2003 · 271 citations · 15 references
Natural SciencesMathematicsSystems EngineeringHybrid Vehicle SystemsOptimizationProcess ControlControl TheoryConvex OptimizationHybrid SystemsLinear ProgrammingOptimal ControlOptimization TheoryHybrid ControlHybrid Dynamical Systems ControlHybrid System ControlHybrid Systems ControlLower Bound ComputationOptimal Control FormulationOptimal Feedback Control
A Bellman‑type inequality is used to derive a lower bound on the optimal value function for hybrid systems. The paper proposes a method for optimal control of hybrid systems. The method discretizes the hybrid Bellman inequality into a finite‑dimensional linear program, solves it, and constructs a value function that preserves the lower bound. The resulting approximation of the optimal feedback control law is demonstrated on several examples.
This paper presents a method for optimal control of hybrid systems. An inequality of Bellman type is considered and every solution to this inequality gives a lower bound on the optimal value function. A discretization of this "hybrid Bellman inequality" leads to a convex optimization problem in terms of finite-dimensional linear programming. From the solution of the discretized problem, a value function that preserves the lower bound property can be constructed. An approximation of the optimal feedback control law is given and tried on some examples.
15
Rajeev Alur, David L. Dill · Theoretical Computer Science · 1994 · 6.5K citations
The Mathematical Theory of Optimal Processes
Richard Bellman, L. S. Pontryagin, V. G. Boltyanskiĭ et al. · Econometrica · 1965 · 4.3K citations