We consider the synthesis of optimal controls for continuous feedback systems by recasting the problem to a hybrid optimal control problem: synthesize optimal enabling conditions for switching between locations in which the control is constant. An algorithmic solution is obtained by translating the hybrid automaton to a finite automaton using a bisimulation and formulating a dynamic programming problem with extra conditions to ensure non-Zenoness of trajectories. We show that the discrete value function converges to the viscosity solution of the Hamilton–Jacobi–Bellman equation as a discretization parameter tends to zero.
Efficient Solution of Optimal Control Using Bisimulations
DI BENEDETTO, MARIA DOMENICA;DI GENNARO, Stefano;
2005-01-01
Abstract
We consider the synthesis of optimal controls for continuous feedback systems by recasting the problem to a hybrid optimal control problem: synthesize optimal enabling conditions for switching between locations in which the control is constant. An algorithmic solution is obtained by translating the hybrid automaton to a finite automaton using a bisimulation and formulating a dynamic programming problem with extra conditions to ensure non-Zenoness of trajectories. We show that the discrete value function converges to the viscosity solution of the Hamilton–Jacobi–Bellman equation as a discretization parameter tends to zero.File in questo prodotto:
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