Greedy control revisited

Achieving asymptotic stability for discrete-time control-affine systems using one-step-ahead optimal feedback control is the subject of this paper. The optimal control solution is called "greedy", since at every evolution stage the feedback is thought to keep an instantaneous cost function to its minimum, without taking into consideration the consequences of such a control action. Using instantaneous cost as a Lyapunov function, new sufficient conditions for asymptotic stability under greedy control are reported. The result is applicable to discrete-time affine-in-control dynamic systems with multiple inputs.