Impulse Control – Concepts, Optimality Conditions and Computational Methods

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• Richard Vinter, Imperial College London
• Wednesday 22 March 2023, 16:00-17:00
• 909b.

If you have a question about this talk, please contact Giordano Scarciotti.

Abstract: The study of optimal impulse controls dates back to the early days of aeronautical control, when an impulse control was interpreted as the idealization of an intense fuel burn of short duration, for mid-flight course correction. For scalar impulse control inputs, limit taking, as a ‘classical’ approximating control converges to an impulse control, provides a well-defined concept of impulse state trajectories, which takes account of the instantaneous evolution of the state at the time of an impulse input. A striking feature of control systems with vector impulse inputs, explored by Bressan, Rampazzo, Sussmann and others, is that there is no longer a unique state trajectory defined in this way, i.e. the limiting state trajectory can depend on the way that the impulse control is approximated by classical controls. In optimization studies it then becomes appropriate to optimize over all possible state trajectories, despite this non-uniqueness phenomenon, because, ultimately for implementation, we will approximate our chosen impulse control by a classical control, and we can choose this classical to give an approximation to the most favourable impulse trajectory. This talk will dwell on underlying ideas, not technical details. We trace the history of impulse control, introduce different concepts of solutions to differential equations with impulse control that have been used (those arising in aeronautical control outlined above but also in mechanical control with impacts and mathematical economics). We address some of key questions that arise. Can we identify special cases of control systems with vector inputs, where impulse state trajectories are uniquely defined by limit taking? When are optimal impulse controls not needed, because we can achieve equally good results with classical controls alone? How can we derive optimality conditions and devise computational schemes that take account of non-uniqueness? We also cover interesting recent developments for time-delay impulse control systems. Here we encounter non-unique state trajectories even for scalar impulse controls, because of the way an impulse control can now interact with the time delays.

Biography: Richard Vinter obtained his PhD at Cambridge University followed by a postdoctoral position (Harkness Fellowship) at the Massachusetts Institute of Technology. Returning to England, he joined the EEE Department, Imperial College, becoming Professor of Control Theory in 1991. He is a former Head of the Research and Power Group in the Department and former Consul in the Faculty of Engineering. His research activities range over nonlinear systems, optimal control, dynamic optimization, filtering and stochastic optimization. He has published over 130 journal articles and two books, which include Optimal Control, a standard reference in this field. He is a Life Fellow of IEEE and a Fellow of the Royal Academy of Engineering. Jointly with M. Palladino, he received the SIAM J . of Control and Optimization Best Paper Award, 2017.

This talk is part of the Control and Power Seminars series.

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• 909b
• Andrea Picciau's list
• Control and Power Seminars

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