KAIST-MIC-Lab · DDingR · Jul 30, 2026
diff --git a/_data/navigation.yml b/_data/navigation.yml
@@ -11,7 +11,13 @@
   dropdown:
     - name: Overview
       group: research
-      link: "/research"
+      dropdown:
+        - name: Control Problems
+          group: research
+          link: "/research/control_problems/00_future_mobility_control_landscape"
+        - name: Research Themes
+          group: research
+          link: "/research/research_themes/00_online_learning_based_optimal_control"
     # - name: Learning + Control Theory
     #   group: research
     #   link: "/research/control_learning"
@@ -55,4 +61,3 @@
 - name: Contact
   link: "/contact"
   group: contact
-
diff --git a/_includes/footer.html b/_includes/footer.html
@@ -13,6 +13,28 @@
     <script src="/static/js/jquery.min.js"></script>
     <script src="/static/js/popper.min.js"></script>
     <script src="/static/js/bootstrap.min.js"></script>
+    <script>
+      $(function () {
+        $('.dropdown-submenu > .dropdown-toggle').on('click', function (event) {
+          event.preventDefault();
+          event.stopPropagation();
+
+          var submenu = $(this).next('.dropdown-menu');
+          var isOpen = submenu.hasClass('show');
+
+          $(this).closest('.dropdown-menu').find('.dropdown-submenu > .dropdown-menu').removeClass('show');
+          $(this).closest('.dropdown-menu').find('.dropdown-submenu > .dropdown-toggle').attr('aria-expanded', 'false');
+
+          submenu.toggleClass('show', !isOpen);
+          $(this).attr('aria-expanded', String(!isOpen));
+        });
+
+        $('.navbar .dropdown').on('hide.bs.dropdown', function () {
+          $(this).find('.dropdown-submenu > .dropdown-menu').removeClass('show');
+          $(this).find('.dropdown-submenu > .dropdown-toggle').attr('aria-expanded', 'false');
+        });
+      });
+    </script>
     <script src="/static/js/parallax.min.js"></script>
   </body>
 </html>
diff --git a/_includes/header.html b/_includes/header.html
@@ -19,6 +19,22 @@
     <!-- <link href="/static/css/bootstrap-responsive.css" rel="stylesheet"> -->
     <link href="/static/css/syntax.css" rel="stylesheet">
     <link href="/static/css/custom.css" rel="stylesheet">
+
+    {% if page.math %}
+    <script>
+      window.MathJax = {
+        tex: {
+          inlineMath: [['$', '$'], ['\\(', '\\)']],
+          displayMath: [['$$', '$$'], ['\\[', '\\]']],
+          processEscapes: true
+        }
+      };
+    </script>
+    <script
+      defer
+      src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js">
+    </script>
+    {% endif %}
   </head>
 
   <body>
@@ -51,7 +67,20 @@
 
                 <div class="dropdown-menu" aria-labelledby="navbarDropdown{{forloop.index}}">
                   {% for sublink in link.dropdown %}
-                    <a class="dropdown-item" href="{{ sublink.link }}">{{ sublink.name }}</a>
+                    {% if sublink.dropdown %}
+                      <div class="dropdown-submenu">
+                        <button class="dropdown-item dropdown-toggle" type="button" aria-haspopup="true" aria-expanded="false">
+                          {{ sublink.name }}
+                        </button>
+                        <div class="dropdown-menu">
+                          {% for nestedlink in sublink.dropdown %}
+                            <a class="dropdown-item" href="{{ nestedlink.link }}">{{ nestedlink.name }}</a>
+                          {% endfor %}
+                        </div>
+                      </div>
