Robust Adaptive Control

Several concepts and results in robust adaptive control are are discussed and is organized in three parts. The first part surveys existing algorithms. Different formulations of the problem and theoretical solutions that have been suggested are reviewed here. The second part contains new results related to the role of persistent excitation in robust adaptive systems and the use of hybrid control to improve robustness. In the third part promising new areas for future research are suggested which combine different approaches currently known

Discrete-Time Adaptive Control of a Class of Nonlinear Systems Using High-Order Tuners

This paper concerns the adaptive control of a class of discrete-time nonlinear systems with all states accessible. Recently, a high-order tuner algorithm was developed for the minimization of convex loss functions with time-varying regressors in the context of an identification problem. Based on Nesterov's algorithm, the high-order tuner was shown to guarantee bounded parameter estimation when regressors vary with time, and to lead to accelerated convergence of the tracking error when regressors are constant. In this paper, we apply the high-order tuner to the adaptive control of a particular class of discrete-time nonlinear dynamical systems. First, we show that for plants of this class, the underlying dynamical error model can be causally converted to an algebraic error model. Second, we show that using this algebraic error model, the high-order tuner can be applied to provably stabilize the class of dynamical systems around a reference trajectory.Comment: 8 pages, submitted to the 2023 AC

Connections Between Adaptive Control and Optimization in Machine Learning

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.Comment: 18 page

Robust adaptive posicast controller

Adaptive Posicast Controller that is robust to delay-mismatch is introduced in this paper. Inspired from a recent result on guaranteed delay margins in adaptive control, the original adaptive laws of the above mentioned controller are modified using projection to compensate the uncertainty in the input delay. It is conjectured and shown in simulations that even though the assumed upper bound for the delay value is exceeded, Adaptive Posicast Controller with projection algorithm keeps all the system signals bounded. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved

Adaptive Control of a Generic Hypersonic Vehicle

This paper presents an adaptive augmented, gain-scheduled baseline LQR-PI controller applied to the Road Runner six-degree-of-freedom generic hypersonic vehicle model. Uncertainty in control effectiveness, longitudinal center of gravity location, and aerodynamic coefficients are introduced in the model, as well as sensor bias and noise, and input time delays. The performance of the baseline controller is compared to the same design augmented with one of two different model-reference adaptive controllers: a classical open- loop reference model design, and modified closed-loop reference model design. Both adaptive controllers show improved command tracking and stability over the baseline controller when subject to these uncertainties. The closed-loop reference model controller offers the best performance, tolerating a reduced control effectiveness of 50%, rearward center of gravity shift of up to -1.6 feet (11% of vehicle length), aerodynamic coefficient uncertainty scaled 4× the nominal value, and sensor bias of up to +3.2 degrees on sideslip angle measurement. The closed-loop reference model adaptive controller maintains at least 70% of the delay margin provided by the robust baseline design when subject to varying levels of uncertainty, tolerating input time delays of between 15-41 ms during 3 degree angle of attack doublet, and 80 degree roll step commands.Approved for Public Release; Distribution Unlimited. Case Number 88ABW-2013-3392

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

This paper presents a new method of synthesizing an output feedback adaptive controller for a class of uncertain, non-square, multi-input multi-output systems that often occur in hypersonic vehicle models. The main challenge that needs to be addressed is the determination of a corresponding square and strictly positive real transfer function. This paper proposes a new procedure to synthesize two gain matrices that allows the realization of such a transfer function, thereby allowing a globally stable adaptive output feedback law to be generated. The unique features of this output feedback adaptive controller are a baseline controller that uses a Luenberger observer, a closed-loop reference model, manipulations of a bilinear matrix inequality, and the Kalman-Yakubovich Lemma. Using these features, a simple design procedure is proposed for the adaptive controller, and the corresponding stability property is established. The proposed adaptive controller is compared to the classical multi-input multi-output adaptive controller. A numerical example based on a scramjet powered, blended wing-body generic hypersonic vehicle model is presented. The 6 degree-of-freedom nonlinear vehicle model is linearized, giving the design model for which the controller is synthesized. The adaptive output feedback controller is then applied to an evaluation model, which is nonlinear, coupled, and includes actuator dynamics, and is shown to result in stable tracking in the presence of uncertainties that destabilize the baseline linear output feedback controller.This research is funded by the Air Force Research Laboratory/Aerospace Systems Directorate grant FA 8650-07-2-3744 for the Michigan/MIT/AFRL Collaborative Center in Control Sciences and the Boeing Strategic University Initiative. Approved for Public Release; Distribution Unlimited. Case Number 88ABW- 2014-2551

Control of Uncertain Sampled-Data Systems: An Adaptive Posicast Control Approach

This technical note proposes a discrete-time adaptive controller for the control of sampled-data systems. The design is inspired from the Adaptive Posicast Controller (APC) which was designed for time-delay systems in continuous time. Due to the performance degradation caused by digital approximation of continuous laws, together with the problem of assuming time-delays as integer multiples of sampling intervals, the benefits of APC could not be fully realized. In this technical note, these approximations/assumptions are eliminated. In addition, a disturbance observer is incorporated into the controller design which minimizes the effect of disturbances on the system. Extension to the case of uncertain input time-delay is also presented. The proposed approach is verified in simulation studies. © 1963-2012 IEEE