On this Friday, June 10, 2016 at 11:00 in room No.641 Assistant Professor Boris Houska, Ph.D. from ShanghaiTech University will deliver a seminar on "Nonlinear and Robust MPC Using Min-Max Differential Inequalities", and "Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control".
Speaker: Assistant Professor Boris Houska, Ph.D.
He received a diploma in mathematics and physics from the University of Heidelberg in 2007, and a Ph.D. in Electrical Engineering from KU Leuven in 2011. From 2012 to 2013 he was a postdoctoral researcher at the Centre for Process Systems Engineering at Imperial College London. From 2013-2014 Boris Houska worked as faculty member at the Department of Automation at Shanghai Jiao Tong University. In August and September 2014 he was a guest professor at the Institute for Microsystems Engineering at the University of Freiburg. Since October 2014 Boris Houska is an assistant professor at the School of Information Science and Technology at ShanghaiTech University.
Nonlinear and Robust MPC Using Min-Max Differential Inequalities
This talk is about tube-based model predictive control (MPC) for both linear and nonlinear continuous-time dynamic systems that are affected by time-varying disturbances. We derive a min-max differential inequality describing the support function of positive robust forward invariant tubes, which can be used to construct a variety of conservative, but computationally tractable, tube-based model predictive controllers. The implementation of these robust MPC controllers is based on an automatic C-code generation strategy for real-time nonlinear model predictive control. We illustrate the performance of the proposed methods with applications in the field of mechatronics.
Slides: Download PDF (approx. 1 MB)
Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control
Finding globally optimal solutions to nonlinear optimal control problems is a practically relevant, but challenging task. Although nonlinear optimal control methods and tools based on local optimization are satisfactory for many practical purposes, they can get trapped into local optima, possibly suboptimal by a large margin. Such situations can occur in the field of control of chemical and biochemical processes, as these processes can present complex and highly nonlinear behavior leading for instance to steady-state multiplicity. For such problems, it is often unclear how to initialize a local solver in order to find a control input leading to the best possible performance. Moreover, there are important classes of problems for which obtaining a certificate of global optimality is paramount, for instance in the field of robust or scenario-integrated optimization.
Existing global optimal control algorithms based on dynamic programming have run-times that scale exponentially with the number of differential states. Global optimization algorithms based on direct methods, on the other hand, present worst-case run-times that scale exponentially with the number of optimization variables in the discretized NLP problem approximating the solution of the original optimal control problem. Moreover, a priori parameterization of the control functions in direct methods does not allow control over the accuracy of a given parameterization, and therefore this approach is not suitable for rigorous search of globally optimal solutions in optimal control problems.
In this talk, we present a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a spatial branch-and-bound algorithm in order to eliminate control subregions that are either infeasible or that provably cannot contain any global optima. A new operation, called lifting, is introduced, which enables systematic branching in the infinite-dimensional space of control functions by refining the control parameterization via a Gram-Schmidt orthogonalization process. We illustrate the practical applicability of branch-and-lift with numerical examples from the field of bio-chemical process control.
Slides: Download PDF (approx. 3 MB)