Hello,

I am attempting to rewrite the following second order cone program (SOCP) as is given by this paper:

http://arc.aiaa.org | DOI: 10.2514/1.G004155

The problem is called SOCP1 and is the following:

In this problem, I have managed to obtain a solution without implementing the control rate constraint (outlined in red).

In code, the constraint is written as the following:

```
m_wet=1000;
s(:,i+1) >= s(:,i)-Ts*Tdmax/m_wet;
s(:,i+1) <= s(:,i)+Ts*Tdmax/m_wet;
```

Where m_wet is m(t), which the authors consider as a constant mass to keep convexity intact. The reason why I am almost certain that **it is not the values I am giving these variables that is causing the issue**, is because I have tried giving a very large bound for s(:,i+1) by making m_wet either really small, or Tdmax really big, or both. The index i takes place of k, Tdmax the Tmax term with the dot, and Ts the T with the s subscript, and s is the sigma variable.

**Iâ€™ve gone through** https://yalmip.github.io/debugginginfeasible/ and didnâ€™t receive a solution but bisecting the code ultimately led me to believe that there is something wrong with the way I am writing this constraint.

What I havenâ€™t tried doing is using CVXQUAD to replace expressions with log in my code. However, I havenâ€™t considered this yet because my log expressions are only for **constant variables** (thus not the declared variables after the line cvx_begin) and I do not believe that is what the amendments that CVXQUAD makes target.

So, when I do include this constraint, the problem returns unbounded. Why is this the case? Any help is appreciated.

EDIT: Ts is defined by

Ts=(tf-tv(i))/(N-1);

Where tf is the fixed final time, tv is a predeclared vector outside of the cvx routine, and N is the fixed number of discretization nodes for the problem (N=length(tv)).

SOLUTION: The issue with the unboundedness of the problem was fixed by giving a larger final time (tf) for the problem. This wasnâ€™t directly obvious because the final time is a constant input which isnâ€™t applied directly to any of the decision variables. In conclusion, there was no problem in the formulation/syntax of the constraint, but it was simply a matter of artificial unboundedness brought by the fixed final time.