Authors:
Pierpaolo Soravia,
Volume: 1, Page 79 Paper number 2073
Abstract:
We consider a class of Hamilton-Jacobi equations with discontinuous
coefficients that contains as examples the eikonal equation with discontinuous
refraction index, or the Hamilton-Jacobi equation of shape-from-shading
with discontinuous intensity function. In general the Dirichlet problem
for such equations does not have unique solution, however we can characterize
the minimal and maximal solution and, under appropriate compatibility
conditions, prove existence of a unique solution in the sense of viscosity
solutions.
Authors:
Steffen Jørgensen,
Peter M. Kort,
Volume: 1, Page 85 Paper number 129
Abstract:
The paper studies an optimal control problem of pricing and inventory
replenishment in a system with sequential inventories. Consumer demand
for a specific product depends on price as well as the in-store stock
of the product. The hypothesis is that for some consumer goods, a large
volume of displayed goods leads consumers to buy more than if the stock
is small. In addition to the displayed stock, there is an inventory
of the product in a central warehouse. We consider a setup in which
management of the two stocks is decentralized such that pricing decisions
are made by the store manager who also decides on the level of in-store
inventory. The manager of the warehouse makes replenishment decisions
about the stock in the warehouse. We also study the problem where decisions
are centralized and investigate the policy impacts of having a stock-dependent
demand. Phase diagrams and a synthesizing procedure are used to derive
optimal inventory, replenishment, and retail price policies.
Authors:
Tsutomu Mita,
Sang-Ho Hyon,
Taek-Kun Nam,
Volume: 1, Page 91 Paper number 1033
Abstract:
In order to control gymnastic and jumping robots, we will derive the
complete analytical solutions to the time optimal posture control problem
of a two-link free flying object with initial angular momentum. The
obtained analytical solutions include simple closed form formulae of
the control law and show that the problem leads to a singular optimal
control problem depending upon the initial posture; the switching time
is once when the singular solution does not occur while is twice when
the singular solution is used. As an application, the somersault motion
of a diver approximated by the two link system is simulated.
Authors:
Goetz P. Grammel,
Volume: 1, Page 95 Paper number 1091
Abstract:
For nonlinear nonconvex control systems we investigate the approximation
properties of Lipschitz controls. In case that the control range is
connected, any trajectory produced by a measurable control can be approximated
by trajectories produced by Lipschitz controls. The approximation is
of order O(M^-1/2), where M is the Lipschitz constant. An example shows
that this approximation order is optimal.
Authors:
Blas M. Vinagre,
Vicente Feliu,
Volume: 1, Page 97 Paper number 1482
Abstract:
In this paper, the authors propose a generalization of the well known
Wiener-Hopf design method of optimal controllers and filters, applicable
to certain class of systems described by fractional order differential
equations, the so called commensurate order systems, i.e., in the Laplace
domain, systems described by transfer functions which are not quotients
of polynomials in s, but in s^a, a =1/q, being q a positive integer.
As can be verified in the literature, such transfer functions arise
in the characterization of many industrial processes and physical systems
which can be adequately modeled using fractional calculus, or when
modelling some distributed parameter systems by finite dimensional
models. Taking into account that fractional-order systems and controllers
have a limited diffusion, after a brief exposition of the principal
results of the traditional Wiener-Hopf method, some fundamental considerations
about the dynamical properties of such systems are made. After that,
the authors propose a procedure that allows the application of the
method to the mentioned class of systems. An illustrative example
is given.
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