Ladies Night for Women in Engineering Sciences

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Linear parameter varying (LPV) systems are described by linear dierential equations whose describing matrices depend on time-varying parameters. The goal in synthesis is to design a controller of the very same structure such that the overall controlled system satises certain desired specications on stability and performance for the entire set of permissible parameter trajectories. The implementation of LPV controllers takes on-line measurements of the time-varying parameters into account in order to improve the performance over robust controllers, compensators without any adaptation capabilities. In this talk, we highlight the challenges in synthesizing controller in order to meet certain desired stability and performance properties. Furthermore, we address a long-standing open problem in robust control and present novel algorithms that allow to systematically reduce conservatism by relying on frequency-dependent stability multipliers. In the nal part of the talk we reveal how the developed framework enables the design of distributed controllers for spatially interconnected systems with reduced conservatism. [more]

Mixed-Integer Nonlinear Optimization is the mother of all deterministic optimization models. As such, it has enormous modeling power, with applications in all kinds of areas like manufacturing and transportation logistics, design of water and gas networks, chemical engineering, portfolio optimization, etc. But of course in its full generality, it is foolhardy to consider algorithms and meaningful positive theoretical results. On the other hand, there are many well-known positive results for the linear case, so it is natural to seek to build up from the linear case, to get positive results (both theoretical and computational) for broader models. Natural extensions involve convexity and separability, and their relatives, and polynomials. A natural step in this direction involves attempting to exploit quadratic functions. I will survey some recent results in this direction --- both negative and positive complexity results and practical methods. [more]

Renewable energy supply chain optimization problems are characterized by a large number of options, significant amounts of uncertainty and multi-scale nature of decisions. This presentation examines these characteristics through practical examples and offers some promising research directions. The problem of large number of processing stages/options will be first introduced through a microalgae-based bio-refinery design problem. Superstructure based modeling and optimization will be presented as a tool to investigate the problem at a high level. Then, the presentation will move onto the issue of coupling between long-term planning decisions like capital investment and policy and shorter-term decisions like production capacity operation and logistics. This aspect manifests itself as a large number of decision variables and constraints complicating solution of the optimization. The optimization complexity gets greatly amplified when the issue of uncertainty is added to the problem. We will examine both two stage and multi-stage problems. Examples of biofuel processing supply chain and energy portfolio optimization for power generation will be used to bring out the essential features and complications. For solutions, stochastic programming and approximate dynamic programming will be introduced. [more]

The use of second order sliding modes, namely the generalized super-twisting algorithm or one of its variants, is illustrated for two applications in bioprocesses. Both the theoretical framework and some practical aspects are discussed. Two applications are considered: the design of a variable-gain super-twisting observer to robustly estimate the reaction rate in a bioreactor, and the proposal of a pseudo-super-twisting controller that maximizes the product output rate for a simplified model of a bioprocess. The case studies are the on-line estimation of the nitrogen quota in a microalgae bioreactor, and the maximization of biogas production during anaerobic wastewater treatment. [more]

The H∞ norm of a transfer matrix function for a continuous-time control system is the maximum of the norm of the transfer matrix on the imaginary axis, or equivalently, the reciprocal of the largest value of ε such that the associated ε-spectral value set is contained in the left half-plane. We start by defining spectral value sets and discussing some of their fundamental properties, including the intricate relationship between the singular vectors of the transfer matrix and the eigenvectors of the corresponding perturbed system matrix. We then introduce an iterative method for approximating the ε-spectral value set abscissa (the maximum of the real part of the points in the set), characterizing the fixed points of the iteration, and explain how the procedure can be combined with a Newton-bisection outer iteration to approximate the H∞ norm. We then explain why this idealized algorithm sometimes breaks down and introduce a method called hybrid expansion-contraction to address this deficiency. Under reasonable assumptions, the new algorithm finds locally maximal values of the norm of the transfer matrix on the imaginary axis and although these are only lower bounds on the H∞ norm, it typically finds good approximations in cases where we can test this. It is much faster than the standard Boyd-Balakrishnan-Bruinsma-Steinbuch algorithm to compute the H∞ norm when the system matrices are large and sparse. The main work required by the algorithm is the computation of the rightmost eigenvalues of a sequence of matrices that are rank-one perturbations of a sparse matrix. [more]

In the last two decades the design of nonlinear model predictive control (NMPC) schemes has received widespread attention by theoreticians and practitioners in the field of systems and control. The main reasons for this interest are (a) that NMPC allows considering input and state constraints in a structured manner, and (b) that NMPC allows handling nonlinear systems with multiple inputs. NMPC is built upon the repeated solution of an optimal control problem and the partial application of optimal input trajectories. Often, stability of NMPC schemes is enforced by means of computationally intensive terminal constraints and end penalties. In this talk, we discuss the design of NMPC schemes based on turnpike properties. We show that these properties enable avoiding terminal constraints. We begin the talk with a formal introduction of turnpike properties of optimal control problems. It is worth to be mentioned that the concept of turnpike properties has received widespread attention in optimal control approaches to economic dynamic systems. However, it is surprising that turnpike properties have received only limited attention in the context of NMPC. In this presentation, we present results attempting to partially bridge this gap. We show that exact turnpikes allow establishing stability of NMPC controlled systems as well as recursive feasibility without any terminal constraints. We draw upon examples from different areas such as process control and biology to illustrate our results. [more]