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Efficient solution of optimal control problems using hybrid systems. (English) Zbl 1098.49027

Summary: 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.

MSC:

49M05 Numerical methods based on necessary conditions
49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
65N99 Numerical methods for partial differential equations, boundary value problems
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