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

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

Normative EMG activation patterns of school-age children during gait

Gait analysis is widely used in clinics to study walking abnormalities for surgery planning, definition of rehabilitation protocols, and objective evaluation of clinical outcomes. Surface electromyography allows the study of muscle activity non-invasively and the evaluation of the timing of muscle activation during movement. The aim of this study was to present a normative dataset of muscle activation patterns obtained from a large number of strides in a population of 100 healthy children aged 6-11 years. The activity of Tibialis Anterior, Lateral head of Gastrocnemius, Vastus Medialis, Rectus Femoris and Lateral Hamstrings on both lower limbs was analyzed during a 2.5-min walk at free speed. More than 120 consecutive strides were analyzed for each child, resulting in approximately 28,000 strides. Onset and offset instants were reported for each observed muscle. The analysis of a high number of strides for each participant allowed us to obtain the most recurrent patterns of activation during gait, demonstrating that a subject uses a specific muscle with different activation modalities even in the same walk. The knowledge of the various activation patterns and of their statistics will be of help in clinical gait analysis and will serve as reference in the design of future gait studie

Cross-Sectional Associations Bet ween Abdominal and Thoracic Adipose Tissue Compartments and Adiponectin and Resistin in the Framingham Heart Study

OBJECTIVE: To test the association of regional fat depots with circulating adiponectin and resistin concentrations and to assess the potential mediating effect of adipokines on associations between abdominal fat depots and cardiometabolic risk factors. RESEARCH DESIGN AND METHODS: Participants from the Framingham Heart Study offspring cohort (n = 916, 55% women; mean age 59 years) free of cardiovascular disease underwent computed tomography measurement of visceral adipose tissue (VAT), subcutaneous adipose tissue (SAT), pericardial fat, and intrathoracic fat volumes and assays of circulating adiponectin and resistin. RESULTS: VAT, SAT, pericardial fat, and intrathoracic fat were negatively correlated with adiponectin (r = −0.19 to −0.34, P < 0.001 [women]; r = −0.15 to −0.26, P < 0.01 [men] except SAT) and positively correlated with resistin (r = 0.16–0.21, P < 0.001 [women]; r = 0.11–0.14, P < 0.05 [men] except VAT). VAT increased the multivariable model R2 for adiponectin from 2–4% to 10–13% and for resistin from 3–4% to 3–6%. Adjustment for adipokines did not fully attenuate associations between VAT, SAT, and cardiometabolic risk factors. CONCLUSIONS: Adiponectin and resistin are correlated with fat depots cross-sectionally, but none of the adipokines can serve as surrogates for the fat depots. Relations between VAT, SAT, and cardiometabolic risk factors were not fully explained by adiponectin or resistin concentrations.National Insitute's of Health National Heart, Lung, and Blood Institute’s Framingham Heart Study (N01-HC-25195); the National Institutes of Health; National Center for Research Resources; General Clinical Research Centers Program (M01-RR-01066); Career Development Award from the American Diabetes Association; National Institute of Diabetes and Digestive and Kidney Diseases (K24 DK080140, RO1 DK080739); National Heart, Lung, and Blood Institute, National Institutes of Health (2K24HL04334