control science, that there was a perception. âthat some ... nique in computer science that some control engineer .... these subjects are just as hard and time con-.
Some Remarks on Control and Computer Science W. M. Wonham Therefore it is necessary to follow the
common; but although the Logos is common to all, the many live as though each had his own private understanding. Heraclitus of Ephesus In seeking guidance on what was expected on this occasion, I was told not to prepare either a survey or a tutorial. It was alsostated that the occasion had arisen (in part) because of an “identity crisis” among workers in control science, that there was a perception “that some of our colleagues are wasting time on nonsense” (no specifics provided or sought), and that, in any case, one was s u p posed to be controversial and ”advocate” a firm position on something or other. Personally, I have not noticed an identity crisis; nor do I mind if my colleagues waste time on nonsense (if one were bothered by it, he could change his problems or change his colleagues), and it runs counter to my nature to advocate firm positions on anything much. Unfortunately, these disclaimers did not have the hoped-for result of getting me off the hook.
The time is out of joint. Oh, cursPd spite That ever I was born to set it right!
Control Science Anyhow, it seems to me that control science is actually alive and kicking. How could matters be otherwise-with so many exciting control problems lying about unsolved, so many tools to attack them with lying ready at hand, and (in some places at least) sufficient money around to support the corps of dedicated control scientists willing to work on them? Maybe all that is really bothering some people is that a lot of the exciting work on control problems is being done outside the community of the blue-and-white journal! And, of course, there is the public perception that space vehicles and nuclear rePresented at Santa Clara Workshop, Santa Clara University, Santa Clara,California.September 18-19, 1986. Professor W. M. Wonham is with the Control Systems Group of the Department of Electrical Engineering, University of Toronto, Toronto, Ontario M5S 1A4, Canada.
actors and grandiose arrangements for national defense and so forth are controlled . . . “bycomputers.” If you are prone to identity crises, then admittedly all this is truly enough to make you paranoid at social gatherings. So I guess the issue we ought to address is what to doabout computer science. In one sense, it is not an issue at all. Look at all the ongoing activity (e.g., SOCOCO 86) in real-time languages, computer-aided design, AI (artificial intelligence) and logic-based approaches to adaptive control, distributed control systems, fault-tolerant control software, and on and on. As far as I can see, there is hardly a single issue, idea, or technique in computer science that some control engineer somewhere has not picked up on already and is adapting to his purpose. It seems that in the engineering world, crosscultural communications aretoo good and the economic incentives are too high for matters to beotherwise. In absolute numbers and in their conviction of a manifest destiny, these people undoubtedly rival the blue-andwhites still at work (say) on the Riccati equation; and this is said with admiration for all.
New Control Scientist Therefore, it is not clear to me what specifically the issue (if any) is or ought to be. However, I am supposed to advocate something, so let us set up a mythical being and follow his adventures.Let us postulate a compleat control scientist, named Boffin (say), who wishes to come to grips intellectually with the Computer Revolution and the New Paradigms. Suppose, starting the wmng way, Boffin tries to read a few textbooks on computer science. Now these are, as a class, probably the most boring kind of textbook ever written, not infrequently ranking with instruction manuals on automobiles and washing machines. The reason for thisis simply that computer scientists would really prefer to compute with programs than write about programs; like driving a car, it is much more fun that way. And in this connection, Boffin soon notices a first cultural difference: by and large, computer people tend to think procedurally while control people tend to think descriptively. At least it appears so.
This is because control people (compleat ones) have been used to formalizing their problems for a long time now. In fact, computer science textbooks often remind you of classical control texts of the 1950s: in those days, there were already a lot of solutions, but the author would never quite tell you what the problems were. Because the solutions were good ones, people are still trying to figure out exactly what those problems were. Boffin begins to suspect that the computer scientists are actually solving control problems. So he perseveres. One day he stumbles on something that is really good: A Discipline of Programming, by Edsger Dijkstra. Light dawns! Computer science is really about the intelligent management of complexity; it is rooted in mathematical logic and mediated through formal language. It would still be interesting (if not fun or profitable) even if there were no computers. Brimming with enthusiasm, Boffin learns Pascal and C and LISP and PROLOG and plunges into the computer science research literature. A horrendous experience. A zoological garden of private understandings, bottomless in extent, nothing like “ X = Ax + Bu” anywhere to be seen,
Ah qUMto a dir qual era P cosa dura esta selva selvaggia e aspra e forte che ne1 pensier rinova la paura! But pearls are found, too many to enumerate here: Boffin particularly notices Chomsky on formal languages, Kleene on regular languages and automata, more of Dijkstra on structured programming, Hoare on communicating sequential processes and logic for program verification, Pamas on modularity, Manna and Pnueli and Lamport on temporal logic and concurrency.
