Anthony M. D'Amato

Frequency-domain stability analysis of retrospective-cost adaptive control for systems with unknown nonminimum-phase zeros

We develop a multi-input, multi-output direct adaptive controller for discrete-time, possibly nonminimum-phase, systems with unknown nonminimum-phase zeros. The adaptive controller requires limited modeling information about the system, specifically, Markov parameters from the control input to the performance variables. Often, only a single Markov parameter is required, even in the nonminimum-phase case. We analysis the stability of the algorithm using a time-and-frequency-domain approach. We demonstrate the algorithm on disturbance-rejection problems, where the disturbance spectra are unknown. This controller is based on a retrospective performance objective, where the controller is updated using either batch or recursive least squares.

Retrospective-cost-based adaptive model refinement for the ionosphere and thermosphere

Mathematical models of physical phenomena are of critical importance in virtually all applications of science and technology. This paper addresses the problem of how to use data to improve the fidelity of a given model. We approach this problem using retrospective cost optimization, a novel technique that uses data to recursively update an unknown subsystem interconnected to a known system. Applications of this research are relevant to a wide range of applications that depend on large-scale models based on first- principles physics, such as the Global Ionosphere-Thermosphere Model (GITM). Using GITM as the truth model, we demonstrate that measurements can be used to identify unknown physics. Specifically, we estimate static thermal conductivity parameters, and we identify a dynamic cooling process.

Retrospective Cost Adaptive Control for Systems with Unknown Nonminimum-Phase Zeros

We develop a multi-input, multi-output direct adaptive controller for discrete-time, possibly nonminimum-phase, systems with unknown nonminimum-phase zeros. The adaptive controller requires limited modeling information about the system, specifically, Markov parameters from the control input to the performance variables. Often, only a single Markov parameter is required, even in the nonminimum-phase case. We demonstrate the algorithm on command-following and disturbance-rejection problems, where the command and disturbance spectra are unknown. This controller is based on a retrospective performance objective, where the controller is updated using either batch or recursive least squares.

Robustness of retrospective cost adaptive control to Markov-parameter uncertainty

In this paper we investigate the robustness of an extended version of retrospective cost adaptive control (RCAC), in which less modeling information is required than in prior versions of this method. RCAC is applicable to MIMO possibly nonminimum-phase (NMP) plants without the need to know the locations of the NMP zeros. The only required modeling information is an FIR approximation of the plant, which may be based on a limited number of Markov parameters. In this paper we investigate the effect of phase mismatch between the true plant and the FIR approximation. Numerical examples demonstrate the relationship between phase mismatch at the command and disturbance frequencies as well as the required level of regularization in the controller update.

System identification using a retrospective correction filter for adaptive feedback model updating

In this paper we use a retrospective correction filter (RCF) to identify MIMO LTI systems. This method uses an adaptive controller in feedback with an initial model. The goal is to adapt the closed-loop response of the system to match the response of an unknown plant to a known input. We demonstrate this method on numerical examples of increasing complexity where the initial model is taken to be a one-step delay. Minimum-phase and nonminimum-phase SISO and MIMO examples are considered. The identification signals used include zero-mean Gaussian white noise as well as sums of sinusoids. Finally, we examine the robustness of this method by identifying these systems in the presence of actuator noise.

Sensor-Only Noncausal Blind Identification of Pseudo Transfer Functions

Abstract Motivated by passive health monitoring applications, we consider blind identification where only sensor measurements are available. The goal is to identify a pseudo transfer function (PTF) between two sensors in the presence of an unknown initial state and unknown exogenous input. For this problem, we choose one sensor to be the pseudo input to the system and we delay the second sensor, treating it as the pseudo output.We show that the order of the pseudo-transfer function is no larger than one higher than the order of the system. We demonstrate this method on a two-degree-of-freedom mass-spring-damper system and validate the identified PTFs by comparing them with analytical results.

Linear Fractional Transformation Identification Using Retrospective Cost Optimization

Abstract In this paper we use retrospective cost optimization to identify linear fractional transformations (LFTs). This method uses an adaptive controller in feedback with a known system model. The goal is to identify the feedback portion of the LFT by adapting the controller with a retrospective cost. We demonstrate this method on numerical examples of increasing complexity, ranging from linear examples with unknown feedback terms to nonlinear examples. Finally, we examine methods for improving the retrospective cost optimization performance.

Retrospective Cost Adaptive Control of Spacecraft Attitude

We apply retrospective cost adaptive control (RCAC) to spacecraft attitude control. First, we develop results for angular rate control. These results are then extended to attitude control. We examine two problems for each of the controllers. For both problems, the spacecraft has an arbitrary initial angular rate, and in the case of attitude control, an arbitrary initial attitude. The objective for the first problem is to bring the body to rest and to a specified attitude in the attitude control case. The second problem seeks to bring the spacecraft to spin about a specified body axis, which, in the case of attitude control, is inertially pointed. We first test the algorithm using an estimate of the spacecraft’s Markov parameters obtained from discretization of the linearized Euler’s and Poisson’s equations. Then, we limit the dependence on knowledge of the mass properties by removing inertia information from the Markov parameter. Finally, we test for robustness by scaling the Markov parameter and rotating the actuator matrix.

Retrospective-cost-based model refinement for system emulation and subsystem identification

We consider the problem of data-based model refinement, where we assume the availability of an initial model, which may incorporate both physical laws and empirical observations. With this initial model as a starting point, our goal is to use additional measurements to refine the model. In particular, components of the model that are poorly modeled can be updated, thereby resulting in a higher fidelity model. We consider two special cases, namely, system emulation and subsystem identification. In the former case, the main system is assumed to be uncertain and we seek an estimate of the unknown subsystem that allows the overall model to approximate the true system. In this case, there is no expectation that the constructed subsystem model approximates the unknown subsystem. In the latter case, we assume that the main system is accurately modeled and we seek an estimate of the unknown subsystem that approximates the unknown subsystem.

Structural Health Determination and Model Refinement for a Deployable Composite Boom

The Air Force Research Laboratory Space Vehicles Directorate previously developed a novel composite boom that enables simplified on-orbit deployment for a class of space structures. These composite members are self deploying, reducing the need for hinge and complex motor mechanisms and resulting in decreased weight and structural complexity. Due to its unique capabilities, NASA chose to incorporate this boom architecture into their Nano-Sail D experiment. This composite boom technology was also chosen as the candidate for an investigation into structural health monitoring (SHM) for space structures. Generally, health monitoring has been used on civil and aeroelastic structures for maintenance applications. It is proposed that SHM concepts can be used on space structures to determine health and indirectly predict changes in structural dynamics, which may be crucial for high precision pointing, maneuvering, and life-prediction applications. To begin investigating this topic, a testbed, capable of cyclically damaging the composite booms with a high degree of repeatability, is constructed. As the composite booms are progressively damaged, a series of dynamic interrogations are used to assess the boom. The goal of this research is to correlate SHM features with dynamic properties, leading to an ability to determine a component’s dynamic characteristics purely from SHM data. Using data gathered for SHM testing, the concept of adaptively updating structural models is demonstrated.