To Z. Khan: could you explain more about D-MARC and how it works?

It seems that there is some misunderstanding between my question and you. D-MRAC is one of the adaptive methods that is criticized by engineers, and the reason has already been explained in my question. The reference that you listed is the application of D-MRAC to PUMA manipulator, where, indeed, the controller gains are bounded, yet, one does not know where they would go.

Still, I would like to thank you for your efforts.

To Ilhan Polat:

Thank you for your in-depth answer and comment.

One can say that adaptive control is (globally) convergent in the sense that the tracking error is convergent while the parameter estimation error not (only bounded). This latter property is both elegant and problematic(e.g., parameter drift may be induced). The robustness problem (i.e., parameter drift) is not due to the specific system but inherent when using adaptive control.

Adaptive control at the present stage is not mature, which yet does not prevent it from being a standard control approach. The reason of saying so is that adaptability is indeed ubiquitous in the activities of humans and animals, and then why not in control of physical plants (perhaps in the near future). Of course, it does not mean that it is very suitable to all cases, e.g., the process control that has a quite slow bandwidth. However, even in that case, I do not see an adequate reason of refusing adaptive control, which may be employed to improve performance in the long run.

Generally, application tends to be somewhat conservative when compared with its counterpart "theory". There is one famous saying (by some big man) that this gap is the impetus of science and technology.

There is not a strategy control that can overcome all control problems. The main objective for adaptive control is for parametric identification of a plant whose parameters are unknown, in most cases assumed as unknown but constant. We can not design a control law for a system whose parameters are unknown, so, in some way, we must identify its parameters, to then sinthesize the controller. Actually, there are some intelligent control techniques which offers to design a not based in the model controller, where the determination of the system's parameters is not a necessary task, as fuzzy control and neural control. Although this latter technique requires of the implementation of an adaptive law in order to adjusting the weights of the neural network.

To Fransisco Jurado,

Thank you for your intuitive explanation.

The neural control with adaptation has the similar robustness problem encountered in the standard adaptive control based on linearity-in-parameters property. Even if it is not based on the mechanism based physical model of the plants, the neural control stands on the rule that there is a neural model corresponding to the physical plant, and the updating of the weights still comes across the problems, e.g., parameter drift, etc.

As pretty commonly understood and as also expressed in this exchange of messages, Adaptive Control is generally identified with estimation of parameters that will then do the job.

I read what was written above about “academy” and Adaptive Control. Although I may play Prof or Dr., I myself am an Engineer first and so, first of all, I am interested in the practical aspects of Adaptive Control, even though, to make it really safe, I may be have to use some very high-level Math. So, if one does not use Adaptive Control, one uses any of the classical fix design methods and hopes that the resulting design would still cope with the real system, even though the actual plant parameters are not the nominal parameters used in design. The first and basic idea of Adaptive Control actually was to have the right control gains fit the right situation. Even in a fixed environment with just one main loop gain, one would rather have a low gain when no maneuver is required, because a high gain would only amplify noise and waste fuel in vain. Then, when better performance is required, the adaptive gain should raise, do the job and then come back down.

At an Adaptive Control meeting at Yale, I presented a simple manipulator and using a simple fixed PD controller, I showed good results, so I asked: “…Then who on Earth needs Adaptive Control?”

Instead of answer, I just added some noise, negligible for all (other) practical purposes. Here, even though there was no required motion, the robot started vibrating like crazy as if it were just going to brake, because good performance require high fixed PD gains.

When I replaced the fixed controller with what I call Simple Adaptive Control (SAC), the robot was standing still and when required, was performing very well. The issue is that the random noise does not affect the integral adaptive gains too much and so, they were small. When performance was needed, the gains went up, yet the required dynamics was dominant and the response was good in spite of the noise that now was irrelevant in comparison with the dynamics.

The problem is that you cannot just replace fixed control gains with time-varying gains and guarantee stability, even if the gains only vary within some “admissible range” that was established for fixed gains (root locus, etc.).

Here, one must learn about positive Realness, Passivity and all that and guarantee that the controlled plant satisfies some conditions before applying Adaptive Control. However, once these basic conditions are satisfied, the rate of adaptation does NOT have to be slow, SAC allows obtaining performance that cannot be obtained otherwise, etc.

What recent users observed that even using SAC as an Add-On to a fixed control design improves performance (time and errors) of even the best prior design. Besides, it maintains performance in spite of internal parameter changes.

If you write “Simple Adaptive Control” on the web, you get many references, both theory and applications of robots, reentry vehicles, UAVs, missiles, etc.

In a very recent review I tried to gives a brief presentation of the various important aspects that are related both to robust stability and performance of SAC:

I. Barkana: “Simple Adaptive Control - A Stable Direct Model Reference Adaptive Control Methodology - Brief Survey,” International Journal of Adaptive Control and Signal Processing (published On-Line) DOI: 10.1002/acs.2411

I would like to thank Prof. Itzhak Barkana for the in-depth and interesting answer. May I say that performance can possibly be obtained by low-gain (thus robust) adaptive control, yet by high-gain (thus not so robust) fixed controller? I think this is the interesting point of adaptive control or SAC. I will spend some time to study your survey paper. Great thanks.

