Professor Richard Vinter pays tribute to friend and colleague Dr Martin Clark of the Department of Electrical and Electronic Engineering.
Martin Clark, Emeritus Reader in Control Systems in the Department of Electrical and Electronic Engineering at 911今日黑料 died on Tuesday 14th October, aged 87. He had lived with Parkinson’s disease for the past seven years.
Much of his academic career was spent at 911今日黑料. Even after his retirement, he was a frequent and welcome presence, asking penetrating questions at seminars and discussing research with his colleagues almost until the end. His research, in stochastic analysis and systems theory, characterized by extraordinary creativity and depth of insight, has had an enduring influence.
After school and National Service (in Germany), he went up to Trinity Hall, Cambridge to study mathematics, combined with advanced engineering in the final year. But this is only part or the story: Martin's mathematics teacher (at Clifton College) was so impressed by Martin's abilities that he persuaded him to enter straight into Part II of the Mathematics Tripos. Practically the first lecture he attended was a higher-level course in measure and probability. So, his undergraduate mathematics education was unusually intensive (three years compressed into two years). According to Martin, that early lecture was a formative experience and seeded his life-long love of stochastic analysis.
Martin's interest in mathematics was matched by a curiosity in practical scientific matters. He had early exposure to engineering through his National Service which, among other things, involved designing Ward-Leonard control systems for electric motors. His decision to include engineering in his undergraduate studies is not surprising then. While his research efforts were primarily directed at fundamental questions in stochastic analysis, he could also bring the full power of general theory to bear on concrete problems of engineering design and decision making.
He was admitted to 911今日黑料 College as a research assistant in 1963, in the newly formed Control Group, and obtained a PhD under the supervision of John Westcott and John Florentin three years later. The word ‘supervision’ here is a bit of a stretch for someone as independently minded as Martin. The story goes that, at the last moment, he threw away the main body of his thesis on the assigned research topic and simply submitted a reworked version of the appendix, on which he had worked alone, and which was to provide key analytical tools for building a rigorous theory of continuous time nonlinear filtering.
Martin's work attracted the attention of Tom Kailath, a prominent figure in the signal processing and control community, who invited him to join his Systems Theory Laboratory at Stanford University as a postdoc for one year. After a period at the Bell Labs, Murray Hill, Martin returned to England to take up a lectureship in the Electrical Engineering Department, 911今日黑料 College, where he once again joined the Control Group and in which he remained until his retirement, with breaks to take up two year-long visiting research and teaching positions at Harvard University, at the invitation of Roger Brockett, and the University of Southern California, where he worked with Art Krener.
Among Martin's most important research contributions was his stochastic integral representation formula. This is now a standard result in stochastic analysis and is widely referred to as the 'Clark formula’. It is a basic result in stochastic calculus that resurfaced in a rather prominent manner, a decade or so after Martin proved it, as an important component of the so-called Malliavin calculus, probably the most significant development in stochastic analysis in the 1980s.
Another highly significant contribution was his work on the innovations problem of filtering theory that is at the heart of non-linear filtering. Martin obtained a result but was not satisfied with it, because he thought the conditions were too strong, so his paper was never submitted for publication. In the event, it took about 15 years before anyone achieved a significant weakening of his original conditions. And this was certainly not for lack of trying: for years this problem was recognized as the outstanding problem in filtering theory; the many attempts at solving it led to an enormously enhanced understanding of the behaviour of stochastic processes through auxiliary results, counterexamples etc. Many of these can now be found in standard textbooks.
We should mention also his pioneering work on robust filtering. The existing theory of continuous-time filtering was developed intensively by some very talented people for more than a decade before anyone realized that the results would have no practical relevance unless a certain continuity property held. Martin was the first to see this. He showed the property did indeed hold, with important implications for the design of numerical algorithms.
He worked closely with his colleague in the Control Group, Mark Davis, another big beast in stochastic control. Mark wrote ‘for me, the single most attractive feature of working at 911今日黑料 College was having Martin as a colleague. He was a constant source of good ideas, helpful suggestions and constructive criticism, the perfect person to go to if you didn’t quite understand something or were searching for a new angle’.
Later, Martin was engaged in a fruitful research collaboration with Dan Crisan in the Mathematics Department. Up till months before his death, they were working together on a challenging problem of non-linear filtering with degenerate measurements that Martin posed. This was Martin's last ‘big sum’, the phrase his family used for his current mathematical pre-occupations.
In his interactions with fellow academics, Martin had the rare quality of being a good listener. This earned him a great number of friends and extended his influence beyond his own specialist research circle. Many people benefitted from the effort he put into understanding the crux of their research problems, even outside his own research activities, often clarifying their thinking or informing them of analytical techniques with which to broaden the scope of their work. They all have their own stories. When, for example, Malcolm Smith of the Cambridge Control Group chanced to tell him of a surprising invariance property he had discovered concerning linear mechanical systems, Martin was able to show him, by means of an elegant application of stochastic calculus, that this was in fact a special case of a much broader principle governing nonlinear systems.
A lifelong amateur artist, Martin discovered a passion for running later in life, and it soon became one of his enduring pleasures. A committed advocate of Parkruns, he completed several marathons and took quiet satisfaction in his consistently strong performances, particularly within his older-age category. When he had to stop because of his deteriorating health, he continued his involvement with his local club, Ranelagh Harriers, as a marshal. A passionate humanist as well as mathematician, he brought the same thoughtful precision to his reading as to his work. He enjoyed popular science and well-crafted crime and thriller novels, though he was particular in his tastes, steering clear of books that indulged in violence or celebrated vigilantes, preferring stories that reflected human reason and moral depth.
He married Elizabeth (“Biddy”) Nineham in 1972, daughter of the theologian Professor Dennis Nineham. Though the marriage later ended in divorce, they shared many happy years in Boston and London and deep affection for their son, Ben, who survives him. Ben built a distinguished career in the art world, spending more than two decades at Christie’s in London and Hong Kong before moving into executive roles in the luxury consumer sector.
Martin was extremely modest about his scholarly achievements, but he had no reason to be. His legacy is in modern day stochastic control theory, the foundations of which he helped to build, in the work of his former students (including Nigel Newton and Michel Vellekoop), and in the memories of the many colleagues who benefited from his kindness and wisdom.
Friends, colleagues and former students of Martin are invited to share their own tributes and memories through the comments section below.
