Successive Collocation : An Approximation to

A novel approach to solving the optimal nonlin-ear control problem is presented. Instead of seeking a global approximation to the Hamilton-Jacobi-Bellman equation, a local approximation is obtained by successively solving the Generalized Hamilton-Jacobi-Bellman (GHJB) equation on a local region of the state space. The optimal control is generated by solving the GHJB equation algebraically at several points close to the current state and using this information to generate a value function that ts the optimal value function close to the current state. This method (the method of orthogonal collocation and successive approximation) is applied to a two-dimensional nonlinear oscillator system, and it is shown to be a practical control law that converges to the optimal control signal.