Tkachev

pp. 16–26

pp. 81–92

pp. 497-509

pp. 128-142

For four-dimensional model describing the helicopter motion along a given horizontal line the problem of automated synthesis of programmed motion is solved. This solution provides a helicopter motion from a given state of rest in the given state of rest. Time to perform the maneuver is not set. The considered helicopter model is a control dynamic system, which is not a flat system. For such systems general approaches to the terminal problem solution are presently unknown. To solve the terminal problem two approaches are applied. The first approach is based on the use of finite symmetry, which converts the initial conditions of the problem in the final conditions. The use of such symmetry can reduce the number of final conditions. The second approach is based on the use of covers and consists in the construction of a special mapping, which for two given dynamic systems surjectively maps the set of solutions of the first system in the set of solutions of the second system. The programmed motion in this case can be found as the solution of two related specifically posed Cauchy problems for these dynamic systems. The resulting programmed control is a piecewise continuous function of time.

In the paper the presentation of push-down automation as oriented multigraphs is described. The language of  push-down automata, which is represented by its multigraph, is defined and equivalence of this definition with standard one is proved. In terms of this representation some properties of push-down automata (such as regularity  of  push-down stack strings set) are considered. 

For multi-input nonlinear dynamic systems the problem of state feedback design stabilizing an equilibrium point is solved using the method of virtual outputs. Affine systems are considered for which smooth function (a system output) defining transformation of the system to a normal form with a vectorial relative level of an output (2, …, 2) is known. If zero dynamics of the system isn't asymptotically stable, that is the nonlinear system isn't minimum-phase, for the specified class of systems necessary and sufficient conditions of existence of such new outputs having the relative level (2, …, 2) for which the corresponding normal form has asymptotically stable zero dynamics are proved. The received results generalize the results received earlier for affine systems with scalar input.

Trajectory planning problem of the unmanned aerial vehicle (UAV) was considered in this article. UAV should flied by the preset traveling points during the preset moments of time. State and control variables were also restricted.The main problem is to find the permissible trajectory, which satisfy given restrictions. The approach based on design of a trajectory from a certain set of sample maneuvers was proposed. These maneuvers were formed with use of a combination of analytical methods of trajectories calculation, methods of mathematical simulation and various heuristic algorithms.The sequence of traveling points breaks required trajectory into segments. Essential simplification of the problem can be obtained by the demand that calculation of the trajectory segment does not affect on calculation of the subsequent segments and depends only on values of state and control variables of UAV obtained on the previous segment. In this case planning of a trajectory was carried out consistently, from one segment to another.In this paper the maneuver planning problem of an echelon change was solved. This maneuver in a combination with rectilinear uniform movement allowed to plan those segments of a UAV trajectory where movement can take place in the vertical plane, i.e. with constant value of a traveling angle.The nonlinear mathematical model of UAV movement as material point in the trajectory coordinates was described. The proposed method of the solution of a terminal problem was based on usage of polynoms on time. Two heuristic algorithms of maneuver planning of echelon change were described. Examples were included. Results of simulation and the scheme of testing of proposed planning method were presented.

Position stabilization problem for non-linear dynamic system with scalar control was considered based on differnetial-geometrical approach. Basic theoretical fundamentals about controlled dynamic system transformation into quasi-cannonical form, and controlled dynamic system with an output transformation into normal form. Attention was paid to the case when zero dynamics of the system wasn’t asymptotically stable, that is non-linear system wasn’t minimal-phase. Usage of the method of virtual outputs for stabilization of these systems isn’t always possible because of the difficulties raised from the search of virtual controls with required properties. It was shown that for building of virtual outputs with the required properties linearization of the subsystem defining zero dynamics could be used. For the dynamic system describing inverted pendulum placed on the truck the state feedback control synthesis problem was solved with the method of virtual outputs and linearization of the part of variables; this solution allowed to stabilize both upper equilibrium position of pendulum and given position of the truck.