Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the switched-affine optimal control problem,  i.e. , the problem of selecting a sequence of affine dynamics from a finite set in order to minimize a sum of convex functions of the system state.  develop a new reduction of this problem to a mixed-integer convex program (MICP), based on perspective functions. Relaxing the integer constraints of this MICP results in a convex optimization problem, whose optimal value is a lor bound on the original problem value.  show that this bound is at least as tight as similar bounds obtained from two other ll-known MICP reductions (via conversion to a mixed logical dynamical system, and by generalized disjunctive programming), and our numerical study indicates it is often substantially tighter. Using simple integer-rounding techniques,  can also use our formulation to obtain an upper bound (and corresponding sequence of control inputs). In our numerical study, this bound was typically within a few percent of the optimal value, making it attractive as a stand-alone heuristic, or as a subroutine in a global algorithm such as branch and bound.  conclude with some extensions of our formulation to problems with switching costs and piecewise affine dynamics.
['Nicholas Moehle', 'Stephen P. Boyd']
I am writing a research paper on a idea A perspective-based convex relaxation for switched-affine optimal control
[{"from": "human", "value": "I am writing a research paper on a idea A perspective-based convex relaxation for switched-affine optimal control"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the switched-affine optimal control problem,  i.e. , the problem of selecting a sequence of affine dynamics from a finite set in order to minimize a sum of convex functions of the system state.  develop a new reduction of this problem to a mixed-integer convex program (MICP), based on perspective functions. Relaxing the integer constraints of this MICP results in a convex optimization problem, whose optimal value is a lor bound on the original problem value.  show that this bound is at least as tight as similar bounds obtained from two other ll-known MICP reductions (via conversion to a mixed logical dynamical system, and by generalized disjunctive programming), and our numerical study indicates it is often substantially tighter. Using simple integer-rounding techniques,  can also use our formulation to obtain an upper bound (and corresponding sequence of control inputs). In our numerical study, this bound was typically within a few percent of the optimal value, making it attractive as a stand-alone heuristic, or as a subroutine in a global algorithm such as branch and bound.  conclude with some extensions of our formulation to problems with switching costs and piecewise affine dynamics."}]