Simultaneous optimal parameter and mode transition time estimation

This paper presents a method of simultaneous mode transition time and parameter estimation for hybrid systems based on switching time optimization techniques. A concise derivation of first- and second-order optimality conditions with respect to both mode transition times and parameter values is presented, including cross-derivative terms between the switching times and the parameters. The estimation algorithm is shown to be effective for estimating transition times as well as unknown parameter values from coarsely sampled data for a skid-steered vehicle, which traverses unknown or changing terrain and transitions between discrete dynamic modes. It is shown that second-order optimization methods using the exact Hessian provide far superior convergence, compared to first-or approximate second-order methods, to correct values in simulated and experimental scenarios.