We study optimal control problems for hyperbolic equations (focusing on the multidimensional wave equation) with control functions in the Dirichlet boundary conditions under hard/pointwise control and state constraints. Imposing appropriate convexity assumptions on the cost integral functional, we establish the existence of optimal control and derive new necessary optimality conditions in the i...

The purpose of this paper is to present an alternate derivation of optimal linear filters. The basic technique is the use of a matrix version of the maximum principle of Pontryagin coupled with the use of gradient matrices to derive the optimal values of the ; '1 filter coefficients for minimum variance estimation under the require­ :11" ment that the estimates be unbiased. The optimal filter w...

Abstract In this paper, we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems Pontryagin maximum principle. As an important result, among others, develop a principle that permits to deal with problems dissipation. We also consider the Herglotz problem, which is simultaneously generalization of variational problem. An application study thermodynamic syst...

This paper presents characterization of shortest paths for differentialdrive mobile robots with classifying solutions in the spirit of Dubins curves and Reeds-Shepp curves for car-like robots. Not only optimal paths for mobile robots are interesting with respect to the optimized criteria, but also they offer a family of motion primitives that can be used for motion planning in the presence of o...

We consider the optimal control of stochastic delayed systems with jumps, in which both the state and controls can depend on the past history of the system, for a value function which depends on the initial path of the process. We derive the Hamilton-Jacobi-Bellman equation and the associated verification theorem and prove a necessary and a sufficient maximum principles for such problems. Expli...

Optimal control theory of viscous flow has several applications in engineering science. In [20], a fundamental optimal control problem in exterior hydrodynamics was studied. In that paper, the task of accelerating an obstacle from rest to a given speed in a given time, minimising the energy expenditure, was considered. In [13] a unified formulation of optimal control problems in viscous hydrody...

A long time ago, since the launch of the first artificial satellite in 1957, controling attitude of satellites has been considered by the designers and engineers of aerospace industry. Considering the importance of this issue various methods of control in response to this need have been presented and analyzed until now. In this paper, we propose and analyze a three-axis optimal control on the s...

In this article we present a geometric discrete-time Pontryagin maximum principle (PMP) on matrix Lie groups that incorporates frequency constraints on the controls in addition to pointwise constraints on the states and control actions directly at the stage of the problem formulation. This PMP gives first order necessary conditions for optimality, and leads to twopoint boundary value problems t...

Inhaltsverzeichnis Liste der wichtigsten Bezeichnungen 5 1. Einleitung 7