Infinite-horizon optimal control of nonlinear stochastic systems: a neural approach

A feedback control law is proposed that drives the controlled vector v_t of a dynamic system (in general, nonlinear) to track a reference v_t* over an infinite time horizon, while minimizing a given cost function (in general, nonquadratic). The behaviour of v_t* over time is completely unpredictable. Random noises (in general, non-Gaussian) act on both the dynamic system and the state observation channel, which may also be nonlinear. The proposed solution is based on three main approximating assumptions: 1) the optimal control problem is stated in a receding-horizon framework where v_t⁰ is assumed to remain constant within a shifting-time window; 2) the control law is assigned a given structure (the one of a multilayer feedforward neural network) in which a finite number of parameters have to be determined in order to minimize the cost function; and 3) the control law is given a “limited memory”, which prevents the amount of data to be stored from increasing over time. The errors resulting from the second and third assumptions are discussed