Models and algorithms for self-maintenance and self-recovery systems of engines and mechanics are developed in this paper. Construction of models is based on mathematical formalisms defining hierarchical and topological structure of the state space of a mechanical system. The purpose of such constructions consists in allocation in the state space the system of regions whose boundaries are the physical boundaries of the reversibility of the physical state of the system. Within these regions the state of system under variations of the management parameters is reversible, that is, the system can be restored to its original state or the closest to the original by varying the management parameters. The trajectory of return and the temporal dependence of the management parameters are determined in this case. Under the self-maintenance here is defined the construction of algorithms for automatic calculating of trajectories and temporal variations of the management parameters set for bringing the system to previously specified circular or nearly circular trajectory. In the regions of the solution of cyclic task of self-maintenance has a solution. Problem of optimization of state evolution trajectory in order to maximize spent by the system in the preassigned trajectory is set out-side boundaries of regions of the return for the self-maintenance. (Maximization problem). But a return to cyclical trajectory is already impossible due to the physical irreversibility. Taking into account the hierarchy in states of mechanism for all time of its life cycle, there are several levels on each of which the problem of self-maintenance is solved in the sense of maximization problems. The last hierarchical level is designated by boundary outside of which the failure region is located. Therefore, the problem of self-maintenance is the maximum holding of the system on the trajectory reaching the boundary of failure region. Automatic construction of an optimal management strategy involves a comprehensive automated parameter management in the field of their allowable values. The situation is considered when a complex incorrect, unoptimized parameter management mechanism leads to failure. These situations must be excluded in the construction of management strategy. In particular, it is demonstrated that the cause of failure of mechanics is changes of the engine management parameters on transition regimes are not consistent with the degeneracy space of PDF. This discordance leads to the destruction of symmetry and the appearance of heavy - tails of distribution functions. Experimental situations are demonstrated on internal combustion engines and friction pairs in the mechanisms.
