Eugene Lavretsky

Travis E. Gibson, Zheng Qu, Anuradha M. Annaswamy et al.

This note presents the design and analysis of an adaptive controller for a class of linear plants in the presence of output feedback. This controller makes use of a closed-loop reference model as an observer, and guarantees global stability and asymptotic output tracking.

Benjamin M. Jenkins, Anuradha M. Annaswamy, Eugene Lavretsky et al.

The convergence properties of adaptive systems in terms of excitation conditions on the regressor vector are well known. With persistent excitation of the regressor vector in model reference adaptive control the state error and the adaptation error are globally exponentially stable, or equivalently, exponentially stable in the large. When the excitation condition however is imposed on the reference input or the reference model state it is often incorrectly concluded that the persistent excitation in those signals also implies exponential stability in the large. The definition of persistent excitation is revisited so as to address some possible confusion in the adaptive control literature. It is then shown that persistent excitation of the reference model only implies local persistent excitation (weak persistent excitation). Weak persistent excitation of the regressor is still sufficient for uniform asymptotic stability in the large, but not exponential stability in the large. We show that there exists an infinite region in the state-space of adaptive systems where the state rate is bounded. This infinite region with finite rate of convergence is shown to exist not only in classic open-loop reference model adaptive systems, but also in a new class of closed-loop reference model adaptive systems.

Eugene Lavretsky, Travis E. Gibson

The projection algorithm is frequently used in adaptive control and this note presents a detailed analysis of its properties.

Travis E. Gibson, Anuradha M. Annaswamy, Eugene Lavretsky

This paper explores the properties of adaptive systems with closed-loop reference models. Using additional design freedom available in closed-loop reference models, we design new adaptive controllers that are (a) stable, and (b) have improved transient properties. Numerical studies that complement theoretical derivations are also reported.

Travis E. Gibson, Anuradha M. Annaswamy, Eugene Lavretsky

Closed-loop reference models have recently been proposed for states accessible adaptive systems. They have been shown to have improved transient response over their open loop counter parts. The results in the states accessible case are extended to single input single output plants of arbitrary relative degree.

Heather S. Hussain, Megumi M. Matsutani, Anuradha M. Annaswamy et al.

Robust adaptive control of scalar plants in the presence of unmodeled dynamics is established in this paper. It is shown that implementation of a projection algorithm with standard adaptive control of a scalar plant ensures global boundedness of the overall adaptive system for a class of unmodeled dynamics.

Eugene Lavretsky

The main focus of this talk is to present mathematical fundamentals, state-of-the-art, technical challenges and open problems in control of flight for atmospheric vehicles, such as aircraft and other aerial platforms. Reduced order modeling and flight simulation key features for control applications will be discussed. The emphasis is on the theoretical and engineering aspects of creating and transitioning to practice guidance and flight control systems with guarantees of closed-loop stability, robustness and performance.

Marcel Menner, Heather Hussain, Eugene Lavretsky

This paper introduces a systematic method for designing robust linear controllers using output feedback in the presence of operational constraints. The design uses Nagumo's Theorem and the Comparison Lemma to guarantee constraint satisfaction, while incorporating min-norm optimal control principles inspired by Control Barrier Functions. The resulting controller is a continuous piecewise-linear output feedback policy that preserves the closed-loop system's analyzability using linear systems theory. Due to the linear control design, multi-input multi-output (MIMO) robustness margins can be derived with and without active operational constraints. This paper shows that operational constraints on the system's state can be satisfied using an observer-based output feedback control design. Through flight control trade studies, we demonstrate the practical relevance of the framework in safety-critical aircraft control applications.

Joseph E. Gaudio, Anuradha M. Annaswamy, Eugene Lavretsky et al.

This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error trajectories to tend exponentially fast towards a compact set whenever excitation conditions are satisfied. This algorithm is employed in a large class of problems where unknown parameters are present and are time-varying. It is shown that this algorithm guarantees global boundedness of the state and parameter errors of the system, and avoids an often used filtering approach for constructing key regressor signals. In addition, intervals of time over which these errors tend exponentially fast toward a compact set are provided, both in the presence of finite and persistent excitation. A projection operator is used to ensure the boundedness of the learning rate matrix, as compared to a time-varying forgetting factor. Numerical simulations are provided to complement the theoretical analysis.

Joseph E. Gaudio, Travis E. Gibson, Anuradha M. Annaswamy et al.

This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are examined. Concepts in stability, performance, and learning, common to both fields are then discussed. Building on the similarities in update laws and common concepts, new intersections and opportunities for improved algorithm analysis are provided. In particular, a specific problem related to higher order learning is solved through insights obtained from these intersections.