Approximate Nonlinear Regulation via Identification-Based Adaptive Internal Models

This article concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear Luenberger observers. Adaptation is performed by means of discrete-time system identification schemes, in which every algorithm fulfilling some optimality and stability conditions can be used. Practical and approximate regulation results are given relating the prediction capabilities of the identified model to the asymptotic bound on the regulated variables, which become asymptotic whenever a “right” internal model exists in the identifier's model set. The proposed approach, moreover, does not require “high-gain” stabilization actions

Automatic Retraction and Full Cycle Operation for a Class of Airborne Wind Energy Generators

Airborne wind energy systems aim to harvest the power of winds blowing at altitudes higher than what conventional wind turbines reach. They employ a tethered flying structure, usually a wing, and exploit the aerodynamic lift to produce electrical power. In the case of ground-based systems, where the traction force on the tether is used to drive a generator on the ground, a two phase power cycle is carried out: one phase to produce power, where the tether is reeled out under high traction force, and a second phase where the tether is recoiled under minimal load. The problem of controlling a tethered wing in this second phase, the retraction phase, is addressed here, by proposing two possible control strategies. Theoretical analyses, numerical simulations, and experimental results are presented to show the performance of the two approaches. Finally, the experimental results of complete autonomous power generation cycles are reported and compared with first-principle models.Comment: This manuscript is a preprint of a paper submitted for possible publication on the IEEE Transactions on Control Systems Technology and is subject to IEEE Copyright. If accepted, the copy of record will be available at IEEEXplore library: http://ieeexplore.ieee.or

"Class-Type" identification-based internal models in multivariable nonlinear output regulation

The paper deals with the problem of output regulation in a “non-equilibrium” context for a special class of multivariable nonlinear systems stabilizable by high-gain feedback. A post-processing internal model design suitable for the multivariable nature of the system, which might have more inputs than regulation errors, is proposed. Uncertainties in the system and exosystem are dealt with by assuming that the ideal steady state input belongs to a certain “class of signals" by which an appropriate model set for the internal model can be derived. The adaptation mechanism for the internal model is then cast as an identification problem and a least square solution is specifically developed. In line with recent developments in the field, the vision that emerges from the paper is that approximate, possibly asymptotic, regulation is the appropriate way of approaching the problem in a multivariable and uncertain context. New insights about the use of identification tools in the design of adaptive internal models are also presented

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

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

Notions of Input to Output Stability

This paper deals with several related notions of output stability with respect to inputs. The inputs may be thought of as disturbances; when there are no inputs, one obtains generalizations of the classical concepts of partial stability. The main notion studied is called input to output stability (IOS), and it reduces to input to state stability (ISS) when the output equals the complete state. Several variants, which formalize in different manners the transient behavior, are introduced. The main results provide a comparison among these notions. A companion paper establishes necessary and sufficient Lyapunov-theoretic characterizations.Comment: 16 pages See http://www.math.rutgers.edu/~sontag/ for many related paper

Optimal Output Modification and Robust Control Using Minimum Gain and the Large Gain Theorem

When confronted with a control problem, the input-output properties of the system to be controlled play an important role in determining strategies that can or should be applied, as well as the achievable closed-loop performance. Optimal output modification is a process in which the system output is modified in such a manner that the modified system has a desired input-output property and the modified output is as similar as possible to a specified desired output. The first part of this dissertation develops linear matrix inequality (LMI)-based optimal output modification techniques to render a linear time-invariant (LTI) system minimum phase using parallel feedforward control or strictly positive real by linearly interpolating sensor measurements. H-ininifty-optimal parallel feedforward controller synthesis methods that rely on the input-output system property of minimum gain are derived and tested on a numerical example. The H2- and H-infinity-optimal sensor interpolation techniques are implemented in numerical simulations of noncolocated elastic mechanical systems. All mathematical models of physical systems are, to some degree, uncertain. Robust control can provide a guarantee of closed-loop stability and/or performance of a system subject to uncertainty, and is often performed using the well-known Small Gain Theorem. The second part of this dissertation introduces the lessor-known Large Gain Theorem and establishes its use for robust control. A proof of the Large Gain Theorem for LTI systems using the familiar Nyquist stability criterion is derived, with the goal of drawing parallels to the Small Gain Theorem and increasing the understanding and appreciation of this theorem within the control systems community. LMI-based robust controller synthesis methods using the Large Gain Theorem are presented and tested numerically on a robust control benchmark problem with a comparison to H-infinity robust control. The numerical results demonstrate the practicality of performing robust control with the Large Gain Theorem, including its ability to guarantee an uncertain closed-loop system is minimum phase, which is a robust performance problem that previous robust control techniques could not solve.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143934/1/caverly_1.pd