  This paper presents a new model-based algorithm that computes predictive
optimal controls on-line and in closed loop for traditionally challenging
nonlinear systems. Examples demonstrate the same algorithm controlling hybrid
impulsive, underactuated, and constrained systems using only high-level models
and trajectory goals. Rather than iteratively optimize finite horizon control
sequences to minimize an objective, this paper derives a closed-form expression
for individual control actions, i.e., control values that can be applied for
short duration, that optimally improve a tracking objective over a long time
horizon. Under mild assumptions, actions become linear feedback laws near
equilibria that permit stability analysis and performance-based parameter
selection. Globally, optimal actions are guaranteed existence and uniqueness.
By sequencing these actions on-line, in receding horizon fashion, the proposed
controller provides a min-max constrained response to state that avoids the
overhead typically required to impose control constraints. Benchmark examples
show the approach can avoid local minima and outperform nonlinear optimal
controllers and recent, case-specific methods in terms of tracking performance,
and at speeds orders of magnitude faster than traditionally achievable.
