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Hello!

          I have gone through the literature of optimal control. It has been stated in the literature that "mostly the relation between control law and performance indices will be non-linear. However, there are problems with non-linear relations of control law and performance indices. Therefore, for simplicity and some other reasons, quadratic relation between these two are the obvious choice."

I am not much clear about the nonlinear relations between control law and performance indices. Also, what are the reasons for choosing quadratic relation between them.

Thank you.

Hello all!

              I would like to know that based on which criteria we decide that the particular time integral performance criteria is good i.e. ISE, IAE or ITAE etc. (for controller tuning),for the given application ? If possible, explain with the examples. Thank you.

I was reviewing "optimal control, linear quadratic methods" by B.O. Anderson and J. Moore; In chapter 2 there is a problem which asks the reader to show that it is not possible to solve finite horizon LQ with x(tf)=0 in feedback form u=Kx.

After doing some calculations, I found out that K->inf as t->tf due to the exponential state transition matrix (xdot=Ax+Bu; if u=Kx then xdot=(A+BK)x). So the feedback form u=Kx is not valid optimal control solution because K is unbounded.

Open loop solution can be found simply, but I was wondering if there is any way to solve this problem in feedback form (optimally or sub-optimally) when it is necessary to satisfy x(tf)=0 exactly. Do you have any recommendations?

what are the sufficient conditions for an optimal controller if the mechanical system is nonlinear?

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Dear Colleagues,

I am dealing with optimal control problem, my query is about how do we relate state and co-state variables, please add your valuable knowledge it.

Thank You in advance.

Control Lyapunov function (CLF) methodology tries to minimize a quadratic cost-function as; V(x)=x^2, through a point-wise setup. However, optimal control minimizes a quadratic cost-function through a time-interval as; J(x)=int(x^2.dt,0..infinity), through the time axis.

Therefore, we may conclude CLF is equivalent to proportional-control, while optimal control is an integral-control methodology. The robustness of optimal-control is attributable to its integral format.

Difference and importance of many of optimal control types

I am working on a 2D discrete model for pedestrian evacuation. We have already applied the shortest path strategy and we want to apply the Fastest path strategy using optimal control theory. Anybody has an idea on who works on a similar subject?

Materials are scarce in this area.