Data-based Control of Feedback Linearizable Systems

We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems. We study the effect of approximating the unknown nonlinearities with a choice of basis functions that depend only on input and output data, then provide error bounds on the results of the data-based simulation and output matching control problems. Furthermore, we use this data-based approximation of the trajectories of the nonlinear system to design a multi-step robust data-based nonlinear predictive control scheme. We show that this control scheme is recursively feasible and renders the closed-loop system practically exponentially stable. Finally, we illustrate our results on a model of a fully-actuated double inverted pendulum.Comment: submitted to IEEE Transactions on Automatic Contro

On the design of persistently exciting inputs for data-driven control of linear and nonlinear systems

In the context of data-driven control, persistence of excitation (PE) of an input sequence is defined in terms of a rank condition on the Hankel matrix of the input data. For nonlinear systems, recent results employed rank conditions involving collected input and state/output data, for which no guidelines are available on how to satisfy them a priori. In this paper, we first show that a set of discrete impulses is guaranteed to be persistently exciting for any controllable LTI system. Based on this result, for certain classes of nonlinear systems, we guarantee persistence of excitation of sequences of basis functions a priori, by design of the physical input only

Neural Network Controller Development and Implementation for Spark Ignition Engines with High EGR Levels

Past research has shown substantial reductions in the oxides of nitrogen (NOx) concentrations by using 10% -25% exhaust gas recirculation (EGR) in spark ignition (SI) engines (see Dudek and Sain, 1989). However, under high EGR levels, the engine exhibits strong cyclic dispersion in heat release which may lead to instability and unsatisfactory performance preventing commercial engines to operate with high EGR levels. A neural network (NN)-based output feedback controller is developed to reduce cyclic variation in the heat release under high levels of EGR even when the engine dynamics are unknown by using fuel as the control input. A separate control loop was designed for controlling EGR levels. The stability analysis of the closed-loop system is given and the boundedness of the control input is demonstrated by relaxing separation principle, persistency of excitation condition, certainty equivalence principle, and linear in the unknown parameter assumptions. Online training is used for the adaptive NN and no offline training phase is needed. This online learning feature and model-free approach is used to demonstrate the applicability of the controller on a different engine with minimal effort. Simulation results demonstrate that the cyclic dispersion is reduced significantly using the proposed controller when implemented on an engine model that has been validated experimentally. For a single cylinder research engine fitted with a modern four-valve head (Ricardo engine), experimental results at 15% EGR indicate that cyclic dispersion was reduced 33% by the controller, an improvement of fuel efficiency by 2%, and a 90% drop in NOx from stoichiometric operation without EGR was observed. Moreover, unburned hydrocarbons (uHC) drop by 6% due to NN control as compared to the uncontrolled scenario due to the drop in cyclic dispersion. Similar performance was observed with the controller on a different engine

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