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The authors present a two-step method for identifying single-input, single-output (SISO) Wiener systems. First, using a single harmonic input, they estimate a non-parametric model of the static non-linearity, which is assumed to be only piecewise continuous. Second, using the identified non-parametric map, the authors use retrospective cost optimisation to identify a parametric model of the linear dynamic system. This method is demonstrated on several examples of increasing complexity.

We provide numerical examples and analysis to show that the adaptive controller given by Theorem 3.1 of Yucelen et al.1 may fail to stabilize plants under the stated conditions. Copyright © 2011 John Wiley & Sons, Ltd.

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.

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.

Input reconstruction is a process where the inputs to a system are estimated using the measured system output and knowledge of the system model. One way to achieve this goal is to invert the system model and cascade delays to guarantee that the inverse is proper. A standing issue in input reconstruction lies in the inversion of nonminimum-phase systems, since the inverse model is unstable. In the present paper we assume that the unknown input is bounded and we present a novel technique that uses Markov parameters to determine the unknown state that minimizes the difference between the unknown input and the estimated input.

We extend retrospective cost adaptive control (RCAC) to command following for uncertain Hammerstein systems. We assume that only one Markov parameter of the linear plant is known and that the input nonlinearity is monotonic but otherwise unknown. Auxiliary nonlinearities are used within RCAC to account for the effect of the input nonlinearity.

We apply an extension of retrospective cost adaptive control (RCAC) to a command-following problem for the uncertain electromagnetically controlled oscillator (ECO). We assume that an estimate of the first Markov parameter of the discretized and linearized plant is known, but RCAC does not require knowledge of the inertia, damping, or stiffness of the plant. RCAC uses a setpoint feedback path and an auxiliary nonlinearity to stabilize the unstable ECO at the commanded equilibria.© 2012 ASME

We apply retrospective cost adaptive control (RCAC) to command-following and disturbance-rejection problems for a diesel engine model. The engine is a multi-input, multi-output system with strong static and dynamic interactions, nonlinearities, uncertainties and nonminimum phase characteristics. We demonstrate that RCAC is effective for both the linearized and nonlinear engine models provided that two Markov parameters of the linearized engine plant model are known, either analytically or through system identification. For the command-following and disturbance-rejection problems, we consider the case when the disturbance is harmonic but otherwise unknown, and while the command signal is harmonic and known but no advance knowledge of its spectrum is assumed to be available.Copyright © 2012 by ASME

We apply retrospective cost adaptive control (RCAC) with auxiliary nonlinearities to a command-following problem for uncertain Hammerstein systems with rate-dependent hysteretic input nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. To account for the hysteretic input nonlinearity, RCAC uses auxiliary nonlinearities that reflect the monotonicity properties of the input nonlinearity. The hysteresis nonlinearity is modeled using the rate-dependent Prandtl-Ishlinskii model.Copyright © 2012 by ASME

We consider the problem of identifying unknown physical processes and estimating inaccessible parameters in the global ionosphere and thermosphere model (GITM). In previous work, we took advantage of developments in the retrospective cost method to estimate unknown thermal conductivity and rate coefficients in a one dimensional column in the atmosphere. In the present work, we extend the application of this method to the identification of unknown inaccessible parameters in 3D GITM, as well as the identification of the unknown subsystem that governs the radiative nitrous oxide cooling process in 1D GITM.

A method is presented to obtain state estimates for a possibly nonminimum-phase system in the presence of unknown harmonic inputs. The method estimates the states and reconstructs the unknown harmonic input. An adaptive feedback model injects an input into the estimator such that the error between the estimator output and the actual output converges to zero despite the presence of the unknown harmonic input. Using input reconstruction based on a retrospective cost, the unknown harmonic input is reconstructed. Using the reconstructed input, the parameters of the adaptive feedback system are updated using recursive least squares. Results are presented for a rigid body, a damped rigid body, and a 2D missile with a three-loop autopilot topology.

We consider the problem of estimating the unknown solar driver F10.7 and physical states in the ionosphere and thermosphere using retrospective cost adaptive state estimation (RCASE). We interface RCASE with the Global Ionosphere Thermosphere Model (GITM) to demonstrate state estimation and F10.7 input reconstruction. We further examine the various factors that affect F10.7 estimation including saturation limits, initial estimates, and RCASE tuning parameters.

We apply an extension of retrospective cost adaptive control (RCAC) to a commandfollowing problem for uncertain Hammerstein systems. In particular, RCAC with a NARMAX controller strucuture is applied to linear systems cascaded with input nonlinearities. We assume that one Markov parameter of the linear plant is known. RCAC also uses knowledge of the monotonicity properties of the input nonlinearity. The goal is to determine whether RCAC with a NARMAX controller structure can improve the command-following performance compared to the linear RCAC controller.

In this paper we apply extensions of retrospective cost adaptive control (RCAC) to a 2D missile model considered in prior papers as a benchmark test of adaptive control methods. The dynamics of the missile are highly nonlinear, and instantaneous linearizations are nonminimum phase due to nose sensing and tail actuation. The results that we present in this paper show that the RCAC controller provides results that are comparable to a highly tuned autopilot based on aerodynamic modeling, whereas the RCAC controller uses no knowledge of the missile’s aerodynamics. These results significantly improve the results obtained on the same problem using an earlier version of RCAC, presented at the 2010 GNC.

