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The basic idea of inverse optimal control theory for nonlinear systems is to find a feedback control law based on a priori knowledge of a Control-Lyapunov function (CLF), that leads to Lyapunov stability of the system and minimizes a cost functional [1], [4]. The problem of inverse optimal control leads to the Hamilton-Jacobi-Bellman (HJB) equation, but in case of non-linear systems it does not have exact analytical solution. HJB equation in the linear case, may be reduced to Riccati equation when using the linear quadratic regulator (LQR). Kalman’s inverse optimal control theory in linear systems for finding a certain state feedback should provide an optimal control, relative to a useful performance index. The problem addressed in this article is the construction of the control Lyapunov function for non-linear systems for which there are no well-established techniques. One option is to use a global recursive adjustment of time dependent parameters of the Liapunov quadratic control function by means of the extended Kalman filter algorithm (EKF). Inverse optimal control applied in the case of following a robot trajectory is to design a control law u for tracking the desired trajectory, generated by a reference robot. A recursive high-order neural network identifier (RHONN) will also be used in this process [3], [4]. In order to identify the model of the trained plant by an extended Kalman filter algorithm (EKF), we assume that the whole state-space is available for measurement. Also, inverse optimal control is designed to track the speed of the robot on the desired trajectory. By applying the inverse optimal control for non-linear systems, we intend to avoid solving HJB equations, to apply feedback control to stabilize the system and then to prove that this control optimizes a cost functional. Using MATLAB simulation, we have made a test to justify the exposed theory [5].
Control Lyapunov function, extended Kalman filter, Hamilton-Jacobi-Bellman equation, inverse optimal control, robot tracking optimization.
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