+                    {% else %}
+                      <a class="dropdown-item" href="{{ sublink.link }}">{{ sublink.name }}</a>
+                    {% endif %}
                   {% endfor %}
                 </div>
 

diff --git a/_projects/2020-소형.md b/_projects/2020-소형.md
@@ -12,5 +12,5 @@ amount: '₩ 91,000,000'
 startdate: '2020.07.01'
 enddate: '2021.06.30'
 pmid: '2020-소형'
-image: '/static/img/research/projects/2020-소형.jpg'
+image: '/static/projects/img/2020-소형.jpg'
 ---
diff --git a/_projects/2021-수소버스.md b/_projects/2021-수소버스.md
@@ -12,5 +12,5 @@ amount: '₩ 50,000,000'
 startdate: '2021.01.01'
 enddate: '2021.12.31'
 pmid: '2021-수소버스'
-image: '/static/img/research/projects/2021-수소버스.jpg'
+image: '/static/projects/img/2021-수소버스.jpg'
 ---
diff --git a/_projects/2022-동기전동기를.md b/_projects/2022-동기전동기를.md
@@ -12,5 +12,5 @@ amount: '₩ 70,000,000'
 startdate: '2023.03.01'
 enddate: '2024.02.29'
 pmid: '2022-동기전동기를'
-image: '/static/img/research/projects/2022-동기전동기를.jpg'
+image: '/static/projects/img/2022-동기전동기를.jpg'
 ---
diff --git a/_projects/2022-미래형자동차.md b/_projects/2022-미래형자동차.md
@@ -12,7 +12,7 @@ amount:
 startdate: '2022.03.01'
 enddate: '2025.02.28'
 pmid: '2022-미래형자동차'
-image: '/static/img/research/projects/2022-미래형자동차.jpg'
+image: '/static/projects/img/2022-미래형자동차.jpg'
 link: 
   - name: '미래형자동차 핵심기술 R&D 전문인력양성'
     url: 'https://i4ft.yonsei.ac.kr/index.php'

diff --git a/_projects/2022-자율주행.md b/_projects/2022-자율주행.md
@@ -12,5 +12,5 @@ amount: '₩ 50,000,000'
 startdate: '2022.06.01'
 enddate: '2023.05.31'
 pmid: '2022-자율주행'
-image: '/static/img/research/projects/2022-자율주행.jpg'
+image: '/static/projects/img/2022-자율주행.jpg'
 ---
diff --git a/_projects/2022-전기자동차의.md b/_projects/2022-전기자동차의.md
@@ -12,5 +12,5 @@ amount: '₩ 40,000,000'
 startdate: '2022.05.01'
 enddate: '2023.04.30'
 pmid: '2022-전기자동차의'
-image: '/static/img/research/projects/2022-전기자동차의.jpg'
+image: '/static/projects/img/2022-전기자동차의.jpg'
 ---
diff --git a/_projects/2022-초실감.md b/_projects/2022-초실감.md
@@ -15,5 +15,5 @@ amount: '₩ 500,000,000'
 startdate: '2022.12.01'
 enddate: '2027.11.30'
 pmid: '2022-초실감'
-image: '/static/img/research/projects/2022-초실감.jpg'
+image: '/static/projects/img/2022-초실감.jpg'
 ---
diff --git a/_projects/2023-자율주행을.md b/_projects/2023-자율주행을.md
@@ -12,5 +12,5 @@ amount: '₩ 30,000,000'
 startdate: '2023.08.01'
 enddate: '2023.11.30'
 pmid: '2023-자율주행을'
-image: '/static/img/research/projects/2023-자율주행을.jpg'
+image: '/static/projects/img/2023-자율주행을.jpg'
 ---
diff --git a/_projects/2023-전기차.md b/_projects/2023-전기차.md
@@ -12,5 +12,5 @@ amount: '₩ 22,000,000'
 startdate: '2023.10.18'
 enddate: '2024.01.31'
 pmid: '2023-전기차'
-image: '/static/img/research/projects/2023-전기차.jpg'
+image: '/static/projects/img/2023-전기차.jpg'
 ---
diff --git a/_projects/2024-급변부하.md b/_projects/2024-급변부하.md
@@ -12,5 +12,5 @@ amount: '₩ 20,000,000'
 startdate: '2024.05.20'
 enddate: '2024.08.18'
 pmid: '2024-급변부하'
-image: '/static/img/research/projects/2024-급변부하.jpg'
+image: '/static/projects/img/2024-급변부하.jpg'
 ---
diff --git a/_projects/2025-RWS.md b/_projects/2025-RWS.md
@@ -12,5 +12,5 @@ amount: # not need to fill (will be not displayed)
 startdate: '2025.07.01'
 enddate: '2026.07.01'
 pmid: '2025-RWS'
-image: '/static/img/research/projects/2025-RWS.jpg'
+image: '/static/projects/img/2025-RWS.jpg'
 ---
diff --git a/_projects/2025-심층학습의.md b/_projects/2025-심층학습의.md
@@ -12,5 +12,5 @@ amount: '₩ 250,000,000'
 startdate: '2025.05.12'
 enddate: '2028.12.31'
 pmid: '2025-심층학습의'
-image: '/static/img/research/projects/2025-심층학습의.jpg'
