Abstract
The problem considered in this paper is the identification of states and parameters in noisy nonlinear dynamic systems. It is a well-known fact that the identification problem for nonlinear systems results in the problem of solving the nonlinear two-point boundary value problem (T. P.B.V.P). The methods of quasilinearization and invariant imbedding are often used as computational algorithms for solving this type of nonlinear T.P.B.V.P.
From the point of view of the computational aspect, the quasilinearization method is a nonsequential or off-line algorithm, namely, a batch one. On the other hand, the invariant imbedding is a sequential or on-line algorithm.
A computational algorithm by the combined use of quasilinearization and invariant imbedding was already given as the optimization technique in order to solve nonlinear T.P.B.V. P in the optimal control problem and the system identification problem. The algorithm is a predictor-corrector formula in which the invariant imbedding predicts the missing initial condition and the quasilinearization procedure corrects this predicted value.
In this paper, a new computational algorithm which differs from the predictor-corrector algorithm is proposed as the optimization technique. The algorithm presented involves a batch-sequential computational process in which the states and parameters are estimated by invariant imbedding at a sub-time interval in a forward sweep after processing the data by the quasilinearization method at the interval. For this reason, this algorithm will be called a batch-sequential identification algorithm. The algorithm requires less computational effort than the predictor-corrector formula and also has better convergence properties and identification accuracy than the filter algorithm via invariant imbedding, taking an appropriate choice of initial conditions and sub-time intervals.
Experimental results from an example of a simple identification problem indicate that the proposed batch-sequential identification scheme is feasible for the nonlinear system identification problem.
