givne a system $\dot x = f(x, u)$ where $x$ are state variables and $u$ control inputs,
we want to find a trim point $x_t, u_t$ that satisfies a set of trim conditions. In the absence of any user-specified
conditions, this reduces to finding a stationary point
$$0 = f(x,u)$$
i.e., $\dot x = 0$ is typically an implicit trim condition.
The user-specified trim conditions may take many forms, for example
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$x_i \approx 5$ should be close to 5 (called a soft constraint)
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$x_i = 5$ should be exactly 5 (called a hard constraint)
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$\dot{x}_i$ is free, i.e., is not bound to be 0 like the other derivatives.
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$-10 < u_i < 10$ may specify inequality constraints (may be more complicated than this).
After structural_simplify, we may get a system where some states in $x$ have been moved to observed,
let $x_r$ be the reduced state vector and $x_o$ be the observed states.
The cost function looks something like this
$\sum_i (x_i - x_i^d)^2 + \sum_i (\dot{x}_i - \dot{x}_i^d)^2$
$\text{subject to} \quad c_0(\dot x, x, u) = 0$
$\text{subject to} \quad c_1(\dot x, x, u) \leq 0$
where $x_i^d$ specifies a desired value for $x_i$, and $c_0, c_1$ are constraint functions that indicate the hard constraints.
Specification of the loss function and $c_0, c_1$ despite $x$ having been split up in $x_r, x_o$
