Tight Bounds on Polynomials and Its Application to Dynamic Optimization Problems
This work addresses dynamic optimization for control systems, offering incremental improvements in cost reduction and constraint enforcement.
The paper tackles dynamic optimization problems by introducing a pseudo-spectral method with flexible sub-intervals to achieve tight polynomial bounds, resulting in up to a tenfold reduction in relative cost in example optimal control problems.
This paper presents a pseudo-spectral method for Dynamic Optimization Problems (DOPs) that allows for tight polynomial bounds to be achieved via flexible sub-intervals. The proposed method not only rigorously enforces inequality constraints, but also allows for a lower cost in comparison with non-flexible discretizations. Two examples are provided to demonstrate the feasibility of the proposed method to solve optimal control problems. Solutions to the example problems exhibited up to a tenfold reduction in relative cost.