A Hybrid Bellman Equation for Bimodal Systems
نویسندگان
چکیده
In this paper we present a dynamic programming formulation of a hybrid optimal control problem for bimodal systems with regional dynamics. In particular, based on optimality-zone computations, a framework is presented in which the resulting hybrid Bellman equation guides the design of optimal control programs with, at most, N discrete transitions.
منابع مشابه
A New Near Optimal High Gain Controller For The Non-Minimum Phase Affine Nonlinear Systems
In this paper, a new analytical method to find a near-optimal high gain controller for the non-minimum phase affine nonlinear systems is introduced. This controller is derived based on the closed form solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with the cheap control problem. This methodology employs an algebraic equation with parametric coefficients for the systems with s...
متن کاملTheory of Optimal Control Using Bisimulations
We consider the synthesis of optimal controls for continuous feedback systems by recasting the problem to a hybrid optimal control problem: to 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 programm...
متن کاملOptimal Control of Hybrid Systems
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 finitedimensional linear programming. From the solution of the discretized problem, a value ...
متن کاملOptimal Control of Hysteresis in Smart Actuators: A Viscosity Solutions Approach
Hysteresis in smart materials hinders their wider applicability in actuators. The low dimensional hysteresis models for these materials are hybrid systems with both controlled switching and autonomous switching. In particular, they belong to the class of Duhem hysteresis models and can be formulated as systems with both continuous and switching controls. In this paper, we study the control meth...
متن کاملOptimal Control of Uncertain Switched Systems Based on Model Reference Adaptive Control
Switched systems are an important subclass of hybrid systems that consists of subsystems with continuous dynamics and a rule to regulate the switching behavior between them. Switched systems appear in a wide range of applications, such as intelligent transportation systems and smart energy systems. Due to the desire to drive switched systems toward optimal behavior, e.g. maximization of traffic...
متن کامل