49J15 Optimal control problems involving ordinary differential equations
Refine
Language
- English (2)
Keywords
- BVD pencil (1)
- Cayley transformation (1)
- Trajectory planning, optimal control problem, collision avoidance, (1)
- disk function method (1)
- even pencil (1)
- graph search algorithm, initialization, robotics (1)
- optimal control (1)
- pencil arithmetic (1)
- structured doubling algorithm (1)
- symplectic pencil (1)
Application Area
- C (2)
A coupling of discrete and continuous optimization to solve kinodynamic motion planning problems
(2014)
This paper studies the relationship between the material derivative method, the shape derivative method, the min-max formulation of Correa and Seeger, and the Lagrange method introduced by Cea. A theorem is formulated
which allows a rigorous proof of the shape differentiability without the usage of material derivative;
the domain expression is automatically obtained and the boundary expression is easy to derive.
Furthermore, the theorem is applied to a cost function which depends on a quasi-linear transmission
problem. Using a Gagliardo penalization the existence of optimal shapes is established.
We propose a generalization of the Structured Doubling Algorithm (SDA) to compute invariant subspaces
of structured matrix pencils
that arise in the context of solving linear quadratic optimal control problems.
The new algorithm is
designed to attain better accuracy when the classical Riccati equation approach for the solution of the optimal control problem is not well suited because
the stable and unstable invariant subspaces are not well separated (due to eigenvalues near or on the imaginary
axis) or in the case when the Riccati solution does not exist at all. We analyze the convergence
of the method and compare the new method with the classical SDA algorithm as well as some recent structured QR-methods.