Abstract: Consideration was given to identification of discrete processes, which is reducible to the functional decomposition of discrete functions, where by the decomposition is meant the representation of a function by a formula in the basis of binary operations. A procedure of optimal formula design was based on a novel approach of spectral expansion. Both exact and asymptotic complexity est...

The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be perform...

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.

The problem of designing an Extended Regulator is defined as designing an algorithm that can adjust the optimal regulator gains for a time-variant linear system appropriately to match the variations in system parameters with time. Due to conditions of positive definiteness on the unknown variable in the Riccati equation for quadratic optimal control it is possible to show that repetitive iterat...

This paper is devoted to the study of the connections among risk-sensitive stochastic optimal control, dynamic game optimal control, risk-neutral stochastic optimal control and deterministic optimal control in a nonlinear, discrete-time context with complete state information. The analysis worked out sheds light on the profound links among these control strategies, which remain hidden in the li...

This paper focuses on hybrid systems whose discrete state transitions depend on both deterministic and stochastic events. For such systems, after introducing a suitable hybrid model called Discrete Hybrid Stochastic Automaton (DHSA), different finite-time optimal control approaches are examined: (1) Stochastic Hybrid Optimal Control (SHOC), which “optimistically” determines the trajectory provi...

In this paper we analyze an alternative formulation of the rigid body equations, their relationship with the discrete rigid body equations of Moser–Veselov and their formulation as an optimal control problem. In addition we discuss a general class of discrete optimal control problems.