In particular, the VPG was run on the same network tens of thousands of times, but with the order of constraint placements randomly reshuffled each time.
Interestingly, the set of independent constraints that this recursive process identifies is not unique, because the identification of redundancy depends on the specific ordering of constraint placement.
He compared the constraint smoother and unconstrained regression splines and concluded that the former can have better performance when the order of derivative constraints increases.
The ordering of these constraints is FAITH-INT, CONSISTENCY, STRENGTH.
In general, the order of the state constraints in optimal control problems is defined through Lie derivatives as we will show on the example in Section 7.1.5.
In this order of ideas, displacement constraints involving clamped outer radius and rigid core at the inner radius, deriving from the theoretical reference model of Spot Joint Element, are taken into account.
This paper presents a technique of multi-objective optimization for Model Predictive Control (MPC) where the optimization has three levels of the objective function, in order of priority: handling constraints, maximizing economics, and maintaining control.
More precisely, the Lie derivative is used to define the order of the state constraints, the Lie and Poisson brackets are used to analyze the singular extremals and to derive higher order optimality conditions, and the optimality conditions (order one, two and higher) are used to analyze the chattering extremals (see Section 3.4 for the chattering phenomenon).
The conditions followed each other in a random order that was different for every participant, with 2 constraints on the order of conditions: The first constraint was that no condition was repeated twice in a row.
In fact it is from such eruptions that a civilization learns; and its notions of order, its constraints on passion and its ideas of propriety shape war in turn.
