Dissipative systems theory : analysis and synthesis

Finite L2 gain and passivity (or positive real) methods have recently played an important role in a large number of robust, high performance engineering designs for both nonlinear and linear systems. This has renewed interest in the classical concept of dissipative systems. In particular, in various finite gain or passivity system synthesis methods in the literature, one studies a relevant dissipation inequality and looks for an appropriate solution to it. When such a solution exists, one then constructs the desired system by using this solution. The main theme of the thesis is the development of a framework for general dissipative systems analysis and synthesis. We firstly present a numerical method for testing dissipativity of a given system. We characterize a dissipative system in terms of a weak (viscosity) solution to a partial differential inequality (PDI) which is the relevant dissipation inequality for the system being considered and develop a finite-difference based discretization method that results in a partial difference inequality approximating the PDI. We then propose two iterative methods to solve the partial difference inequality. We report a number of computational experiment results to demonstrate the utility of the method. Under certain circumstances, strict dissipativity is of the main concern. We provide characterization of a strongly stable, strictly quadratic dissipative nonlinear system in terms of a solution to a PDI or a solution to a partial differential equation (PDE), in the viscosity sense. When the solution to the PDE is smooth, then it also has a stabilizing (in some sense) property. These results generalize the strict bounded real lemma in the linear H control literature. We also provide characterization of a stable, strictly quadratic dissipative linear system in terms of a stabilizing solution to an algebraic Riccati equation (ARE). Connections between quadratic dissipative systems and finite gain related systems are given. In the thesis, we propose a synthesis method for a general dissipative control problem for nonlinear and linear systems with state feedback. We express the solution to the roblem in terms of a solution to a Hamilton-Jacobi-Isaacs (HJI) PDI/PDE in the non­ linear systems case (algebraic Riccati equation/inequality in the linear systems case). In particular, in the case of nonlinear systems with a general quadratic supply rate, we show that whenever there exists a static state feedback control that renders the closed loop system dissipative, then there exists a solution to the Hamilton-Jacobi-Isaacs PDI/PDE in the viscosity solution. This extends and generalizes a number of synthesis results in the nonlinear H control literature. We then consider a general dissipative output feedback control problem and propose a solution by employing the recently developed information state method. We formulate an information state and then convert the original output feedback problem into a new full state one in which the information state provides the appropriate state. The dynamics of the information state takes the form of a controlled PDE. We then solve the new problem by using game theoretic methods leading to a (infinite dimensional) HJI PDI. This is the relevant (ontrolled) dissipation inequality for the output feedback problem at hand. The solution is then specialized to bilinear and linear systems yielding finite dimensional solutions. As a by product, we formulate and solve a general dissipativity filtering problem for nonlinear and linear systems. The problem takes the nonlinear H filtering as a special case. As in the control case, the solution to the filtering problem is expressed in terms of a controlled PDE describing the dynamics of the corresponding information state and a(infinite dimensional) HJI PDI. When specialized to linear systems with a general quadratic supply rate, the solution reduces to new finite dimensional linear filters with the (central) linear H filter appearing as a special one. Finally, we propose application of general dissipativity control methods to two stabilization problems. In the first problem we look for a controller that stabilizes linear systems possesing sector bounded nonlinearities at their inputs and outputs. In the second one, we look for a controller that stabilizes an uncertain nonlinear systenfconsisting of a nonlinear nominal model and an unknown nonlinear model belonging to a class of general dissipative systems described in terms of a specific suppply rate function. In either case, we pose the stabilization problem as a dissipativity control synthesis one for a related system

Modeling, Analysis, and Optimization Issues for Large Space Structures

Topics concerning the modeling, analysis, and optimization of large space structures are discussed including structure-control interaction, structural and structural dynamics modeling, thermal analysis, testing, and design

SciCADE 95: International conference on scientific computation and differential equations

This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science

NASA Workshop on Distributed Parameter Modeling and Control of Flexible Aerospace Systems

Although significant advances have been made in modeling and controlling flexible systems, there remains a need for improvements in model accuracy and in control performance. The finite element models of flexible systems are unduly complex and are almost intractable to optimum parameter estimation for refinement using experimental data. Distributed parameter or continuum modeling offers some advantages and some challenges in both modeling and control. Continuum models often result in a significantly reduced number of model parameters, thereby enabling optimum parameter estimation. The dynamic equations of motion of continuum models provide the advantage of allowing the embedding of the control system dynamics, thus forming a complete set of system dynamics. There is also increased insight provided by the continuum model approach

Synthesis, optimisation and control of crystallization systems

Process systems engineering has provided with a range of powerful tools to chemical engineers for synthesis, optimisation and control using thorough understanding of the processes enhanced with the aid of sophisticated and accurate multi-faceted mathematical models. Crystallization processes have rarely benefited from these new techniques, for they lack in models that could be used to bridge the gaps in their perception before utilising the resulting insight for the three above mentioned tasks. In the present work, first a consistent and sufficiently complex models for unit operations including MSMPR crystallizer, hydrocyclone and fines dissolver are developed to enhance the understanding of systems comprising these units. This insight is then utilised for devising innovative techniques to synthesise, optimise and control such processes. A constructive targeting approach is developed for innovative synthesis of stage-wise crystallization processes. The resulting solution surpasses the performance obtained from conventional design procedure not only because optimal temperature profiles are used along the crystallizers but also the distribution of feed and product removal is optimally determined through non-linear programming. The revised Machine Learning methodology presented here for continual process improvement by analysing process data and representing the findings as zone of best average performance, has directly utilised the models to generate the data in the absence of real plant data. The methodology which is demonstrated through KNO₃ crystallization process flowsheet quickly identifies three opportunities each representing an increase of 12% on nominal operation. An optimal multi-variable controller has been designed for a one litre continuous recycle crystallizer to indirectly control total number and average size of crystals from secondary process measurements. The system identification is solely based on experimental findings. Linear Quadratic Gaussian method based design procedure is developed to design the controller which not only shows excellent set-point tracking capabilities but also effectively rejects disturbance in the simulated closed loop runs

Proceedings of the 3rd Annual Conference on Aerospace Computational Control, volume 1

Conference topics included definition of tool requirements, advanced multibody component representation descriptions, model reduction, parallel computation, real time simulation, control design and analysis software, user interface issues, testing and verification, and applications to spacecraft, robotics, and aircraft