  Approximate dynamic programming (ADP) faces challenges in dealing with
constraints in control problems. Model predictive control (MPC) is, in
comparison, well-known for its accommodation of constraints and stability
guarantees, although its computation is sometimes prohibitive. This paper
introduces an approach combining the two methodologies to overcome their
individual limitations. The predictive control law for constrained linear
quadratic regulation (CLQR) problems has been proven to be piecewise affine
(PWA) while the value function is piecewise quadratic. We exploit these formal
results from MPC to design an ADP method for CLQR problems. A novel convex and
piecewise quadratic neural network with a local-global architecture is proposed
to provide an accurate approximation of the value function, which is used as
the cost-to-go function in the online dynamic programming problem. An efficient
decomposition algorithm is developed to speed up the online computation.
Rigorous stability analysis of the closed-loop system is conducted for the
proposed control scheme under the condition that a good approximation of the
value function is achieved. Comparative simulations are carried out to
demonstrate the potential of the proposed method in terms of online computation
and optimality.
