Robert L. Kosut

Set-membership identification of systems with parametric and nonparametric uncertainty

A method for parameter set estimation in which the system model is assumed to contain both parametric and nonparametric uncertainty is presented. In the disturbance-free case, the parameter set estimate is guaranteed to contain the parameter set of the true plant. In the presence of stochastic disturbances, the parameter set estimate obtained from finite data records is shown to have the property that it contains the true-plant parameter set with probability one as the data length tends to infinity. >

Robust adaptive control: Conditions for global stability

An input-output approach is presented for analyzing the global stability and robustness properties of adaptive controllers to unmodeled dynamics. The concept of a tuned system is introduced, i.e., the control system that could be obtained if the plant were known. Comparing the adaptive system to the tuned system results in the development of a generic adaptive error system. Passivity theory is used to derive conditions which guarantee global stability of the error system associated with the adaptive controller, and ensure boundedness of the adaptive gains. Specific bounds are presented for certain significant signals in the control systems. Limitations of these global results are discussed, particularly the requirement that a certain operator be strictly positive real (SPR)-a condition that is unlikely to hold due to unmodeled dynamics.

On some key issues in the Windsurfer approach to adaptive robust control

We examine a number of crucial questions that arise in the windsurfer approach to adaptive robust control. Considerations are limited to the case where the plant is stable and has no zeros on the imaginary axis. The key conclusion is that, given a strictly proper stable model of a strictly proper stable plant, we can improve the performance robustness of the closed-loop system through the windsurfer approach if the plant and the existing model have no unstable zeros within the designed closed-loop bandwidth and if the deterioration in performance robustness caused by increasing the closed-loop bandwidth results in a sufficiently high signal-to-noise ratio for a certain closed-loop output error. Situations that may cause the iterative identification and control design process to terminate prematurely are identified. A simulation example is used to illustrate the results discussed.

Toward closed-loop optimization of deep brain stimulation for Parkinson's disease: concepts and lessons from a computational model

Deep brain stimulation (DBS) of the subthalamic nucleus with periodic, high-frequency pulse trains is an increasingly standard therapy for advanced Parkinsons disease. Here, we propose that a closed-loop global optimization algorithm may identify novel DBS waveforms that could be more effective than their high-frequency counterparts. We use results from a computational model of the Parkinsonian basal ganglia to illustrate general issues relevant to eventual clinical or experimental tests of such an algorithm. Specifically, while the relationship between DBS characteristics and performance is highly complex, global search methods appear able to identify novel and effective waveforms with convergence rates that are acceptably fast to merit further investigation in laboratory or clinical settings.

Efficient measurement of quantum dynamics via compressive sensing

The resources required to characterize the dynamics of engineered quantum systems--such as quantum computers and quantum sensors--grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce the experimental configurations required for quantum process tomography. Our method is applicable to processes that are nearly sparse in a certain basis and can be implemented using only single-body preparations and measurements. We perform efficient, high-fidelity estimation of process matrices of a photonic two-qubit logic gate. The database is obtained under various decoherence strengths. Our technique is both accurate and noise robust, thus removing a key roadblock to the development and scaling of quantum technologies.

Stability theory for adaptive systems: Method of averaging and persistency of excitation

A method of averaging is developed for the stability analysis of linear differential equations with small time-varying coefficients which do not necessarily possess a (global) average. The technique is then applied to determine the stability of a linear equation which arises in the study of adaptive systems where the adaptive parameters are slowly varying. The stability conditions are stated in the frequency-domain which shows the relation between persistent excitation and unmodeled dynamics.

Uncertainty model unfalsification: a system identification paradigm compatible with robust control design

It is shown that unfalsification of the standard robust control design uncertainty model is a natural replacement for system identification when the intended use of the model is robust control design. For the ARX model, the unfalsification step requires solving a set of convex programming problems, specifically LMI problems, of which ordinary least-squares is one member. The result is a tradeoff curve between model uncertainty and disturbance uncertainty. Hence, a family of models are unfalsified from the data record. The tradeoff curve is given a frequency domain interpretation via, the DFT and related computational issues are discussed.

Robust Control of Flexible Spacecraft

A well-designed feedback control system exhibits the properties of external disturbance attenuation and performance robustness with respect to plant uncertainty. The plant uncertainties of flexible spacecraft include unmodeled dynamics and parameter uncertainties. Singular value robustness measures are used to compare performance and stability robustness properties of different control design techniques in the presence of residual modal interaction (control and observation spillover) for a design example which is representative of a practical flexible spacecraft system. The control designs evaluated include linear quadratic geometry (LQG) control, integral feedback, bias removal control, innovations feedthrough, and frequency-shaped LQG.

Adaptive control with saturating inputs

An extension of the results from Goodwin, Ramadge and Caines [1] to the case where the input of the linear system saturates is presented. A necessary condition for closed loop stability of such a system is shown to be that the system must remain in a region from which y(t) = 0 is reachable with saturating inputs. With a slight modification of the original algorithm, the closed loop system is shown to be stable whenever the plant is exponentially stable.

Adaptive Proximate Time-Optimal Servomechanisms: Continuous Time Case

A Proximate Time-Optimal Servo (PTOS) is developed, along with conditions for its stability. An algorithm is proposed for adapting the PTOS (APTOS) to improve performance in the face of uncertain plant parameters. Under ideal conditions APTOS is shown to be uniformly asymptotically stable. Simulation results demonstrate the predicted performance.