Ordinary Differential Equations. Ann-dimensional autonomous system of first-order ODEs has the form:\( \mathbf {x}' = f(\mathbf {x}), \)where\(\mathbf {x} = (x_1,\dots ,x_n) \in \mathbb {R} ^n\)is a vector of state variables,\(\mathbf {x}'=(x'_1,\dots ,x'_n)\)d...
Numerical results are obtained using a software package written in Julia with state-of-the-art libraries for automatic differentiation and differential equations. Three case studies are provided to demonstrate the attractive properties of simultaneous optimal design and control approach for certain applicatio...
To construct the shortest tour of these vehicles, in a previous work, we formulated the multiple-vehicle bike sharing system routing problem (mBSSRP) and demonstrated that an optimal solution can be obtained for small-sized instances through a general-purpose mixed-integer linear programming solver....
The real and reactive power balancing equations at load bus, for example, must always be met (at least to a user-defined tolerance) in the OPF, as must the area region MW interchange limitations [108]. Inequality restrictions, on the other hand, may or may not be enforceable. A line ...
To construct the shortest tour of these vehicles, in a previous work, we formulated the multiple-vehicle bike sharing system routing problem (mBSSRP) and demonstrated that an optimal solution can be obtained for small-sized instances through a general-purpose mixed-integer linear programming solver....
Mean squared error (MSE) and normalised MSE (NMSE) are commonly used to express the accuracy of channel estimation. The MSE and NMSE can be expressed as Equations (10) and (11), respectively: 𝑒MSE=𝔼[∥𝑮̂−𝑮∥2F]eMSE=EG^−GF2 (10) 𝑒NMSE=𝔼⎡⎣⎢⎢∥...