Two challenges for systems and control

Systems and Control is now a mature subject with a deep mathematical theory and a powerful engineering methodology; its roots lie in antiquity but it emerged in the form of the Watt governor more than two centuries ago as an enabling technology of the Industrial Revolution, and its development since then involves critical contributions in a broad range of domains stretching from the Space Race to the economically vital area of industrial process control. However, the current natural and designed environment presents a vast array of control problems generated by systems of immense complexity which are often populated by subsystems possessing both discrete and continuous states and which, moreover, display so-called intelligent behaviour. A sample would have to include (i) the need to stabilize and control in a distributed manner the huge communication, information, transportation and economic networks of the modern world, (ii) the control of systems such as agricultural, fisheries and ecological systems with the objective of achieving sustainability, (iii) the management of the current integration of distributed and intrinsically stochastic renewable energy sources into deregulated and immensely expanded transmission networks serving users of all scales, and, finally, the most difficult problem area of all, (iv) the effective stabilization of the planet´s climate through political and economic intervention based on system theoretic concepts and grounded in the physical sciences. Clearly the problem areas above demand a range of responses from various disciplines, but they raise at least two specific, interlinked challenges of a basic nature for Systems and Control: 1. To create fundamental theory and effective methodology to analyze and control systems with both discrete and continuous states and dynamics. Despite two decades of advances, Hybrid System theory is still in an early stage of development, for instance continuous-to-discrete state aggregation still lack- an adequate theory and so hierarchical control is in its infancy. Furthermore, work taking inspiration from the life sciences, such as gene controlled and self-healing systems, is limited to say the least. 2. To create adequate methods for the analysis and decentralized control of networked systems of huge complexity with social characteristics. While there has been progress in the development of game theory for stochastic dynamical systems, in particular Mean Field Game (MFG) theory, many challenges lie ahead, two examples being (i) relating MFG methods to the currently emerging information based control theory wherein the capacity of each of the feedback channels in a network plays a critical role, and (ii) the development of a dynamical game theory of the formation and stability of coalitions. In addition, the state aggregation problem introduced in the first challenge area also naturally falls under this second heading.