Riccati Equation

The Riccati equation, a nonlinear differential equation, plays a crucial role in optimal control theory, aiming to find the best possible control strategy for a dynamical system. Current research focuses on efficient numerical solutions, particularly leveraging algorithms like Riccati recursions and exponential time differencing to handle large-scale problems arising in robotics, Bayesian inference, and machine learning. These advancements enable applications ranging from optimizing human-robot collaboration and safe autonomous navigation to improving inertial estimation in legged robots and solving complex optimal control problems for switched systems.