Minimum time controller in a class of chemical reactors based on Lagrangian approach

The main goal of this work is the construction of a class of controller, which employs directly a Lagrangian formulation to resolve the classical brachistochrone problem, this allows to obtain an optimal controller which reaches in a minimum time the stabilization of an isothermal continuous stirred tank reactor, whose chemical kinetic model is based on the power law. The proposed methodology is compared with an input/output linearizing which achieve asymptotic and exponential closed-loop convergence, sliding-mode controller with a finite time convergence and an exact gradient optimal control to compare the time convergence performance. Numerical experiments show the satisfactory performance of the proposed controller, despite sustained disturbances in the concentration input feed.

On the structure of the optimal thrust for the “intermediate” aircraft model

The paper considers a brachistochrone problem modification including in the objective function a fuel consumption penalty apart from the process time. The material point moves in a vertical plane under gravity, viscous nonlinear friction and traction. The trajectory slope angle and thrust are considered as a control variables. The Pontryagin maximum principle allows reducing the optimal control problem to a boundary value problem for a system of two nonlinear differential equations. Qualitative analysis of the resulting system allows studying the key features of extreme trajectories, including their asymptotic behavior. Extreme thrust control is obtained as a function of the velocity and the trajectory slope angle. The structure of extreme thrust is determined, and the number of switches is analytically determined. The results of numerical solving the boundary value problem are presented, illustrating the analytical conclusions.