Practical Bounds of Dynamic System Simulator for Stability Verification

There are recent shifts in demand for design controllers from simple to complex dynamic systems. Stability verification is one of the important steps in finalising the design of control systems. Stability checks including the complexity of dynamic systems have become increasingly important. Growing computational power provides opportunities to implement efficient tools to address stability verification. To provide the stability confirmation for dynamic simulators, we first establish state propagation bounds for the simulator implemented using the Runge-Kutta 4th-order method. Secondly, we establish computational methods to verify the stability of dynamic systems with finite numbers of simulations over the given range of state space using the state propagation bounds. The algorithms provide the deterministic stability guarantee for the continuous state space. Finally, we demonstrate the effectiveness and limitations of the algorithms using an inverted pendulum system with a reinforcement learning controller combined with an LQR (Linear Quadratic Regulator) controller.