A geometric approach to structural model matching by output feedback in linear impulsive systems

AbstractThis paper provides a complete characterization of solvability of the problem of structural model matching by output feedback in linear impulsive systems with nonuniformly spaced state jumps. Namely, given a linear impulsive plant and a linear impulsive model, both subject to sequences of state jumps which are assumed to be simultaneous and measurable, the problem consists in finding a linear impulsive compensator that achieves exact matching between the respective forced responses of the linear impulsive plant and of the linear impulsive model, by means of a dynamic feedback of the plant output, for all the admissible input functions and for all the admissible sequences of jump times. The solution of the stated problem is achieved by reducing it to an equivalent problem of structural disturbance decoupling by dynamic feedforward. Indeed, this latter problem is formulated for the so-called extended linear impulsive system, which consists of a suitable connection between the given plant and a modified model. A necessary and sufficient condition for the solution of the structural disturbance decoupling problem is first shown. The proof of sufficiency is constructive, since it is based on the synthesis of the compensator that solves the problem. The proof of necessity is based on the definition and the geometric properties of the unobservable subspace of a linear impulsive system subject to unequally spaced state jumps. Finally, the equivalence between the two structural problems is formally established and proven

Survey of Gain-Scheduling Analysis & Design

The gain-scheduling approach is perhaps one of the most popular nonlinear control design approaches which has been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide application of gain-scheduling controllers and a diverse academic literature relating to gain-scheduling extending back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in interest in gain-scheduling in the literature with many new results obtained. An extended review of the gainscheduling literature therefore seems both timely and appropriate. The scope of this paper includes the main theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition of nonlinear design into linear sub-problems) control with the aim of providing both a critical overview and a useful entry point into the relevant literature

Regelungstheorie

The workshop “Regelungstheorie” (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering

High-Efficiency Self-Adjusting Switched Capacitor DC-DC Converter with Binary Resolution

Switched-Capacitor Converters (SCC) suffer from a fundamental power loss deficiency which make their use in some applications prohibitive. The power loss is due to the inherent energy dissipation when SCC operate between or outside their output target voltages. This drawback was alleviated in this work by developing two new classes of SCC providing binary and arbitrary resolution of closely spaced target voltages. Special attention is paid to SCC topologies of binary resolution. Namely, SCC systems that can be configured to have a no-load output to input voltage ratio that is equal to any binary fraction for a given number of bits. To this end, we define a new number system and develop rules to translate these numbers into SCC hardware that follows the algebraic behavior. According to this approach, the flying capacitors are automatically kept charged to binary weighted voltages and consequently the resolution of the target voltages follows a binary number representation and can be made higher by increasing the number of capacitors (bits). The ability to increase the number of target voltages reduces the spacing between them and, consequently, increases the efficiency when the input varies over a large voltage range. The thesis presents the underlining theory of the binary SCC and its extension to the general radix case. Although the major application is in step-down SCC, a simple method to utilize these SCC for step-up conversion is also described, as well as a method to reduce the output voltage ripple. In addition, the generic and unified model is strictly applied to derive the SCC equivalent resistor, which is a measure of the power loss. The theoretical predictions are verified by simulation and experimental results

Robust hybrid estimation and rejection of multi-frequency signals

We consider the problem of output regulation for LTI systems in the presence of unknown exosystems. The knowledge about the multi-frequency signals exosystem consists in the maximum number of frequencies and their maximal value. The control scheme relies on two main components: an estimation algorithm, to reconstruct the signal generated by the exosystem, and a controller, to enforce the output regulation property to the closed-loop system. To tackle the first task, we propose a hybrid observer for the estimation of the (possibly piece-wise continuous) number and values of the frequencies contained in the exogenous signal. The hybrid observer is particularly appealing for numerical implementations, and it is combined with a self-tuning algorithm of the free parameters (gains), thus improving its performance even in case of noisy measurements. Semi-global exponential convergence of the estimation error is provided. As far as the second task is concerned, a robust hybrid regulator is designed for practical rejection of the multi-frequency disturbance signal acting on the plant. The result is achieved by exploiting the frequencies estimated by the hybrid observer. The effectiveness of the proposed control scheme is shown by means of numerical simulations

Hybrid optimization method with general switching strategy for parameter estimation

