In order to control gymnastic and jumping robots, we will derive the complete analytical solution to the posture control problem of a two-link free flying object with initial angular momentum. We will show that the solution involves singular control and derive formulas to calculate the optimal switching condition, optimal terminal time and optimal trajectories. As an application, a high diving ...

Bolza problem governed by PDE control systems with unbounded controls is considered. The motivating example is fluid structure interaction model with boundary-interface controls. The aim of the work is to provide optimal feedback synthesis associated with well defined gain operator constructed from the Riccati equation. The dynamics considered is of mixed parabolic-hyperbolic type which prevent...

In order to control gymnastic and jumping robots, we will derive the complete analytical solution to the posture control problem of a two-link free flying object with initial angular momentum. We will show that the solution involves singular control and derive formulae to calculate the optimal switching condition, optimal terminal time and optimal trajectories. As an application, a high diving ...

In this paper, an optimal singular stochastic control problem is considered. For this model, it is obtained a general stochastic maximum principle by using a time transformation. This is the first version of the stochastic maximum principle that covers the singular control problem in the nonlinear case.

A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the value function is C and its directional derivatives are the value functions of certain optimal stopping problems. Guided by the optimal stopping problem we then introduce the associated no-action region and the free boundary and show that, under appropriate conditions, an optimally contro...

In this paper, we address the problem of numerical implementation of optimal control for switched affine systems with state constraints. In order to properly solve the problem, a relaxed system is introduced and the connection between the solution of this system and the solution of the initial one is established. One of the main difficulties is then related to the fact that the optimal solution...

Plant structure is utilized for the simpli cation of system analysis and controller synthesis. For plants where the directionality is independent of frequency, the singular value decomposition (SVD) is used to decouple the system into nominally independent subsystems of lower dimension. In H2and H1-optimal control, the controller synthesis can thereafter be performed for each of these subsystem...

In this paper, we consider the minimum-time reorientation problem of an axi-symmetric rigid spacecraft with two independent control torques mounted perpendicular to the spacecraft symmetry axis. The spacecraft is allowed to spin about its symmetry axis. All possible control structures, including both singular and nonsingular arcs, are studied completely by deriving the corresponding formulae, a...

A nonlinear control model of a firm describing the change of production and accumulated R&D investment is investigated. An optimal control problem with R&D investment rate as a control parameter is solved. Optimal dynamics of economic growth of a firm versus the current cost of innovation is studied. It is analytically determined that dependent on the model parameters, the optimal control must ...

We study a two-sided singular control problem in a general linear diffusion setting and provide a set of conditions under which an optimal control exists uniquely and is of singular control type. Moreover, under these conditions the associated value function can be written in a quasi-explicit form. Furthermore, we investigate comparative static properties of the solution with respect to the vol...