Tools for Nonlinear Control Systems Design

This is a brief statement of the research progress made on Grant NAG2-243 titled "Tools for Nonlinear Control Systems Design", which ran from 1983 till December 1996. The initial set of PIs on the grant were C. A. Desoer, E. L. Polak and myself (for 1983). From 1984 till 1991 Desoer and I were the Pls and finally I was the sole PI from 1991 till the end of 1996. The project has been an unusually longstanding and extremely fruitful partnership, with many technical exchanges, visits, workshops and new avenues of investigation begun on this grant. There were student visits, long term.visitors on the grant and many interesting joint projects. In this final report I will only give a cursory description of the technical work done on the grant, since there was a tradition of annual progress reports and a proposal for the succeeding year. These progress reports cum proposals are attached as Appendix A to this report. Appendix B consists of papers by me and my students as co-authors sorted chronologically. When there are multiple related versions of a paper, such as a conference version and journal version they are listed together. Appendix C consists of papers by Desoer and his students as well as 'solo' publications by other researchers supported on this grant similarly chronologically sorted

On output feedback nonlinear model predictive control using high gain observers for a class of systems

In recent years, nonlinear model predictive control schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in connection to nonlinear predictive control. Most of the existing approaches for output feedback nonlinear model predictive control do only guarantee local stability. Here we consider the combination of stabilizing instantaneous NMPC schemes with high gain observers. For a special MIMO system class we show that the closed loop is asymptotically stable, and that the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme are recovered for a high gain observer with large enough gain and thus leading to semi-global/non-local results

Robust Output Feedback of Minimum Phase Nonlinear Systems

A robust output feedback controller is synthesized for minimum phase multivariable nonlinear systems based on thedifferential geometry approach. Using the internal model control structure within the input-output (I/O) linearizationframework, the controller is combined with a closed-loop observer to estimate transformed states in the outer-loop. It isshown that the controller-observer combination achieves robust tracking and estimation using simple tuningparameters. The effectiveness of the proposed system is illustrated by a simulation example for control of concentrationin a chemical reactor

Composite nonlinear feedback control for systems with actuator saturation - Towards improved tracking performance

Ph.DDOCTOR OF PHILOSOPH

A receding horizon generalization of pointwise min-norm controllers

Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a CLF based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuous-time receding horizon control law. The issue of implementation under discrete-time sampling is then discussed as a modification. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem. Finally, stronger connections to both optimal and pointwise min-norm control are proved

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Robust asymptotic stabilization of nonlinear systems by state feedback

International audienceWe show that regulation to a constant value of the output of a process can be achieved robustly by designing a stabilizer for a model augmented with an integrator of the output and by having the model dynamics close enough to the process ones. This is nothing but the PI controller paradigm extended to the case of nonlinear systems. We recall also that the forwarding technique is well suited for this particular stabilizer design. Finally we illustrate our result with solving the problem of regulating the flight path angle of the longitudinal mode of a plane

Robust Asymptotic Stabilization of Nonlinear Systems with Non-Hyperbolic Zero Dynamics

In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to design locally Lipschitz stabilizers under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models.Comment: 30 pages. Preliminary versions accepted at the 47th IEEE Conference on Decision and Control, 200

Backstepping Control and Transformation of Multi-Input Multi-Output Affine Nonlinear Systems into a Strict Feedback Form

This dissertation presents an improved method for controlling multi-input multi-output affine nonlinear systems. A method based on Lie derivatives of the system\u27s outputs is proposed to transform the system into an equivalent strict feedback form. This enables using backstepping control approaches based on Lyapunov stability and integrator backstepping theory to be applied. The geometrical coordinate transformation of multi-input multi-output affine nonlinear systems into strict feedback form has not been detailed in previous publications. In this research, a new approach is presented that extends the transformation process of single-input single-output nonlinear. A general algorithm of the transformation process is formulated. The research will consider square feedback linearizable multi-input multi-output systems where the number of inputs equals to the number of outputs. The preliminary mathematical tools, necessary and sufficient feedback linearizability conditions, as well as a step-by-step transformation process is explained in this research. The approach is applied to the Western Electricity Coordinating Council (WECC) 3-machine nonlinear power system model. Detailed simulation results indicate that the proposed design method is effective in stabilizing the WECC power system when subjected to large disturbances