The optimality principle for second-order discrete and discrete-approximate inclusions

This paper deals with the necessary and sufficient conditions of optimality for the Mayer problem of second-order discrete and discrete-approximate inclusions. The main problem is to establish the approximation of second-order viability problems for differential inclusions with endpoint constraints. Thus, as a supplementary problem, we study the discrete approximation problem and give the optimality conditions incorporating the Euler-Lagrange inclusions and distinctive transversality conditions. Locally adjoint mappings (LAM) and equivalence theorems are the fundamental principles of achieving these optimal conditions, one of the most characteristic properties of such approaches with second-order differential inclusions that are specific to the existence of LAMs equivalence relations. Also, a discrete linear model and an example of second-order discrete inclusions in which a set-valued mapping is described by a nonlinear inequality show the applications of these results.

Comparative effectiveness of throttled and relay rocket engines for low-gravity near-Earth flights

Within the framework of solving the Mayer problem of optimal control of a flight from an elongated elliptical orbit to a geostationary one with a maximum payload at a given initial mass of the low-thrust spacecraft and a fixed duration of the dynamic maneuver, a comparative analysis was made of the efficiency of throttled and relay thrust modes. Based on the data of the numerical solution of the corresponding twopoint boundary value problem, the expected gain was confirmed of the throttling mode over the relay mode in the case of practically interesting low-thrust near-Earth maneuvers. Also the numerical results confirmed the adequacy of the constructed fixed-power relay rocket engine mathematical model and made it possible to reveal a number of qualitative features of the control functions along the optimal transition trajectories.

Geometric and numerical methods for a state constrained minimum time control problem of an electric vehicle

In this article, the minimum time control problem of an electric vehicle is modeled as a Mayer problem in optimal control, with affine dynamics with respect to the control and with state constraints. The candidates as minimizers are selected among a set of extremals, solutions of a Hamiltonian system given by the maximum principle. An analysis, with the techniques of geometric control, is used first to reduce the set of candidates and then to construct the numerical methods. This leads to a numerical investigation based on indirect methods using the HamPath software. Multiple shooting and homotopy techniques are used to build a synthesis with respect to the bounds of the boundary sets.