&#39;&gt;CTParser&lt;/a&gt;)
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style B fill:#FBF275</div><p>OptimalControl heavily relies on CTBase. We refer to <a href="https://control-toolbox.org/CTBase.jl/stable/index.html">CTBase API</a> for more details.</p><script type="module">import mermaid from 'https://cdn.jsdelivr.net/npm/mermaid@11/dist/mermaid.esm.min.mjs';
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</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="api-optimalcontrol-user.html">« OptimalControl.jl - User</a><a class="docs-footer-nextpage" href="api-ctdirect.html">CTDirect.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.15.0 on <span class="colophon-date" title="Wednesday 29 October 2025 04:55">Wednesday 29 October 2025</span>. Using Julia version 1.12.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>CTDirect.jl · OptimalControl.jl</title><meta name="title" content="CTDirect.jl · OptimalControl.jl"/><meta property="og:title" content="CTDirect.jl · OptimalControl.jl"/><meta property="twitter:title" content="CTDirect.jl · OptimalControl.jl"/><meta name="description" content="Documentation for OptimalControl.jl."/><meta property="og:description" content="Documentation for OptimalControl.jl."/><meta property="twitter:description" content="Documentation for OptimalControl.jl."/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="search_index.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script><link href="https://control-toolbox.org/assets/css/documentation.css" rel="stylesheet" type="text/css"/><script src="https://control-toolbox.org/assets/js/documentation.js"></script><link href="assets/custom.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="index.html">OptimalControl.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="index.html">Getting Started</a></li><li><span class="tocitem">Basic Examples</span><ul><li><a class="tocitem" href="example-double-integrator-energy.html">Energy minimisation</a></li><li><a class="tocitem" href="example-double-integrator-time.html">Time mininimisation</a></li></ul></li><li><span class="tocitem">Manual</span><ul><li><a class="tocitem" href="manual-abstract.html">Define a problem</a></li><li><a class="tocitem" href="manual-ai-llm.html">Use AI</a></li><li><a class="tocitem" href="manual-model.html">Problem characteristics</a></li><li><a class="tocitem" href="manual-initial-guess.html">Set an initial guess</a></li><li><a class="tocitem" href="manual-solve.html">Solve a problem</a></li><li><a class="tocitem" href="manual-solve-gpu.html">Solve on GPU</a></li><li><a class="tocitem" href="manual-solution.html">Solution characteristics</a></li><li><a class="tocitem" href="manual-plot.html">Plot a solution</a></li><li><input class="collapse-toggle" id="menuitem-3-9" type="checkbox"/><label class="tocitem" for="menuitem-3-9"><span class="docs-label">Compute flows</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="manual-flow-api.html">Flow API</a></li><li><a class="tocitem" href="manual-flow-ocp.html">From optimal control problems</a></li><li><a class="tocitem" href="manual-flow-others.html">From Hamiltonians and others</a></li></ul></li></ul></li><li><span class="tocitem">API</span><ul><li><a class="tocitem" href="api-optimalcontrol-user.html">OptimalControl.jl - User</a></li><li><input class="collapse-toggle" id="menuitem-4-2" type="checkbox" checked/><label class="tocitem" for="menuitem-4-2"><span class="docs-label">Subpackages - Developers</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="api-ctbase.html">CTBase.jl</a></li><li class="is-active"><a class="tocitem" href="api-ctdirect.html">CTDirect.jl</a></li><li><a class="tocitem" href="api-ctflows.html">CTFlows.jl</a></li><li><a class="tocitem" href="api-ctmodels.html">CTModels.jl</a></li><li><a class="tocitem" href="api-ctparser.html">CTParser.jl</a></li><li><a class="tocitem" href="api-optimalcontrol-dev.html">OptimalControl.jl</a></li></ul></li></ul></li><li><a class="tocitem" href="rdnopa-2025.html">RDNOPA 2025</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">API</a></li><li><a class="is-disabled">Subpackages - Developers</a></li><li class="is-active"><a href="api-ctdirect.html">CTDirect.jl</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="api-ctdirect.html">CTDirect.jl</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/control-toolbox/OptimalControl.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/control-toolbox/OptimalControl.jl/blob/main/docs/src/api-ctdirect.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="CTDirect.jl"><a class="docs-heading-anchor" href="#CTDirect.jl">CTDirect.jl</a><a id="CTDirect.jl-1"></a><a class="docs-heading-anchor-permalink" href="#CTDirect.jl" title="Permalink"></a></h1><p>The <a href="https://github.com/control-toolbox/CTDirect.jl">CTDirect.jl</a> package is part of the <a href="https://github.com/control-toolbox">control-toolbox ecosystem</a>.</p><div class="mermaid">flowchart TD
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B(&lt;a href=&#39;api-ctbase.html&#39;&gt;CTBase&lt;/a&gt;)
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P(&lt;a href=&#39;api-ctparser.html&#39;&gt;CTParser&lt;/a&gt;)
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D(&lt;a href=&#39;api-ctdirect.html&#39;&gt;CTDirect&lt;/a&gt;)
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F(&lt;a href=&#39;api-ctflows.html&#39;&gt;CTFlows&lt;/a&gt;)
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O --&gt; D
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style D fill:#FBF275</div><p>OptimalControl heavily relies on CTDirect. We refer to <a href="https://control-toolbox.org/CTDirect.jl/stable/index.html">CTDirect API</a> for more details.</p><script type="module">import mermaid from 'https://cdn.jsdelivr.net/npm/mermaid@11/dist/mermaid.esm.min.mjs';
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mermaid.initialize({
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</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="api-ctbase.html">« CTBase.jl</a><a class="docs-footer-nextpage" href="api-ctflows.html">CTFlows.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.15.0 on <span class="colophon-date" title="Wednesday 29 October 2025 04:55">Wednesday 29 October 2025</span>. Using Julia version 1.12.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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