Global Tracking Passivity--based PI Control of Bilinear Systems and its Application to the Boost and Modular Multilevel Converters

This paper deals with the problem of trajectory tracking of a class of bilinear systems with time--varying measurable disturbance. A set of matrices {A,B_i} has been identified, via a linear matrix inequality, for which it is possible to ensure global tracking of (admissible, differentiable) trajectories with a simple linear time--varying PI controller. Instrumental to establish the result is the construction of an output signal with respect to which the incremental model is passive. The result is applied to the boost and the modular multilevel converter for which experimental results are given.Comment: 9 pages, 10 figure

Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

We construct two error feedback controllers for robust output tracking and disturbance rejection of a regular linear system with nonsmooth reference and disturbance signals. We show that for sufficiently smooth signals the output converges to the reference at a rate that depends on the behaviour of the transfer function of the plant on the imaginary axis. In addition, we construct a controller that can be designed to achieve robustness with respect to a given class of uncertainties in the system, and present a novel controller structure for output tracking and disturbance rejection without the robustness requirement. We also generalize the internal model principle for regular linear systems with boundary disturbance and for controllers with unbounded input and output operators. The construction of controllers is illustrated with an example where we consider output tracking of a nonsmooth periodic reference signal for a two-dimensional heat equation with boundary control and observation, and with periodic disturbances on the boundary.Comment: 30 pages, 3 figures, to appear in SIAM Journal on Control & Optimizatio

Approximate robust output regulation of boundary control systems

We extend the internal model principle for systems with boundary control and boundary observation, and construct a robust controller for this class of systems. However, as a consequence of the internal model principle, any robust controller for a plant with infinite-dimensional output space necessarily has infinite-dimensional state space. We proceed to formulate the approximate robust output regulation problem and present a finite-dimensional controller structure to solve it. Our main motivating example is a wave equation on a bounded multidimensional spatial domain with force control and velocity observation at the boundary. In order to illustrate the theoretical results, we construct an approximate robust controller for the wave equation on an annular domain and demonstrate its performance with numerical simulations.Comment: 29 pages, 4 figure

Pension Funding and Individual Accounts in Economies with Life-cyclers and Myopes

The present paper studies the growth and efficiency consequences of pension funding with individual retirement accounts in a general equilibrium overlapping generations model with idiosyncratic lifespan and labor income uncertainty. We distinguish between economies with rational and hyperbolic consumers and compare the consequences of voluntary and mandatory retirement plans. Three major findings are derived in our study: First, we quantify the commitment effect of social security for myopic individuals by roughly 1 percent of aggregate resources. It is possible to recapture this commitment technology in IRAs, if those are annuitized. Second, despite the fact that our consumers have an operative bequest motive, the welfare gain from the (implicit) longevity insurance of the pension system is significant and amounts to roughly 0.5 percent of aggregate resources. However, mandatory annuitization reduces unintended bequests so that future generations are significantly hurt. Finally, our results highlight the importance of liquidity effects for social security analysis. These efficiency gains are only attainable if accounts are voluntary and not mandatory.individual retirement accounts, annuities, stochastic general equilibrium, hyperbolic consumers