🚀 go-pugleaf

jwiegand@moe.eng.temple.edu (James Wiegand) writes:

>In article <1h08q1INNl15@flop.ENGR.ORST.EDU> saleh@ece.orst.edu (Hassan Saleh) writes:
>>
>>   Is there any public domain program available for the solution
>>   of nonlinear optimal control problems ? I tried using colnew
>>   to solve the resulting two-point boundary value problems but
>>   I always get "singular elimination matrix" some where.
>>
>>   H. I. SALEH

>According to what I've heard, there is no single method for nonlinear
>control systems in general. 

>jim
>... willing to be proven wrong.

I'm not an expert in this area, but I think the only general-purpose
approach for nonlinear control systems is the brute-force approach.
That is, you generally can't solve the math analytically (sometimes
it's difficult enough just to formulate it). Therefore you should
apply an adaptive or learning controller to try to optimize your
performance measure empirically, on-line.

In the 60's, King-Sun Fu and others took the approach of partitioning
state space, and "learning" the (sub) optimal control action for
each element of the partition, on-line. The resulting "lookup-table"
allows the controller to select the best control action for each
point in state space. This "brute-force" approach
has the potential for solving any control problem, linear or
nonlinear. The difficulty is that with some systems the partition
must be extremely fine in order to get sufficient accuracy. Also,
since you are trying to learn the best control action within
each partition element, having a fine partition means that your
"training time" becomes large. 

I adapted the lookup table approach in my dissertation, using
a partition which is successively refined to obtain desired
accuracy more quickly and flexibly. I'll be presenting this
approach at the AAAI Spring Symposium on Machine Learning. I'm
hoping it will resurrect the lookup-table approach, in light
of the vastly greater speed and memory available in today's
computers compared with those of the 60's. 

I'd be interested in getting the perspectives of others on this
topic... If anyone's interested in digging up my dissertation (which
I've decided is a bit hard to read!), it was 1989, Univ. of 
Pennsylvania. It also goes into applying this approach hierarchically.

Back to the original question, another brute force approach which
might be useful is artificial neural networks...

-Ralph

-- 
Ralph Gonzalez, Computer Science, Rutgers Univ., Camden, NJ
Phone: (609) 757-6122; Internet: rgonzal@elbereth.rutgers.edu
--