  This work presents a suboptimality study of a particular model predictive
control with a stage cost shaping based on the ideas of reinforcement learning.
The focus of the suboptimality study is to derive quantities relating the
infinite-horizon cost function under the said variant of model predictive
control to the respective infinite-horizon value function. The basis control
scheme involves usual stabilizing constraints comprising of a terminal set and
a terminal cost in the form of a local Lyapunov function. The stage cost is
adapted using the principles of Q-learning, a particular approach to
reinforcement learning. The work is concluded by case studies with two systems
for wide ranges of initial conditions.
