Structure Preserving Moment Matching for Port-Hamiltonian Systems:Arnoldi and Lanczos

Structure preserving model reduction of single-input single-output port-Hamiltonian systems is considered by employing the rational Krylov methods. The rational Arnoldi method is shown to preserve (for the reduced order model) not only a specific number of the moments at an arbitrary point in the complex plane but also the port-Hamiltonian structure. Furthermore, it is shown how the rational Lanczos method applied to a subclass of port-Hamiltonian systems, characterized by an algebraic condition, preserves the port-Hamiltonian structure. In fact, for the same subclass of port-Hamiltonian systems the rational Arnoldi method and the rational Lanczos method turn out to be equivalent in the sense of producing reduced order port-Hamiltonian models with the same transfer function

Extracting and Representing Qualitative Behaviors of Complex Systems in Phase Spaces

We develop a qualitative method for understanding and representing phase space structures of complex systems and demonstrate the method with a program, MAPS --- Modeler and Analyzer for Phase Spaces, using deep domain knowledge of dynamical system theory. Given a dynamical system, the program generates a complete, high level symbolic description of the phase space structure sensible to human beings and manipulable by other programs. Using the phase space descriptions, we are developing a novel control synthesis strategy to automatically synthesize a controller for a nonlinear system in the phase space to achieve desired properties

Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies

Gradient-based methods have been widely used for system design and optimization in diverse application domains. Recently, there has been a renewed interest in studying theoretical properties of these methods in the context of control and reinforcement learning. This article surveys some of the recent developments on policy optimization, a gradient-based iterative approach for feedback control synthesis, popularized by successes of reinforcement learning. We take an interdisciplinary perspective in our exposition that connects control theory, reinforcement learning, and large-scale optimization. We review a number of recently-developed theoretical results on the optimization landscape, global convergence, and sample complexity of gradient-based methods for various continuous control problems such as the linear quadratic regulator (LQR), $\mathcal{H}_\infty$ control, risk-sensitive control, linear quadratic Gaussian (LQG) control, and output feedback synthesis. In conjunction with these optimization results, we also discuss how direct policy optimization handles stability and robustness concerns in learning-based control, two main desiderata in control engineering. We conclude the survey by pointing out several challenges and opportunities at the intersection of learning and control.Comment: To Appear in Annual Review of Control, Robotics, and Autonomous System

On the controllability of fermentation systems

This thesis concerns the controllability of fermentation processes. Fermentation processes are often described by unstructured process models. A control system can be used to reduce the effect of the uncertainties and disturbances. A process is called controllable if a control system satisfying suitably defined control objectives can be found. Controllability measures based on linear process models are identified. The idealised control objective for perfect control allows fast evaluation of the controllability measures. These measures are applied to compare different designs of a continuous fermentation process by identifying the controllability properties of the process design. The operational mode of fed batch fermentations is inherently dynamic. General control system design methods are not readily applicable to such systems. This work presents an approach for the design of robust controllers suitable for these processes. The control objective is to satisfy a set of robustness constraints for a given set of model uncertainties and disturbances. The optimal operation and design problems are combined into a single optimal control problem. The controller design is integrated into the process design problem formulation. In this way the control system and the process are designed simultaneously. Different problem formulations are investigated. The proposed approach is demonstrated on complex fermentation models. The resulting operating strategies are controllable with respect to the aims of control

Systems and control : 21th Benelux meeting, 2002, March 19-21, Veldhoven, The Netherlands

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