When using Dynamic Programming, is there a way to limit the variation rate of the control inputs?
One way is to treat the rate of change of control inputs as model inputs, and penalize their extreme values through either a quadratic or more nonlinear cost function. With this approach, the control inputs will become model states and rate of change of control inputs will become model inputs.
in the same spirit, but somewhat simpler depending on the specifics of the problem: Discretize controls, consider an automaton that accepts only slowly changing controls (e.g. neighboring states), consider then the product of the plant and the automaton. Here, the automaton is a discrete version of the differential equation added by Ameet.
"...e.g. penalize the control inputs that change too fast by a very large number and then add them to the cost function value": The point is that in a standard, discrete-time DP setting, the cost depends on the current state, the next state, and the current control. If you want to punish changes of the control input, you have to supplement the state by future (or past) control inputs. There does not seem to be any other way. Besides, what is your advisor's opinion about all this?
...hm, if you have further questions, let me know. I saw that you also have an unanswered question about hybrid electrical vehicles. What exactly are you working on?
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