How do piecewise linear approximations simplify nonlinear system behavior?

In systems engineering, a mathematical model is essential for describing system interactions in quantitative terms. Because real-world systems are often nonlinear, engineers frequently use piecewise linear approximations to simplify these complex behaviors.1

This technique involves representing a nonlinear curve as a series of short, connected straight lines. By breaking down a complex, nonlinear function into smaller, linear segments, the system becomes easier to analyze using standard mathematical techniques, such as linear programming, which are often more computationally efficient than those required for fully nonlinear problems.12

While these models do not need to be exact, they must be sufficiently accurate to serve their intended purpose in evaluating system operations, conducting trade-off studies, and optimizing performance. This approach allows engineers to manage the complexity of a system while still capturing the essential features necessary for effective design and decision-making.12