• Corpus ID: 239885748

Rotational controls and uniqueness of constrained viscosity solutions of Hamilton-Jacobi PDE

@inproceedings{Colombo2021RotationalCA,
  title={Rotational controls and uniqueness of constrained viscosity solutions of Hamilton-Jacobi PDE},
  author={Giovanni Colombo and Nathalie T. Khalil and Franco Rampazzo},
  year={2021}
}
The classical inward pointing condition (IPC) for a control system whose state x is constrained in the closure C ∶= Ω̄ of an open set Ω prescribes that at each point of the boundary x ∈ ∂Ω the intersection between the dynamics and the interior of the tangent space of Ω̄ at x is nonempty. Under this hypothesis, for every system trajectory x(.) on a time-interval [0, T ], possibly violating the constraint, one can construct a new system trajectory x̂(.) that satisfies the constraint and whose… 

Figures from this paper

References

SHOWING 1-10 OF 25 REFERENCES
OPTIMAL CONTROL WITH STATE-SPACE CONSTRAINT II
Optimal control of piecewise deterministic processes with state space constraint is studied. Under appropriate assumptions, it is shown that the optimal value function is the only viscosity solution
Degenerate Optimal Control Problems with State Constraints
TLDR
Conditions for the existence of nontrivial multipliers are given, based on refined estimates of the distance of a given state trajectory from the set of state trajectories satisfying the state constraint, originating in the dynamic programming literature.
Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems
In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semicontinuous generalized solution of the Hamilton-Jacobi
On constraint qualifications for nondegenerate necessary conditions of optimality applied to optimal control problems
We address necessary conditions of optimality (NCO), in the form of a maximum principle, for optimal control problems with state constraints. In particular, we are interested in the NCO that are
Nondegenerate Necessary Conditions for Nonconvex Optimal Control Problems with State Constraints
Standard versions of the maximum principle for optimal control problems with pathwise state inequality constraints are satisfied by a trivial set of multipliers in the case when the left endpoint is
On Trajectories Satisfying a State Constraint: W1, 1 Estimates and Counterexamples
TLDR
It is shown, by counterexample, that linear, linear estimates are not in general valid for multiple state constraints, and it is shown that it is possible to justify linear, $W^{1,1}$ estimates by means of a modification of earlier constructive techniques, when there is only one state constraint.
Optimality conditions for optimal control problems and applications
TLDR
It is proved that under an additional information involving mainly the Clarke tangent cone, necessary conditions in the form of the Extended Euler-Lagrange condition are derived in the normal and non-degenerate form for two different classes of state constrained optimal control problems.
Sensitivity Interpretations of the Costate Variable for Optimal Control Problems with State Constraints
TLDR
This paper provides new sensitivity relations for state constrained optimal control problems, and introduces an auxiliary optimal control problem that possesses a richer set of control variables than the original problem.
...
1
2
3
...