+image: '/static/projects/img/2025-심층학습의.jpg'
 ---
diff --git a/_projects/2025-안정성.md b/_projects/2025-안정성.md
@@ -15,5 +15,5 @@ amount: '₩ 1,056,556,000'
 startdate: '2025.03.01'
 enddate: '2029.02.28'
 pmid: '2025-안정성'
-image: '/static/img/research/projects/2025-안정성.jpg'
+image: '/static/projects/img/2025-안정성.jpg'
 ---
diff --git a/research/index.md → research/_index.md b/research/index.md → research/_index.md
diff --git a/research/control_problems/00_future_mobility_control_landscape.md b/research/control_problems/00_future_mobility_control_landscape.md
@@ -0,0 +1,209 @@
+---
+title: Future Mobility Control Landscape
+layout: default
+group: research
+---
+
+<div class="container-fluid">
+<div class="row no-gutters">    
+<div class="col-12" markdown="1">
+
+# Future Mobility Control Landscape
+
+> **Core idea.** Connected, automated, and electrified vehicles expand the
+> information and decision scope of mobility control while adding coupled
+> control and actuation degrees of freedom (DOFs) at mobility-system, vehicle,
+> and component levels. Realizing this performance potential is naturally
+> formulated as an optimal-control problem, but computational and information
+> limitations often prevent its direct implementation. These shared barriers
+> motivate learning-based optimal control.
+
+<figure style="margin: 0; text-align: center;">
+  <img class="img-fluid" src="/research/control_problems/assets/future_mobility_control_landscape.png" alt="qFit" style="width: 95%; height: auto;">
+  <figcaption>
+    Future-mobility Control Problems at three levels lead through two representative barriers 
+    and online learning-based optimal control to the MIC Lab Research Themes.
+  </figcaption>
+</figure>
+
+*The two main axes organize where and what is controlled (Control Problems)
+and what is learned or adapted (Research Themes). Computational and
+information/formulation barriers motivate online learning-based optimal
+control as the bridge between them.*
+
+> **How to read this overview.** Sections 1–3 establish the CAEV context, the
+> common optimal-control principle, and the three control domains. Section 4
+> explains their shared implementation barriers and why they motivate the
+> laboratory's online learning-based control program. Section 5 maps the two
+> complementary document families.
+
+
+## 1. CAEVs and the need for multilevel optimal control
+
+Future mobility is often described by **CASE**: connected, automated, shared,
+and electrified mobility. This control landscape focuses on **connected,
+automated, and electrified vehicles (CAEVs)**. Shared mobility remains relevant
+when demand, fleets, or shared resources enter a mobility-system problem, but
+it does not define a separate physical control level here.
+
+The three CAEV characteristics change control in complementary ways:
+
+- **Connected:** broadens the available information to include route, traffic,
+  infrastructure, other agents, pedestrians, and cloud services.
+- **Automated:** transfers more planning, coordination, and actuation
+  decisions to feedback controllers.
+- **Electrified:** adds coupled energy and thermal states, multiple power
+  sources, distributed electric actuators, and fast electrical commands.
+
+These characteristics create control opportunities at three levels:
+
+- **Mobility-system level:** use route, traffic, infrastructure, mission,
+  or connected-agent information for trip-scale energy and thermal management
+  or multi-vehicle coordination.
