Analysis, estimation and control for perturbed and singular systems for systems subject to discrete events.

"The principle investigator for this effort is Professor Alan S. Willsky, and Professor George C. Verghese is co-principal investigator."--P. [3].Includes bibliographical references (p. [20]-[25]).Final technical report for grant AFOSR-88-0032.Supported by the AFOSR. AFOSR-88-003

Singular Perturbations and Time-Scale Methods in Control Theory: Survey 1976-1982

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424U.S. Air Force / AFOSR 78-363

Continuity of singular perturbations in the graph topology

AbstractFor a certain model for singular perturbations in control systems, which we motivate by a simple example, we show that under weak assumptions continuity in the graph topology holds as the perturbation parameter tends to zero. This may be contrasted with a result by Cobb, who considered a different model for singular perturbations and who found a strong condition to be necessary for continuity in that model. Our proof techniques are based on the characterization (due to Qiu and Davison) of the graph topology as a topology of uniform convergence

Descriptor Variable and Generalized Singularly Perturbed Systems: A Geometric Approach

Marked with alternative report numbers UILU-80-2214 and UILU-80-2258U.S. Air Force / AFOSR-78-3633National Science Foundation / NSF ECS-79-19396Joint Services Electronics Program / N00014-79-C-0424Ope

Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Simple Tracking Output Feedback H ∞ Control for Switched Linear Systems: Lateral Vehicle Control Application

International audienceIn this paper, the problem of the switched H ∞ tracking output feedback control problem is studied. The control design problem is addressed in the context of discrete-time switched linear systems. Then, the design of continuous-time case becomes trivial. Linear Matrix Inequality (LMI) and Linear Matrix Equality (LME) representations are used to express all sufficient conditions to solve the control problem. Some transformations leading to sufficient conditions for the control problem are also used. All conditions are established for any switching using a switched Lyapunov function and a common Lyapunov function. The effectiveness of the proposed control approach is shown through a steering vehicle control implementation. Interesting simulation results are obtained using real data acquired by an instrumented car

Second order sliding mode observers for fault reconstruction in power networks

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper proposes a 2-sliding mode observer to detect and reconstruct a certain class of load altering faults in a power network. The observer design is based on the recently proposed multivariable super-twisting structure. The IEEE benchmark power networks used to test the scheme are modelled as a semi-explicit class of differential algebraic equations (DAEs). For the purpose of developing the detection scheme, only the phase angles of the generators are measured, which represent a subset of the differential states of the DAEs. The objective is to estimate the differential states (the phase angles and frequencies of the generators), the algebraic states (the phase angles of the load bus tensions) and to reconstruct a class of load altering faults affecting the network. The proposed observer is assessed in simulation on two IEEE benchmarks: the 9-bus and 14-bus networks, so as to verify its capability to correctly estimate the differential and algebraic states of the network in spite of its complexity and uncertainty. Moreover, the capability of the proposed scheme to detect the presence of a load altering fault, to exactly identify its position in the network, and to precisely reconstruct the shape of the fault itself is shown and discussed

The general solutions of singular and non-singular matrix fractional time-varying descriptor systems with constant coefficient matrices in Caputo sense

AbstractIn this paper, we generalize the time-varying descriptor systems to the case of fractional order in matrix forms. Moreover, we present the general exact solutions of the linear singular and non-singular matrix fractional time-varying descriptor systems with constant coefficient matrices in Caputo sense by using a new attractive method. Finally, two illustrated examples are also given to show our new approach