Recursive Approach of Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation

Optimal Input Design (OID) methodologies are developed to find a signal that could best estimate a set of parameters of a given model. Their application in constrained nonlinear systems, especially when the search space limits or the initial conditions are unknown, may present several difficulties due to the numerical instability related to the optimization processes. A good choice over the parameters possible ranges is a trade-off among numerical stability, search space size, and effectiveness, and it is hardly found. To deal with this problem, this paper proposes a series of changes in the Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation (SOESGOPE) methodology. First, the limits over the parameters are tightly adjusted according to their confidence. A recursive approach runs the optimization methodology, analyzes the solution’s feasibility and marginal costs given by the Lagrange Multipliers, and selects a direction that could improve the system’s response. This approach improves the convergence and the assertiveness of the estimation process. To validate this approach, some cases, including a parameters estimation of a mobile robot nonlinear system, are tested.