Efficient Near-Optimal Control of Large-Size Second-Order Linear Time-Varying Systems

Building on the two time-scale decomposition method, we propose a solution to the optimal control problem for second-order Linear Time-Varying (LTV) systems. This solution achieves convergence to that provided by standard numerical solvers such as Pontryagin’s Maximum Principle (PMP), and significantly enhances computational efficiency, making it applicable to large-size systems. We achieve this by developing closed-form solutions to the Continuous Algebraic Riccati Equations (CARE) for second-order systems. We also show through a spring-mass-damper system that our approach is significantly faster and more computationally efficient than standard methods.