Keynote Lectures

Abstract
The impact of successful research in road traffic control spans across various domains, including the scientific, technological, social, and economic spheres. Its significance is profound, as it directly influences safety, quality of life, climate neutrality, energy resource utilization, and transportation costs. However, the development of effective methods and algorithms for road traffic management encounters notable methodological challenges. Traditionally, traffic control strategies have relied on infrastructure-based approaches. Yet, the rapid advancements in automotive technologies, traffic sensors, data processing, and communication have created unprecedented opportunities for the exploitation of connected and automated vehicles (CAVs), offering innovative solutions to longstanding traffic control challenges. This talk will address these challenges and advancements, beginning with an overview of classical traffic control concepts. It will then focus on emerging research trends that exploit the multi-scale nature of traffic systems, from the microscopic scale of the individual CAV to the macroscopic scale of the traffic flow. Furthermore, it will illustrate how these aspects can efficiently coexist within an advanced vehicular traffic control system that optimizes the traffic throughput and mitigates the environmental impact.

Abstract
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Abstract
Youla-Kučera parameterization is the parameterization of all linear controllers that stabilize a given linear plant. D.C. Youla (Polytechnic Institute of New York University) [1], [2] and V. Kučera [3], [4] independently discovered the parameterization formula in the late seventies. A comprehensive account of the result was provided ten years later by M. Vidyasagar [5]. A. Quadrat [6] generalized the parameterization results from lumped-parameter systems to a class of distributed-parameter linear systems. The survey paper by Anderson [7] summarized the first twenty years of theoretical developments. In contrast, the recent survey paper by I. Mahtout, F. Navas, V. Milanes, and F. Nashashibi [8] collects the latest developments and industrial applications; it also provides an impressive list of references.

Parameterization is essential when control systems are designed to be stable and meet additional performance specifications. The specifications beyond stability are achieved by selecting an appropriate parameter. There is a one-to-one correspondence between the set of stabilizing controllers and the set of parameters. Furthermore, the parameter appears linearly in the closed-loop system transfer function, whereas the controller appears nonlinearly. Selecting the parameter instead of the controller thus simplifies the design significantly. The system is made stable first, and then the additional specifications can be accommodated, one at a time. 

Performance specifications, such as optimality and robustness, are often conflicting and challenging to achieve using a single controller. In such a case, parameterization allows the designer to reconfigure the controller to reach satisfactory performance while guaranteeing overall system stability.

The Youla-Kučera parameterization is a fundamental result that launched an entirely new area of research and has been used to solve many control problems, ranging from optimal control, robust control, disturbance and noise rejection, and vibration control to stable controller switching and fault-tolerant control.
There is a dual parameterization, which describes all linear systems stabilized by a given linear controller. The parameter can then describe plant variations. This is useful for solving the problem of closed-loop plant identification. Open-loop identification is more straightforward, but it is often prohibitive to disconnect the plant. Identifying the dual parameter instead of the plant is a linear problem like open-loop identification.

This keynote presentation is a guided tour through the theory and applications of the Youla-Kučera parameterization. It explains the origins of the result, the derivation of the parameterization formula using the transfer functions, and the state-space representation of all stabilizing controllers. It also explains how to select the parameter to satisfy specific design requirements. New and exciting applications of the Youla–Kučera parameterization are then discussed: stabilization subject to input constraints, output overshoot reduction, and fixed-order stabilizing controller design. A selection of applications in different control fields is presented showing the efficiency of this approach in controlling complex systems.

[1] D.C. Youla, J.J. Bongiorno, and H.A. Jabr, “Modern Wiener-Hopf design of optimal controllers, Part I: The single-input case,” IEEE Transactions on Automatic Control, vol. 21, 1976, pp. 3-14.
[2] D.C. Youla, H.A. Jabr, and J.J. Bongiorno, “Modern Wiener-Hopf design of optimal controllers, Part II: The multivariable case,” IEEE Transactions on Automatic Control, vol. 21, 1976, pp. 319-338.
[3] V. Kučera, “Stability of discrete linear control systems,” IFAC Proceedings Volumes, vol. 8, no. 1, part 1, 1975, pp. 573-578.
[4] V. Kučera, Discrete Linear Control: The Polynomial Equation Approach. Chichester, UK: Wiley, 1979.
[5] M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: MIT Press, 1985.
[6] A. Quadrat, “On a generalization of the Youla-Kučera parametrization. Part I: The fractional ideal approach to SISO systems,” Systems & Control Letters, vol. 50, 2003, pp. 135-148.
[7] B.D.O. Anderson, “From Youla-Kucera to identification, adaptive and nonlinear control,” Automatica, vol. 34, 1988, pp. 1485-1506.
[8] I. Mahtout, F. Navas, V. Milanes, F. Nashashibi, “Advances in Youla-Kucera parametrization: A Review,” Annual Reviews in Control, vol. 49, 2020, pp. 81-94.

This work was co-funded by the European Union under Project Robotics and Advanced Industrial Production CZ.02.01.01/00/22_008/0004590.