Generalized Policy Iteration for continuous-time systems

In this paper we present a unified point of view over the approximate dynamic programming (ADP) algorithms which have been developed in the last years for continuous-time (CT) systems. We introduce here, in a continuous-time formulation, the generalized policy iteration (GPI), and show that in effect it represents a spectrum of algorithms which has at one end the exact policy iteration (PI) algorithm and at the other the value iteration (VI) algorithm. At the middle part of the spectrum we formulate for the first time the optimistic policy iteration (OPI) algorithm for CT systems. We introduce the GPI starting from a new formulation for the PI algorithm which involves an iterative process to solve for the value function at the policy evaluation step. The GPI algorithm is implemented on an actor/critic structure. The results allow implementation of a family of adaptive controllers which converge online to the solution of the optimal control problem, without knowing or identifying the internal dynamics of the system. Simulation results are provided to verify the convergence to the optimal control solution.