Data-driven Computational Optimal Control for Uncertain Nonlinear Systems
Professor and Chair of Department
Department of Applied Mathematics
University of California – Santa Cruz - USA
Optimal control problems with unknown parameters and/or uncertain initial conditions have arisen in multiple control applications, including ensemble control, optimal search, and motion planning of autonomous vehicles. This talk discusses recent advances in applying computational techniques to optimal control problems with uncertainty. We will present a flexible numerical framework for producing solutions using a variety of underlying discretization schemes which can be catered to numerical needs; and analytic conditions for analysis in the form of a Pontryagin-like minimum principle. Efficient implementations of numerical methods for uncertain optimal control problem on modern computational platforms, for example, TensorFlow, will also be discussed. Applications on engineering problems including optimal search of unknown targets, and motion planning of autonomous vehicles will be presented.
Qi Gong is a Professor and Department Chair in Applied Mathematics at Baskin School of Engineering, University of California, Santa Cruz. He received his B.S. degree in Automation from Dalian University of Science and Technology in 1996, his M.S. in Automatic Control from Southeast University in 1999, and his Ph.D. in Systems and Control Engineering from Case Western Reserve University in 2004. His research centers on computational methods for nonlinear optimal control, trajectory optimization, optimal control theory, and aerospace control applications. Dr. Gong currently serves as an Associate Editor for AIAA Journal of Guidance, Control and Dynamics. He was a member of the National Organizing Committee and the Area Chair on optimal control for 2016 IFAC Symposium on Nonlinear Control Systems. He served as a member of Organizing Committee for 2013 SIAM Conference on Control and Its Applications, and as a member of Program Committee for 2017 SIAM Conference on Control and Its Applications. From 2007 to 2013 he was an Associate Editor for IEEE Control Systems Society Conference Editorial Board. Dr. Gong received Postdoctoral Research Associateship Award from the National Research Council in 2004.
Sliding Mode Controllers: stages of evolution
Department of Control Engineering and Robotics, Engineering Faculty
National Autonomous University of Mexico (UNAM), Mexico
The history and evolution of sliding control will be discussed. The main problems arising in the usage of the first order sliding modes will be explained. The second order sliding mode control algorithms and their specific features will be presented. The chattering reduction in the continuous second order super-twisting controllers will be illustrated. The precision of the arbitrary order sliding mode controllers will be shown. The continuous arbitrary order sliding mode controllers will be presented and discussed. Videos with the experimental illustration of the properties of the main sliding mode algorithms will be presented.
Fridman L. Sliding Mode Enforcement after 1990: Main Results and Some Open Problems. Sliding Modes after the first Decade of the 21st Century. Fridman, J. Moreno, Rafael Iriarte (Eds.) Lecture Notes in Control and Information Sciences, Vol. 412,Springer Verlag: Berlin, 2011,1-57
Shtessel, C. Edwards, L. Fridman, A. Levant. Sliding Mode Control and Observation, Series: Control Engineering, Birkhauser: Basel, 2013
.Polyakov, L. Fridman, Stability notions and lyapunov functions for sliding mode control systems. Journal of Franklin Institute,Volume 351, Issue 4, 2014, Pages 1831-1865,doi :10.1016/j.jfranklin.2014.01.00
- Fridman, J. Moreno, B. Bandyopadhyay, S. Kamal, A. Chalanga "Continuous Nested Algorithms : The Fifth Generation of Sliding Mode Controllers " In Recent Advances in Sliding Modes: From Control to Intelligent Mechatronics. X. Yu, O. Efe (eds), Studies in Systems, Decision and Control 24, Springer, Switzerland 2015. pp. 5-35, , doi: 10.1007/978-3-319-18290-2_2.
Leonid M. Fridman received an M.S. degree in mathematics from Kuibyshev (Samara) State University, Samara, Russia, in 1976, a Ph.D. degree in applied mathematics from the Institute of Control Science, Moscow, Russia, in 1988, and a Dr. Sc. degree in control science from Moscow State University of Mathematics and Electronics, Moscow, Russia, in 1998. From 1976 to 1999, he was with the Department of Mathematics, Samara State Architecture and Civil Engineering University. From 2000 to 2002, he was with the Department of Postgraduate Study and Investigations at the Chihuahua Institute of Technology, Chihuahua, Mexico. In 2002, he joined the Department of Control Engineering and Robotics, Division of Electrical Engineering of Engineering Faculty at National Autonomous University of Mexico (UNAM), Mexico.
His research interests are Variable Structure Systems. He is an author and editor of ten books and seventeen special issues devoted to the sliding mode control. He is a winner of Scopus prize for the best cited Mexican Scientists in Mathematics and Engineering 2010. He was working as an invited professor in 20 universities and research laboratories of Argentina, Australia, Austria, France, China, Germany, Italy, Israel, and Spain.
Sliding Mode Control: A Frequency Domain Approach
Dr. Hebertt J. Sira Ramírez
Professor - Researcher section Mechatronics
Department of Electrical Engineering
Center for Research and Advanced Studies of IPN (CINVESTAV)
The evolution of part of the developments in sliding mode control are presented for switch commanded systems (i.e., systems with binary-valued inputs). The geometric approach, based on subspace theory, or differential geometry, respectively include linear and nonlinear continuous time systems. Classical limitations of the state space approach are: availability of the state vector components, dependence of the control authority on the maximum allowable disturbance, stringent disturbance matching conditions. An input-output formulation, based on endogenous injections and exogenous feedback, is shown to dispense with all the above limitations for the class of differentially flat systems, bringing in the relevance of the classical frequency domain approach. In this context, an average equivalence is established of sliding mode control with Active Disturbance Rejection Control and Generalized Proportional Integral Control in the form of Flat Filters (for second order systems, the equivalence is with the PID control scheme). Several illustrative examples are presented.