Yes, there's an easy solution: don't use dynamic memory allocation outside of initialization.
It is common (in my experience) in embedded systems to only allow calls to malloc when a program starts (this is usually done by convention, there's nothing in C to enforce this. Although you can create your own wrapper for malloc to do this). This requires more work to analyze what memory your program could possibly use since you have to allocate it all at once. The benefit you get, however, is a complete understanding of what memory your program uses.
In some cases this is fairly straightforward, in particular if your system has enough memory to allocate everything it could possibly need all at once. In severely memory-limited systems, however, you're left with the managing the memory yourself. I've seen this done by writing "custom allocators" which you allocate and free memory from. I'll provide an example.
Let's say you're implementing some mathematical program that needs lots of big matrices (not terribly huge, but for example 1000x1000 floats). Your system may not have the memory to allocate many of these matrices, but if you can allocate at least one of them, you could create a pool of memory used for matrix objects, and every time you need a matrix you grab memory from that pool, and when you're done with it you return it to the pool. This is easy if you can return them in the same order you got them in, meaning the memory pool works just like a stack. If this isn't the case, perhaps you could just clear the entire pool at the end of each "iteration" (assuming this math system is periodic).
With more detail about what exactly you're trying to implement I could provide more relevant/specific examples.
Edit: See sg7's answer as well: that user provides a link to well-established frameworks which implement what I describe here.