+- **Vehicle level:** coordinate onboard drive, brake, steering, or suspension
+  actuators.
+- **Component level:** control device-level variables such as motor
+  voltage, current, flux, and torque.
+
+Connected, automated, and electrified functions contribute across all three
+levels rather than mapping one-to-one to them. Across the levels, CAEVs broaden
+the information available to the controller, enlarge the set of coupled
+decisions, and add control and actuation degrees of freedom (DOFs).
+
+For example, a connected electrified vehicle (xEV) can use previews of road
+grade, signal timing, traffic, weather, or charging opportunities to improve
+present energy and thermal decisions over the trip. Multiple connected
+vehicles can additionally coordinate speed, spacing, lane selection, or
+intersection passage. Optimal control provides a common formulation for using
+this information and the available control DOFs to balance performance and
+constraints.
+
+<!-- Textbook adaptation note: add a sourced CAEV performance example, such as
+quantified energy savings enabled by route/SPaT preview or connected
+coordination, when adapting this overview for the textbook. Keep the present
+web-oriented landscape conceptual. -->
+
+<!-- Textbook adaptation plan: keep the website-facing control-problem pages
+at the generalized problem-formulation level. When preparing the textbook
+version, create separate detailed modeling material with representative
+physical instantiations: an xEV energy/power-balance model for the
+mobility-system level, a 3-DOF or wheel-force vehicle model for the vehicle
+level, and a synchronous-machine dq model for the component level. Do not add
+these detailed derivations to the website pages merely for completeness. -->
+
+## 2. Optimal control as a common decision principle
+
+The details change across applications, but the basic optimal-control question
+is the same:
+
+| | Conceptual problem definition |
+|---|---|
+| **Find** | An admissible control input, control sequence, or feedback policy |
+| **To minimize** | A performance index encoding energy use, travel time, safety penalties, motion error, discomfort, or component loss |
+| **Subject to** | System dynamics, physical and safety constraints, actuator limits, environmental conditions, and the information available to the controller |
+
+The exact states, inputs, costs, models, and constraints depend on the control
+level and application; Section 3 specifies those differences.
+
+## 3. Three mobility control problem domains
+
+The three levels are classified first by the primary performance objective and
+the boundary of the coupled decisions and information—not merely by where an
+actuator is physically located. Physical location and time scale are secondary
+descriptors. The same electric motor can therefore support component-level
+torque control, vehicle-level actuator allocation, and mobility-system-level
+energy management.
+
+#### [Mobility-System-Level Optimal Control](/research/control_problems/01_mobility_system_level_optimal_control)
+
+This domain uses route, traffic, infrastructure, ambient, mission, or
+connected-agent information beyond the local vehicle state. It includes a
+single xEV using such context for predictive or infinite-horizon energy and
+thermal management, as well as multiple vehicles coordinating through shared
+information. A traffic network is therefore one information source within the
+broader mobility system; multiple vehicles are an important case, but not the
+definition of this level. Energy management belongs here when route or
+mobility context and long-horizon coupling define the problem; a local
+power-split problem using only onboard variables can instead be vehicle-level.
+
+#### [Vehicle-Level Optimal Control](/research/control_problems/02_vehicle_level_optimal_control)
+
+This domain coordinates control and actuation DOFs contained in the whole
+vehicle. Representative decisions include propulsion and braking allocation,
+torque vectoring, four-wheel independent drive or steering, and
+steering–suspension coordination. The objectives may combine motion,
+stability, safety, comfort, and efficiency subject to tire, actuator, power,
+and vehicle-dynamics constraints.
+
+A related deployment problem is **Automatic Controller Calibration**: gains,
+maps, cost weights, filters, thresholds, or learned parameters of
+vehicle-motion controllers are adjusted to reproduce the intended behavior
+across maneuvers and operating conditions. The vehicle-level page treats this
+as an outer-loop workflow surrounding the physical control problem.
+
+#### [Component-Level Optimal Control](/research/control_problems/03_component_level_optimal_control)
+
+This domain exploits fast device-level control DOFs. A representative problem
+is optimal torque production in a synchronous machine through voltage or
+inverter-switching decisions that shape current and flux while respecting
+electrical, magnetic, thermal, inverter, and sampling constraints.