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.

Input reconstruction is a process where the inputs to a system are estimated using the measured system output, and possibly some modeling information from the system model. One way to achieve this goal is to invert the system model and cascade delays to guarantee that the inverse is proper. A standing issue in input reconstruction lies in the inversion of nonminimum-phase systems, since the inverse model is unstable. We consider two methods for achieving input reconstruction despite the presence of nonminimum-phase zeros. First, we develop an open-loop partial inversion of the system model using a finite number of frequency points, where the partial inverse is a finite impulse response model and therefore is guaranteed to be asymptotically stable. Second, we examine a closed-loop approach that uses an infinite impulse response model. We demonstrate both methods on several illustrative examples.

In this paper we develop frequency-domain methods for approximating IIR plants with FIR transfer functions. The underlying goal is to increase the performance and robustness of Retrospective-Cost Adaptive Control (RCAC), which 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, or possibly noisy frequency response data. In this paper we investigate the resulting phase mismatch between the true plant and the FIR approximation obtained through linear and nonlinear approximation methods. We consider degradation in the phase mismatch due to uncertainty in the frequency response data.

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.

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.

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.

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.

We develop a method for obtaining state estimates for a possibly nonminimum-phase system in the presence of an unknown harmonic input. We construct a state estimator based on the system model, and then introduce an estimator input provided by an adaptive feedback model whose goal is to drive the estimated output to the measured output despite the presence of the unknown harmonic input. Using input reconstruction based on a retrospective surrogate cost, we reconstruct the unknown harmonic input. Using the reconstructed input we update the parameters of the adaptive model using recursive least squares identification. We then extend the method to nonlinear systems. The performance of this method is compared with the Kalman filter for linear examples, as well as with the extended and unscented Kalman filters for nonlinear examples.

We develop a method for identifying SISO Hammerstein systems with an unknown static nonlinearity, linear dynamics, white input noise and colored output noise. We use least squares with a μ-Markov model to estimate the Markov parameters of the linear time-invariant dynamical system. Since the input to the linear system is not available, we use a substitute (ersatz) nonlinearity to transform the input for use in the regressor matrix. We prove that the Markov parameters of the system can be estimated consistently up to a constant scalar as the amount of data increases. This method is demonstrated with several numerical examples.

We present a two-step method for identifying SISO Hammerstein systems. First, using a persistent input with retrospective cost optimization, we estimate a parametric model of the linear system. Next, we pass a single harmonic signal through the system. We use l-delay input reconstruction with the parametric model of the linear system to estimate the inaccessible intermediate signal. Using the estimate of the intermediate signal we estimate a nonparametric model of the static nonlinearity, which is assumed to be only piecewise continuous. This method is demonstrated on several numerical and experimental examples of increasing complexity.

Data-based model refinement improves the fidelity of a model based on empirical observations. The model refinement structure is a closed-loop system consisting of an initial model, which is assumed to be known, and a feedback correction, which is unknown. We take advantage of the similarity between the feedback structure of model refinement and adaptive feedback control by replacing the unknown correction term with a retrospectivecost-based adaptive control law. The adaptive control law thus estimates the unknown subsystem. We investigate scenarios in which the initial model is derived from physical principles, such as mass-spring-damper systems, in order to obtain estimates of stiffness and damping coefficients. Furthermore, we identify dynamic subsystems for a linear initial model and a nonlinear initial model.

A cumulative retrospective cost adaptive control algorithm is augmented to a gain-scheduled three loop autopilot to assess performance in a nonlinear three-degree-of-freedom missile model. The cumulative retrospective cost adaptive controller requires minimal model information; specifically estimates of the relative degree, 1st nonzero Markov parameter, and nonminimum phase zeros of the linearized missile model. A rate gyro sensor failure is applied to the model and the performance of the control techniques is investigated through an analysis of air-to-air intercept scenarios. The results indicate that an adaptive controller can, to some degree, improve the missile’s ability to engage a target when such a failure occurs. Nomenclature m Missile mass Iyy Missile Inertia g Acceleration due to gravity X;Z Inertial position in the X-Z plane U Inertial velocity component along the body frame x-axis of the center of gravity (CG) W Inertial velocity component along the body frame z-axis of the CG Vm Magnitude of missile velocity M Mach number Az;P Acceleration component along body frame z-axis at pointP along the body x-axis Angle of attack Pitch angle q Body rate Air density Sref Reference area dref Reference length Cx Aerodynamic force coefficient along the body frame x-axis Cz Aerodynamic force coefficient along the body frame z-axis Cm Aerodynamic moment coefficient along the body y-axis at the CG q Dynamic pressure p Tail fin angle T Thrust along body frame x-axis

In this paper we develop a nonlinear observer to estimate the concentration of reactants in a kinetic network when kinetic rate constants are unknown. When kinetic rate constants are unknown a steady-state error is present in the observer states. We thus develop an augmented observer that accounts for this steady-state error. We demonstrate this technique on numerical examples of increasing complexity, starting with a nominal case and then off-nominal cases, where input and output noise corrupt the available measurements, and finally when a kinetic rate constant evolves periodically over time with unknown dynamics.

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.