Adaptive Optimal Stochastic Trajectory Planning and Control (AOSTPC)

Adaptive Optimal Stochastic Trajectory Planning and Control \((\textit{AOSTPC})\) are considered in this chapter: In optimal control of dynamic systems the standard procedure is to determine first offline an optimal open-loop control, using some nominal or estimated values of the model parameters, and to correct then the resulting deviation of the actual trajectory or system performance from the prescribed trajectory (prescribed system performance) by online measurement and control actions. However, online measurement and control actions are very expensive and time consuming. By adaptive optimal stochastic trajectory planning and control (AOSTPC), based on stochastic optimization methods, the available a priori and statistical information about the unknown model parameters is incorporating into the optimal control design. Consequently, the mean absolute deviation between the actual and prescribed trajectory can be reduced considerably, and robust controls are obtained. Using only some necessary stability conditions, by means of stochastic optimization methods also sufficient stability properties of the corresponding feedforward, feedback (PD-, PID-) controls, resp., are obtained. Moreover, analytical estimates are given for the reduction of the tracking error, hence, for the reduction of the online correction expenses by applying (AOSTPC).