+
+The same workflow appears at the component level when current-, torque-,
+speed-, position-, estimator-, or solver-related parameters must be adjusted
+across machine and operating conditions. In both the vehicle and component
+domains, calibration is a deployment and lifecycle workflow rather than a
+fourth physical control level.
+
+## 4. Why direct optimal control is difficult — and what learning contributes
+
+Implementing the principle in Section 2 requires both finding the optimal
+input or policy within the available computation time and having the model,
+state, context, objective, constraints, and transition information needed to
+define and evaluate the decision. Two difficulties recur across all three
+control levels:
+
+- **Computational difficulty:** high-dimensional state and action spaces,
+  long horizons, hybrid decisions, nonlinear constraints, coupled agents, and
+  short control deadlines can make exact policy computation or repeated online
+  optimization impractical.
+- **Information and formulation limitations:** the model, state, context,
+  objective, constraints, or transition law needed to define and evaluate the
+  decision may be incomplete, uncertain, indirectly measured, or changing.
+  Limited real-world data can further restrict identification and validation.
+
+The first difficulty means that an exact optimal decision may be too expensive
+even when the required information is available. The second means that the
+decision problem or its evaluation is incomplete, unreliable, or
+nonstationary. Many mobility problems contain both.
+
+These barriers motivate **learning-based optimal control**. When exact
+decision computation is too expensive, a learned value or policy—or a learned
+object combined with tractable online optimization—can approximate the
+optimal decision. When the required information is incomplete or changing,
+the relevant model, state, context, or representation can instead be
+estimated, learned, or updated.
+
+Within this broad class, the MIC Lab program emphasizes the **online
+realization of learning-based optimal control**, including online learning when
+deployed learned objects must adapt. Current measurements, context, forecasts,
+and constraints may support online estimation, decision improvement, or
+parameter learning; *online learning* is reserved for the last case. The
+common formulation and eight Research Themes are developed in [Online
+Learning-Based Optimal
+Control](/research/research_themes/00_online_learning_based_optimal_control).
+
+## 5. Document map — two complementary views
+
+The two views are complementary rather than one-to-one. A project may involve
+one or more physical Control Problem domains and draw on one or more Research
+Themes.
+
+| View | Organizing question | Overview and child pages |
+|---|---|---|
+| **Mobility Control Problem Domains** | Where and what is controlled? | **Overview (00):** [Future Mobility Control Landscape](/research/control_problems/00_future_mobility_control_landscape)<br>**Domain pages (01–03):**<br>[01 · Mobility-System-Level Optimal Control](/research/control_problems/01_mobility_system_level_optimal_control)<br>[02 · Vehicle-Level Optimal Control](/research/control_problems/02_vehicle_level_optimal_control)<br>[03 · Component-Level Optimal Control](/research/control_problems/03_component_level_optimal_control) |
+| **Learning-Based Control Research Themes** | Which bottleneck and learned object are addressed, and how are they used online? | **Overview (00):** [Online Learning-Based Optimal Control](/research/research_themes/00_online_learning_based_optimal_control)<br>**Theme pages (01–08):**<br>[01 · Real-World RL](/research/research_themes/01_real_world_rl)<br>[02 · Online Multistep Lookahead](/research/research_themes/02_online_multistep_lookahead)<br>[03 · Semantic Critic Learning](/research/research_themes/03_semantic_critic_learning)<br>[04 · Nonstationary Infinite-Horizon OCP](/research/research_themes/04_nonstationary_infinite_horizon_ocp)<br>[05 · Continual Model Learning](/research/research_themes/05_continual_model_learning)<br>[06 · Constrained PINN](/research/research_themes/06_constrained_pinn)<br>[07 · Neuro-Adaptive Control](/research/research_themes/07_neuro_adaptive_control)<br>[08 · Structured Critic Adaptation](/research/research_themes/08_structured_critic_adaptation) |
+
+
+</div>
+</div>
+</div>