Mini-Workshop: Recent Developments on Approximation Methods for Controlled Evolution Equations

This mini-workshop brought together mathematicians engaged in partial differential equations, functional analysis, numerical analysis and systems theory in order to address a number of current problems in the approximation of controlled evolution equations

Control theory: history, mathematical achievements and perspectives

These notes are devoted to present some of the mathematical milestones of Control Theory. To do that, we first overview its origins and some of the main mathematical achievements. Then, we discuss the main domains of Sciences and Technologies where Control Theory arises and applies. This forces us to address modelling issues and to distinguish between the two main control theoretical approaches, controllability and optimal control, discussing the advantages and drawbacks of each of them. In order to give adequate formulations of the main questions, we have introduced some of the most elementary mathematical material, avoiding unnecessary technical difficulties and trying to make the paper accessible to a large class of readers. The subjects we address range from the basic concepts related to the dynamical systems approach to (linear and nonlinear) Mathematical Programming and Calculus of Variations. We also present a simplified version of the outstanding results by Kalman on the controllability of linear finite dimensional dynamical systems, Pontryaguin’s maximum principle and the principle of dynamical programming. Some aspects related to the complexity of modern control systems, the discrete versus continuous modelling, the numerical approximation of control problems and its control theoretical consequences are also discussed. Finally, we describe some of the major challenging applications in Control Theory for the XXI Century. They will probably influence strongly the development of this discipline in the near future.Ministerio de Ciencia y Tecnologí

Efficient Reorientation Maneuvers for Spacecraft with Multiple Articulated Payloads

A final report is provided which describes the research program during the period 3 Mar. 1992 to 3 Jun. 1993. A summary of the technical research questions that were studied and of the main results that were obtained is given. The specific outcomes of the research program, including both educational impacts as well as research publications, are listed. The research is concerned with efficient reorientation maneuvers for spacecraft with multiple articulated payloads

Graph Theoretic Analysis of Multi-Agent system Structural Properties

Ph.DDOCTOR OF PHILOSOPH

Distributed optimal and predictive control methods for networks of dynamic systems

Several recent approaches to distributed control design over networks of interconnected dynamic systems rely on certain assumptions, such as identical subsystem dynamics, absence of dynamical couplings, linear dynamics and undirected interaction schemes. In this thesis, we investigate systematic methods for relaxing a number of simplifying factors leading to a unifying approach for solving general distributed-control stabilization problems of networks of dynamic agents. We show that the gain-margin property of LQR control holds for complex multiplicative input perturbations and a generic symmetric positive definite input weighting matrix. Proving also that the potentially non-simple structure of the Laplacian matrix can be neglected for stability analysis and control design, we extend two well-known distributed LQR-based control methods originally established for undirected networks of identical linear systems, to the directed case. We then propose a distributed feedback method for tackling large-scale regulation problems of a general class of interconnected non-identical dynamic agents with undirected and directed topology. In particular, we assume that local agents share a minimal set of structural properties, such as input dimension, state dimension and controllability indices. Our approach relies on the solution of certain model matching type problems using local linear state-feedback and input matrix transformations which map the agent dynamics to a target system, selected to minimize the joint control effort of the local feedback-control schemes. By adapting well-established distributed LQR control design methodologies to our framework, the stabilization problem of a network of non-identical dynamical agents is solved. We thereafter consider a networked scheme synthesized by multiple agents with nonlinear dynamics. Assuming that agents are feedback linearizable in a neighborhood near their equilibrium points, we propose a nonlinear model matching control design for stabilizing networks of multiple heterogeneous nonlinear agents. Motivated by the structure of a large-scale LQR optimal problem, we propose a stabilizing distributed state-feedback controller for networks of identical dynamically coupled linear agents. First, a fully centralized controller is designed which is subsequently substituted by a distributed state-feedback gain with sparse structure. The control scheme is obtained byoptimizing an LQR performance index with a tuning parameter utilized to emphasize/deemphasize relative state difference between coupled systems. Sufficient conditions for stability of the proposed scheme are derived based on the inertia of a convex combination of two Hurwitz matrices. An extended simulation study involving distributed load frequency control design of a multi-area power network, illustrates the applicability of the proposed method. Finally, we propose a fully distributed consensus-based model matching scheme adapted to a model predictive control setting for tackling a structured receding horizon regulation problem