Timeminimal set point transition for nonlinear SISO systems under different constraints Abstract   Set point transition of nonlinear plants plays an important role in many applications where dynamic process management has to be considered. This transition should be rapid xe2x80x93 as operation in the new set point increases the economical benefit xe2x80x93 but in compliance with all safety regulations. We present a feedforward approach for a timeminimal set point transition of singleinput, singleoutput nonlinear plants with respect to input, state and output constraints. The conceptual idea is based on the design of an optimization problem utilizing a coordinate change of the plant and a special setup function for the output trajectory. This allows the simultaneous planning of the trajectory and determination of the corresponding control signal. The formulation of the set point transition as an optimization problem provides a flexible design with respect to the integration of inequality constraints. Additional flexibility is provided by the type of setup functions, which permit any adjustment of the output trajectory between the set points. In contrast to other works, we focus on the stationarity of the system output, which allows a faster transition compared to the requirement to reach a steady state of all states. Finally, we present an example from the field of process systems engineering to demonstrate the applicability of the proposed methodology.

Optimality conditions for optimal impulsive control problems with multipoint state constraints This paper addresses an optimal impulsive control problem whose trajectories are functions of bounded variation and impulsive controls are regular vector measures. This problem is characterized by two main features. First, the dynamical control system to be considered may not possess the socalled wellposedness property. Second, the constraints on the onesided limits of states are presented. Such constraints are interpreted as multipoint state constraints. For this problem, we derive global optimality conditions based on using of compound Lyapunov type functions which possess strongly monotone properties with respect to the control system. As a motivating case, a model of advertising expenses optimization for mutually complementary products is considered. For this model, we propose four variants of resolving sets of Lyapunov type functions and explain the technique of applying the optimality conditions.