Abstract: The mathematical model of two-rigid links of one-legged walking robot dynamic control system have been modified and adapted. The state-space model and its equilibrium points are found by using implicit function theorem with Newton-Raphson method. Hence, a local linearized dynamic control systems are obtained. Therefore, an optimal control criterion is designed to achieve some system performance objectives. Since, the resulting system of linear-quadratic optimal control problems, the necessary and sufficient conditions leading to a two point's boundary value problem with non-symmetric linear operator with respect to the usual (classical) bilinear form. Hence, non-classical variational approach is not applicable. So, non-classical variational approach mixing with direct Ritz bases in suitable functional spaces have been developed for solvability of this system. The manipulation to this approach leads to the solution of either linear algebraic equations or unconstrained direct optimization problems. Both direction have been adapted. Illustration to this problem using the physical parameter of have been discussed and solved the approximated solution and their comparisons via. the proposed approach for both directions have been obtained numerically which are showing very high accuracy.
Radhi A. Zaboon and Farah J. Al-Zahed, 2018. An Approximate Solution to an Optimal Control Problem of Walking Robot via. Non-Classical Variational Approach. Journal of Engineering and Applied Sciences, 13: 9849-9861.