Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis–Hastings Method

Probabilistic Estimation and Control of Dynamical Systems Using Particle Filter with Adaptive Backward Sampling

Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only as a state estimator and a prior estimator for the dynamics but also as a controller. This approach allows us to handle the nonlinearity of the dynamics and uncertainty of the latent state. We apply two distinct dynamics to verify the effectiveness of our proposed framework: a chaotic system defined by the Lorenz equation and a nonlinear neuronal system defined by the Morris-Lecar neuron model. The results indicate that our proposed framework can simultaneously estimate and control complex nonlinear dynamical systems.