As I already wrote, even though I may play Prof or Dr., I myself am an Engineer first, so first of all please forget the Prof and Dr and let me be Itzhak (to make it easier, Itz-Hak)

BECAUSE of the general opinion about Adaptive Control, I will not even try to convince you BEFORE you play with some examples of your own, and yet, first please read again the Yale story in my previous message. Good performance with a fixed controller implies having high gains always. After some reading, you will see that the SAC methodology not only uses high gains only when needed, but also supplies "help" to the internal loop, so that it can reach the desired performance without requiring too high internal loop-gains.

@Hanlei Wang

If you manage to read the first sentences without turning them upside-down, you then see down the road why practitioners are ENTITLED to be confused and very careful with adaptive control, with the conditions that it seems to require and with the “bursting” and other dangers that only seem to wait for the right opportunity to occur.

Then, you may see how I first try to explain to myself how just one gain can became dangerous even within the so-called “admissible” range and only because is time-variant. From there, one must ask how stability CAN be guaranteed.

However, linear and nonlinear are so different that it is even a shame that I used them both in same sentence. Therefore, without implying that the multivariable linear system theory is that simple, the theory of nonlinear systems is much less simple and needs patience.

And, contrary to what might have been hinted here, your own experience with your control object and classical design is MORE important than any new approach that one might try to teach you. Moreover, as my customers know, if you are satisfied with the performance that fixed controller provides, I wouldn’t even think of using adaptive control. However, because in modern times customers and managements keep requiring better and faster, then you may find out that a small adaptive control addition may come instead of having to replace parts and to buy more expensive equipment and follow this with a totally new redesign.

My UAV paper “Classical and SAC design…” mentioned in the review paper shows exactly what I mean. First, you do some predesign and then let the adaptive Add-On “squeeze” better performance, yet ONLY after the robust stability of the adaptive control system is guaranteed.

More important, try to have some fun. :-)

@Itzhak Barkana

Personally I quite appreciate and agree with your viewpoint about adaptive control, although, it seems a pity that such an unhappy discussion happened. I think there is no need to feel so terrible about this since, this is indeed the gap between theory and application (which is believed to be reasonable and natural). I will continue to give my support to such efforts that aim to possibly enhance the application of advanced control theory.

Every approach has its limit, e.g., typically one achieves something at the expense of losing others. In this sense, "always good" seems not to be a scientific word since nothing is always good under all conditions. In most structural environments, PD control is indeed enough. But when high performance is required, as demonstrated by Prof. Itzhak Barkana, PD control is not robust to noises due to the high-gain feedback. In this case, adaptive control is possible to result in high performance by low-gain feedback and this is possible due to the adequate exploitation of the control input energy. For example, in the tracking problem for robots, adaptive control contains an adaptive compensation of the unknown robot dynamics, while for the same problem, high-magnitude PD control would be required since PD control is not complex enough to reflect the nonlinear system dynamics. However, it seems that the application of adaptive control is mainly hindered by its complexity or the requirement of so many things if we want to use adaptive control in an appropriate way.

Finally, I would like to thank and appreciate all the answers to this question, which indeed enrich my knowledge on adaptive control. Hope that these play the same role for those who are interested in adaptive control.

In general, we think about maintaining performance in spite of uncertainty and here there are many LINEAR Robust Control techniques that take care of this or that variation.

However, I thought about a simple problem: a voltage stabilizer for a power network. Everything is alright and the system maintains the 400 V and works like that for decades.

Nevertheless, In parallel with the "normal" main constant gain, you decide to add an adaptive gain. This has no effect whatsoever, so people keep asking you "why."

Suddenly, a larger load, larger than "normally" predicted, occurs and the main internal gain drops below the "admissible" value. This is certain disaster for the linear system. (Even for normal loads within the "admissible" range, just a faster load variation rate than predicted may have similar results)

However, the adaptive gain senses the tendency of the output voltage to go away from the desired value and brings the total gain back to a “normal” value, so the disaster is replaced by just a little blink on the output voltage.

Barkana I, Fischl R. A simple adaptive enhancer of voltage stability for generator excitation control. Proceedings of the American Control Conference, Evanston ,IL, 1992; 1705–1709.

Ritonja J, Dolinar D, Grcar B. Simple adaptive control for stability improvement. Proceedings of the 2001 IEEE International Conference on Control and Applications, (ICCA), Mexico City, Mexico, 2001; 29–35.

When people read my messages that try to encourage people to play with Adaptive Control, it is hard to believe that for me, the same Adaptive Control used to be the best joke around. That’s why I say "PLAY." Start with something simple, try some adaptation and go from there.

Now, even if one doesn’t believe that adaptive control can guarantee robustness with uncertainty,then who does? Fixed control?

Actually, assume that for your machinery, plane, etc., you use the best design method you have and get very good performance, robustness and everything, So, you are satisfied, only… this is your own opinion, because times have changed and now the customers and the management want 30% faster. Just think what effort, cost and new equipment you need and, assuming that you know exactly what to do, how long will it take to see the new machinery do what is supposed to do? And, does anyone expect to use THE METHOD and solve all problems?

