**Significant risks and risk management:**

**Risk:** Inverted double pendulum simulation has insufficient numerical accuracy for NMPC

**Definition:** Since running the NMPC controller might require a higher numerical accuracy than simulating the dynamics of the inverted double pendulum system, the numerical accuracy of the system might be insufficient when NMPC is integrated into the symbolic simulation.

**Severity:** If the numerical accuracy is insufficient, the progress of the whole project would be *severely* jeopardized, because the system would likely not satisfy NR3 (accuracy).

**Resolution:** We will try to mitigate the risk by synthesizing a NMPC controller that has sufficient robustness against noise, because numerical inaccuracies can usually be seen as noise from the controller’s perspective.

**Changes to the existing design:**

There are no significant changes to the existing design as we’ve just started implementation.

**Changes to the project schedule:**

Similarly, there are no significant changes to the project schedule

**Additional Societal Impacts**

**Part A)**

Optimization is a powerful tool of representing real-world problems mathematically, and fast solvers, like the product we aim to deliver, make solving them easier.

**Health**

Optimization helps make healthcare more efficient and accessible. For example, finding the most efficient distribution of vaccines during a pandemic can be formulated as an optimization problem. Solving this problem quickly can enable more effective control of infectious diseases.

**Safety**

Optimization helps make vehicles safer to operate. Vehicle control with safety guarantees is a classic application of model predictive control (MPC), which is an optimization problem. Our solver has the potential of solving MPC problems in real-time, which can make vehicle control strategies with stronger safety guarantees practical.

**Welfare**

Optimization helps distribute scarce resources efficiently. Logistics is another classic application of optimization, which is critical for fulfilling everyday needs, especially during periods of hardship. Solving these problems efficiently ensures that goods and services are delivered where they are most needed.

**Part B)**

Our analog SQP solver has potentially wide societal implications. This comes from the fact that SQP solvers are used to solve nonlinear optimization problems, which is general class of problems with extensive use cases and applications, spanning from computer science to machine learning to biology and medicine(examples can be found in https://neos-guide.org/case-studies/). Because of the breadth of possible applications, our product solution can potentially affect a large group of people.

In particular for social groups, solving optimization problems can help make management in large organizations more efficient. One example is in the supply chain industry, where creating a supply chain strategy that operates across multiple regions can be formulated into an optimization problem.

**Part C)**

Our applications in analog optimization have significant implications in terms of the related economic factors. Specifically, this is because each of the systems relating to the production, distribution, and consumption of goods and services are areas that can be optimized to be more efficient, which leads to savings in terms of time and money. Furthermore, optimization enhances the general productivity of our society by making production procedures faster, cleaner, safer, and more efficient. As a result, a productive society leads to more sustainable development and more safer environment.

*In the team report, A was written by Thomas Liao, B was written by Alvin Zou and C was written by Andrew Chong.