21,101 research outputs found
A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates
This paper presents a methodology for safety verification of continuous and hybrid systems in the worst-case and stochastic settings. In the worst-case setting, a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do not enter an unsafe region. No explicit computation of reachable sets is required in the construction of barrier certificates, which makes it possible to handle nonlinearity, uncertainty, and constraints directly within this framework. In the stochastic setting, our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound whose validity is proven by the existence of a barrier certificate. For polynomial systems, barrier certificates can be constructed using convex optimization, and hence the method is computationally tractable. Some examples are provided to illustrate the use of the method
Controlled diffusion processes
This article gives an overview of the developments in controlled diffusion
processes, emphasizing key results regarding existence of optimal controls and
their characterization via dynamic programming for a variety of cost criteria
and structural assumptions. Stochastic maximum principle and control under
partial observations (equivalently, control of nonlinear filters) are also
discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Optimal control of risk process in a regime-switching environment
This paper is concerned with cost optimization of an insurance company. The
surplus of the insurance company is modeled by a controlled regime switching
diffusion, where the regime switching mechanism provides the fluctuations of
the random environment. The goal is to find an optimal control that minimizes
the total cost up to a stochastic exit time. A weaker sufficient condition than
that of (Fleming and Soner 2006, Section V.2) for the continuity of the value
function is obtained. Further, the value function is shown to be a viscosity
solution of a Hamilton-Jacobian-Bellman equation.Comment: Keywords: Regime switching diffusion, continuity of the value
function, exit time control, viscosity solutio
Fuel optimum stochastic attitude control
Numerical solution of stochastic Hamilton-Jacobi equation for fuel optimal spacecraft attitude control syste
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