A NUMERICAL-CALCULATION FOR SOME NONLINEAR OPTIMAL-CONTROL PROBLEMS WITH A TERMINAL CONSTRAINT USING SYNTHETIC RICCATI TRANSFORMATION AND ITS APPLICATIONS TO THE MANIPULATOR CONTROL PROBLEM

This paper describes a new numerical calculation algorithm for the non linear quadratic optimal problem with nonlinear terminal constraint. S ynthetic Riccati transformation proposed earlier by the authors is uti lized to solve the forementioned problem. The state differential equat ion is changed into two differential equations with respect to the two substates vector selected from the state vector. Then, based on the m aximum principle and Kronecker's product, two differential equations w ith respect to the adjoint variables can be derived. To solve the fore mentioned differential equations, synthetic Riccati transformation is introduced to obtain a Riccati differential equation and an accessory differential equation. Thus, we can calculate the initial values of th e adjoint variables by solving Riccati equations backward in time. The convergence condition about this algorithm also is provided. As the a pplication of this algorithm, an attempt is made to apply it to an opt imal trajectory control problem for a two-link manipulator. As the res ult of the simulation, it is confirmed that the algorithm not only has a performance of both fast convergence and high computation accuracy but also is not subject to the selection of the normal parameter for c omputation.