ISSN:
1572-9036
Keywords:
49L2S
;
35F30
;
Time-optimal control
;
nonlinear systems
;
Bellman equation
;
verification theorems
;
Hamilton-Jacobi equations
;
Dynamic Programming
;
viscosity solutions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For a general nonlinear system and closed target set ℐ we study the value functionsν and $$\hat \upsilon$$ of the control problems of reaching ℐ and, respectively, its interior, in minimum time. Under no controllability assumptions on the system, we characterize them as, respectively, the minimal viscosity supersolution and the maximal viscosity subsolution of the Bellman equation with appropriate boundary conditions. Then we prove that $$\hat \upsilon$$ is the unique upper semicontinuous ‘complete solution’ of such a boundary value problem, which means in particular that the (completed) graph of $$\hat \upsilon$$ contains the graph of any solution, as well as all the limits of reasonable approximating sequences. We give some applications to verifications theorems and to the stability of the minimum time function with respect to general perturbations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00997118
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