Does anyone expect to use adaptive control instead of all of the above and have the new machinery or plane fly the very next day? Isn’t it worth spending some time just getting used with some of thethat adaptive control methodologies are around and see what may help where, even just to kill the idea?

About machinery, I happened to work for a Company that builds bonding machines for integrated circuits. The technology called wire-bonding has reached the “physical limits’ by 1993. One machine does not change its parameters too much during operation. However, two “identical” machines are so different that each must be tuned separately. Besides, almost any change of any mechanical part, not to even mention motors, requires retuning of the machine, so the best people were travelling around the world to do it. At the rate of 4 machines a month you may cope, yet at 400 a month is another story.

When I naively dared to ask why not adaptive tuning, this, of course, was received as a great joke. However, as it happens when people see no other choice, they decided to let me play. OK, now this is one place in this world where people do not laugh at adaptive tuning any more. The topic of “portability” which used to be the main topic every day of each meeting at the level of Vice President just vanished. There is a button that the operator pushes whenever some [part is replaced or if after a long time people feel any deterioration of the very fine precision and… that’s it. The technology that was "dead" by 1994, is very much alive and kicking. The speed that reached “the physical limit” is now about 4 times higher, same with accuracy (minimal distance between neighboring bonds.) When people ask if there is a proof of stability, I can say that at 4000 to 8000 machines per year, must be more than 100000 "proofs" and they must WORK, not to prove that some error is less than some epsilon.

Why don’t we hear more? Because when things work, they become Company’s internal knowledge.

Anyway, even though no method is “the general solution for the general problem," and even as at the start of my book I was careful to write "is by no means meant to eliminate or replace any other good idea" I think it is worth spending some time getting used with the idea.

I'd to like chime in with a "practioner" viewpoint, as I work with control within the process industries.

First, I'm developing an improvement to our nonlinear Fuzzy control which uses SPSA for direct controller online learning. I guess you could say it's model-free adaptive control, and so far the simulated results have been promising, but it was indeed hard to convince my boss of its usefulness before showing the results.

Second, I always get curious when people say all control must be validated with robustness and stability analysis. In the process industries it's so rare for anyone to know or care about robustness and stability that it's really amusing for me to read this on every academic article or forum. Even the "highly advanced" MPC comes with no such guarantees in practice, but no one cares.

Actually, how can you really prove the stability or robustness of a control system given a linear model, if in the real world no model is linear and your model is most likely wrong? In the process industry stability and robustness is checked visually after deployment by the application engineer and after that by the operators.

GREAT, Pedro!

> Actually, how can you really prove the stability or robustness of a control system given a linear model, if in the real world no model is linear and your model is most likely wrong?

Because people believe in things that they got used to.

Managers want you to report Gain Margin and Phase Margin that tell them how "robust" your system design is, even though, as soon as parameters vary, those estimates are as valid as next month weather prediction.

…and yet,

> Actually, how can you really prove the stability or robustness of a control system given a linear model, if in the real world no model is linear and your model is most likely wrong?

I can only hope that my message now is not misread and totally distorted like my very first message, yet the real answer to your question is: Slowly-slowly and patiently. 

Yes, we have to do something with our nonlinear applications even if theory does not cover everything (yet?).

So, if you do not trust ANY adaptive control, what are you going to do with your nonlinear system? Use a fixed-parameter controller and assume that it will “work,” because your nominal system, or even your linearized nominal system, is assumed to be a good representation for the real-world system? Yes, this is what we actually do and we get something that “works,” yet its performance is naturally limited, because one fixed controller must cover the entire expected range of changes.

So here, the first idea of adaptation is trying to adjust the controller parameters to the specific situation. From idea to proof there is quite a long way that may take many-many years. So, first of all, even if the system itself is linear, the adaptive algorithm is nonlinear and so, one must still prove stability of a nonlinear system. Then one ‘discovers” that it doesn’t help to find the “admissible range” of (fixed) gains and then let the adaptive gains vary only within this range. The danger actually is that actually it might work, yet only until it may just blow up and only because you used nonstationary parameters. So, adaptive control requires new concepts, such as passivity, almost passivity, etc. that can guarantee stability of the adaptive control system.

Then, these concepts must be carefully expended to nonlinear systems.

Why am I writing this? Because most of these things have already been slowly and patiently developed and they are out there already. It is not sufficient, though, to read something about some Adaptive Control methodology and assume you know it all. Actually the apparently required complexity of Adaptive Control scared me, too, like anyone else. However, because the need for fitting the appropriate gains to the appropriate situation is felt in any high precision motion control, aircraft, airspace, robotics, etc., if one writes Simple Adaptive Control on the web, one may find not only the necessary theory that has been developed, but also many applications in all the above mentioned domains.

The report “Adaptive Control? But is so simple!” that I uploaded to Research Gate is trying to briefly present the various ideas and methodologies that together made up a methodology that is not only easy to implement, but also guaranteed to work with some pretty difficult real-world problems.

Best regards,

Itzhak