This article is available from: http://www.biomedcentral.com/1752-0509/2/26[Background] Modeling and simulation of cellular signaling and metabolic pathways as networks of biochemical reactions yields sets of non-linear ordinary differential equations. These models usually depend on several parameters and initial conditions. If these parameters are unknown, results from simulation studies can be misleading. Such a scenario can be avoided by fitting the model to experimental data before analyzing the system. This involves parameter estimation which is usually performed by minimizing a cost function which quantifies the difference between model predictions and measurements. Mathematically, this is formulated as a non-linear optimization problem which often results to be multi-modal (non-convex), rendering local optimization methods detrimental.[Results] In this work we propose a new hybrid global method, based on the combination of an evolutionary search strategy with a local multiple-shooting approach, which offers a reliable and efficient alternative for the solution of large scale parameter estimation problems.[Conclusion] The presented new hybrid strategy offers two main advantages over previous approaches: First, it is equipped with a switching strategy which allows the systematic determination of the transition from the local to global search. This avoids computationally expensive tests in advance. Second, using multiple-shooting as the local search procedure reduces the multi-modality of the non-linear optimization problem significantly. Because multiple-shooting avoids possible spurious solutions in the vicinity of the global optimum it often outperforms the frequently used initial value approach (single-shooting). Thereby, the use of multiple-shooting yields an enhanced robustness of the hybrid approach.This work was supported by the European Community as part of the FP6 COSBICS Project (STREP FP6-512060), the German Federal Ministry of Education and Research, BMBF-project FRISYS (grant 0313921) and Xunta de Galicia (PGIDIT05PXIC40201PM).Peer reviewe

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Sampled-Data Control of Invariant Systems on Exponential Lie Groups

This thesis examines the dynamics and control of a class of systems furnished by kinematic systems on exponential matrix Lie groups, when the plant evolves in continuous-time, but whose controller is implemented in discrete-time. This setup is called sampled-data and is ubiquitous in applied control. The class of Lie groups under consideration is motivated by our previous work concerning a similar class of kinematic systems on commutative Lie groups, whose local dynamics were found to be linear, which greatly facilitated control design. This raised the natural question of what class of systems on Lie groups, or class of Lie groups, would admit global characterizations of stability based on the linear part of their local dynamics. As we show in this thesis, the answer is---or at least includes---left- or right-invariant systems on exponential Lie groups, which are necessarily solvable, nilpotent, or commutative. We examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a matrix Lie group. The map defining such a difference equation has three key properties that facilitate our analysis: 1) its Lie series expansion enjoys a type of strong convergence; 2) the origin is an equilibrium; 3) the algebraic ideals enumerated in the lower central series of the Lie algebra are dynamically invariant. We show that certain global stability properties are implied by stability of the Jacobian linearization of dynamics at the origin, in particular, global asymptotic stability. If the Lie algebra is nilpotent, then the origin enjoys semiglobal exponential stability. We then study the synchronization of networks of identical continuous-time kinematic agents on a matrix Lie group, controlled by discrete-time controllers with constant sampling periods and directed, weighted communication graphs with a globally reachable node. We present a smooth, distributed, nonlinear discrete-time control law that achieves global synchronization on exponential matrix Lie groups, which include simply connected nilpotent Lie groups as a special case. Synchronization is generally asymptotic, but if the Lie group is nilpotent, then synchronization is achieved at an exponential rate. We first linearize the synchronization error dynamics at the identity, and show that the proposed controller achieves local exponential synchronization on any Lie group. Building on the local analysis, we show that, if the Lie group is exponential, then synchronization is global. We provide conditions for deadbeat convergence when the communication graph is unweighted and complete. Lastly, we examine a regulator problem for a class of fully actuated continuous-time kinematic systems on Lie groups, using a discrete-time controller with constant sampling period. We present a smooth discrete-time control law that achieves global regulation on simply connected nilpotent Lie groups. We first solve the problem when both the plant state and exosystem state are available for feedback. We then present a control law for the case where the plant state and a so-called plant output are available for feedback. The class of plant outputs considered includes, for example, the quantity to be regulated. This class of output allows us to use the classical Luenberger observer to estimate the exosystem states. In the full-information case, the regulation quantity on the Lie algebra is shown to decay exponentially to zero, which implies that it tends asymptotically to the identity on the Lie group