Optimization · Control · Modeling · Machine Learning

Engineering intelligent systems.

I develop mathematical and computational methods for dynamic engineering systems, connecting optimization, control, modeling, scientific computing, and data-driven intelligence.

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About

Research across connected disciplines.

My work focuses on understanding, computing, and improving decisions in evolving systems. I move between mathematical theory, dynamic modeling, algorithm development, control, numerical computation, and machine learning depending on the problem.

Dynamic systems Optimization Optimal control MPC Continuous time Multiparametric methods Scientific computing

Interactive driving game

Neon Gate Challenge.

Drive through all three glowing gates. Then finish in the center without moving sideways. The gold car shows the smoothest successful drive calculated by the model.

Pass all 3 gates and finish in the center Touch left or right to turn. Turn the other way to stop sideways movement.

Time left8.00 s

Distance0 / 200 m

Gates0 / 3

FinishNot reached

Turning effort 0.00 Lower is better

READY Pass all three gates.

Touch left or right to turn. Lift your finger to stop turning.

Next gate Gate 1 in 2.00 s

YOUR DRIVE

BEST PATH

0.5 s UPDATES

Touch the left or right side of the road to turn.

8-second driving game

Pass all three glowing gates.

The car moves forward by itself. Touch left or right to turn. Finish in the center without moving sideways.

Your run

Run complete.

Gates passed—

Distance from center—

Sideways movement—

Turning effort—

Your drive and the best drive will replay next.

Touch or drag on the road. You may also use the arrow buttons or keyboard. The clock starts only after you press START.

Forward speed90 km/h

Game time8 seconds

Goal3 gates + center finish

Turn strengthGentle to strong

What the game showed

The best drive is calculated, not drawn.

Best turning effort—

First turn change—

0.5-second turning effort—

Starting position—

Why timing matters

The same turn, made too early or too late, can miss the next gate.

—

Why continuous control matters

Gold can change its turn at any moment. Purple can change only every 0.5 seconds.

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Why multiparametric optimization helps

A different starting position needs a different best drive. These answers can be calculated before the car starts.

—

Your drive Best drive Updated every 0.5 seconds

Driving path

This chart and the gold car use the same calculated trajectory. A gate is the empty space between its two posts. The green PASS point shows where the center of the gold car crosses that gate.

Turn strength over time

Best drive compared with 0.5-second updates

Why multiparametric optimization helps

Different starts need different best drives.

Solving the problem again for every new starting position can be slow. Multiparametric optimization calculates the answers in advance.

Calculate first. Use the answer right away.

It groups starting positions that use the same type of best drive. It then stores the right control rule for each group.

Measure the starting position → Find its group
(critical region) → Use the stored control rule

This demo recalculates the answer when you move the slider so you can see the change. A full multiparametric controller would calculate all groups and rules before the car starts.

Starting position +2.30 m

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Same gold drive — course map

Each gate is the empty space between two glowing posts.

How the best drive is calculated

The computer chooses the sideways acceleration u(t) over the 8-second drive.

Objective

Minimize J = ∫₀⁸ u(t)² dt

Use as little strong sideways movement as possible.

Car model

ẏ(t) = v(t), v̇(t) = u(t)

y is sideways position, v is sideways speed, and u is sideways acceleration.

Starting condition

y(0) = y₀, v(0) = 0

The car starts at the selected position with no sideways movement.

Finish condition

y(8) = 0, v(8) = 0

Finish in the center and stop moving sideways.

Gate conditions

Gate 1 at 2.0 s: −2.0 ≤ y(2.0) ≤ −0.8 m

Gate 2 at 4.1 s: 1.1 ≤ y(4.1) ≤ 2.3 m

Gate 3 at 6.2 s: −1.8 ≤ y(6.2) ≤ −0.6 m

At each gate time, the center of the car must lie inside the listed range. Passing between the two gate posts satisfies the constraint.

Gold car: among all drives that satisfy the model and every condition above, the gold drive has the smallest value of J. The gold car, gold road line, and gold charts all use the same calculated values of y(t).

Automatic mathematical check Gold path verified

PASS ✓

The equations limit the center of the car. The glowing gate is wider so the full car has room to pass.

Check	Gold value	Required range	Result
Gate 1	—	−2.00 to −0.80 m	—
Gate 2	—	1.10 to 2.30 m	—
Gate 3	—	−1.80 to −0.60 m	—
Finish position	—	0.00 m	—
Finish sideways speed	—	0.00 m/s	—

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This simple model is used to make the control idea easy to see.

Portfolio

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Research

Contact

Let’s connect.

I am interested in research collaborations and opportunities in optimization, control, modeling, and scientific computing.

Personal email lida.lamakani@gmail.com Texas A&M email lida.lamakani@tamu.edu GitHub github.com/LidaLMK ↗

Engineering intelligent systems.

Research across connected disciplines.

Neon Gate Challenge.

Pass all three glowing gates.

Run complete.

The best drive is calculated, not drawn.

Why timing matters

Why continuous control matters

Why multiparametric optimization helps

Different starts need different best drives.

Explore my work.

Research directions

Papers and presentations

Selected projects

Code and computational tools

Let’s connect.