New Control Science Boffin now takes stock. It seems that, with all these ideas at one’s disposal,and all these languages, and nifty micros to play with, control science must be ready and set for a great leap forward, to a new level of generality and complexity that Boffin (brought up as he was on poles and zeros andmatrices and differential equations) had hitherto never
0272-1 70818710400-0009 $01.OO 0 1987 IEEE April 1987
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imagined. He now tends to think of standard control science as pretty much limited to small systems and pretty much restricted to objects that live in linear vector spaces, finite-dimensional or infinite as the case may be. The new control science (as yet but mistily envisioned) will surely be vastly more powerful, able to organize and coordinate the small systems into great beautiful structures (see again the SOCOCO catalog of handy means to this end). Of course,the general system theorists have been saying exactly that for years, but we all know about general system theorists.’ Now is the time to do honest work. But how is Boffin to proceed, faced with such a potpourri of notions of which he has acquired at best a half-baked grasp? In the best tradition, he starts by identifying three main foci: The first is mathematical logic. The second is formal languages. The third is (wonderful!) extended state machines (ESMs). Needless to say, none of these subjects has ever been emphasized in the academic curricula of control scientists. No wonder if there is a sense of unease! The first two of these subjects are just as hard and time consuming to learn as differential equations or anything else; luckily, graduate students devour them much faster than their senescent supervisors.
Mathematical Logic When pressed, Boffin maintains that the reason for mathematical logic is obvious: not only is logic at the bottom of computer science (Godel, Church, Turing, . . .) but it is also thebasis of problem-solving in artificial intelligence (Robinson, Kowalski, . . . and the PROLOG language). Furthermore, firstorder logic and its extension to temporal logic is a very natural framework for specifying how our ESMs (see below) ought to behave. So Boffin has to learn logic. Formal Languages
A dreary subject, by and large, but maybe that is because of the unmotivated way it has often been presented. It was certainly not invented for the benefit of control scientists and, for instance, the traditional (Chomsky) classification is perhaps not of great relevance to whatever the needs of control scientists may turn out to be. Nevertheless, the notion of effective generation and recognition of sets of symbol strings via canonical ’The hard core of their December 1980 meeting tastefully located in Acapulco was fuzzy; a few control scientists attended, but only out of a sense of professional responsibility.
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state transition structures is one of the great core ideas of system theory. So Boffin has to learn something about formal languages.
Extended State Machines This is where it all comes together. The qualifier “extended” is a bit of hype; it was thrown in to forestall everyone’s immediate negative recollection of some course in automata theory, automata that never seemed to do anything very interesting. The ESMs are more lively. They can have spontaneous transitions and forced transitions, and they can be coupled together in various sons of ways that embody communicative, cooperative, and hierarchical relations among them. In other words, they support another great core idea of system theory: modularity.‘ Perhaps most important of all, an ESM can be set up as the control structure of a computing program, namely, transitions of the ESM may embody program steps involving variable assignments. In fact, an ESM transition can be taken as a 5-tuple consisting of a transition label (the only item that would appear in the classical case), an enabling condition or guard (this can serve to model nondeterminism among other things), a program step as mentioned previously, and (for real-time modeling) lower and upper time bounds such that once the transition is enabled then it must occur between them. So an ESM offers quite rich modeling possibilities, either as a “plant” (something that computer scientists do not seem to recognize the existence of) or as a controller. Already there exist commercially available computer languages, such as CONIC. that model ESMs very directly or, from the reverse point of view, for which ESMs furnish an abstract operational semantics.
New Control Problems It is now about time to wind this up. All that is left to do is spell out exactly what problems our born-again Boffin intends to solve by putting this machinery to work over the next 10 years or so. I believe that is our present mission. Now, what would anyone expect to happen? If historical experience is a guide, we could look at linear system theory and say, well, there was an initial period ’The principle that big systems will work properly if (and only if?) they are put together in the right way from small systems that work properly. Sometimes associated with togdown design and sometimes with bottom-up design; for as Heraclitus also pointed out c. 500 B.C., the way up and the way down are one and the same. Technical tools in aid of modularity include abstract data structures and object-oriented programming.
when design techniques were accumulated, followed by a period in which the subject got codified and formalized into a number of key problem types. a process that is still going on. In that process, seminal conceptual discoveries were made, like controllability and observability and canonical realization and H , optimization. And these led in turn to new design techniques. Boffin guesses that in our new subject area the scenario will not be much different. For the benefit of funding agencies, we will give the area a Mme. What about discrete-event control (or system) theory? In other words, the control theory of discrete-event dynamic systems (modeled, let us say, by our ESMs). In broad terms, Boffin has already identified the background subjects he needs to know in order to make progress. Now he identifies the following problems: How do you formally specify and form d y reason about discrete-event dynamic systems (DEDS)? In particular, if you have a DEDS, can you find an algorithm to decide whether it satisfies a given set of real-time specifications? What isthe complexity of such a decision procedure? Given a DEDS and set of specifications, can you formulate and solve the existence problem for a controller? When is your solution algorithmically effective? When is the existence problem solvable in some sort of optimal fashion (say in the sense of maximal behavior)? What are the algebras that formalize the notion of modular combination of DEDS? How is modularity exploited, namely how do you translate “abstract” (i.e., global) synchronization expressions into statements concerning local controllers and the communication between them? Again the mystical number three. Boffin could go on to five, seven, . . . , but that would be giving too much away; so at this point, we leave Boffin to his fate. After all, who really wants to rescue his colleagues from wasting time on nonsense? Exciting times, indeed. All things are in flux. With his belief in the inevitability of change but also in the stability that persists through change, Heraclitus’ vision might serve us well today.
Acknowledgments Jonathan Ostroff and JohnThistle made helpful comments. “Boffin” was suggested by Anthony Graham. I have plagiarized a number of well-known poets and computer scientists; their identification is left as an exercise for the reader.
IEEE Control Systems Magazine
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