Optimal Determination of Respiratory Airflow Patterns Using a Nonlinear Multicompartment Model for a Lung Mechanics System

We develop optimal respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. Specifically, we use classical calculus of variations minimization techniques to derive an optimal airflow pattern for inspiratory and expiratory breathing cycles. The physiological interpretation of the optimality criteria used involves the minimization of work of breathing and lung volume acceleration for the inspiratory phase, and the minimization of the elastic potential energy and rapid airflow rate changes for the expiratory phase. Finally, we numerically integrate the resulting nonlinear two-point boundary value problems to determine the optimal airflow patterns over the inspiratory and expiratory breathing cycles

Integrated control-system design via generalized LQG (GLQG) theory

Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations

ROBUST STABILITY AND PERFORMANCE ANALYSIS FOR STATE-SPACE SYSTEMS VIA QUADRATIC LYAPUNOV BOUNDS

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57854/1/BernsteinHaddadRobustStabilitySIMAX.pd

The Optimal Projection Equations for Reduced-Order State Estimation: The Singular Measurement Noise Case

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57879/1/OptProjSingStateEstTAC1987.pd

Robust stabilization with positive real uncertainty: Beyond the small gain theorem

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57858/1/PosRealUncSCL1991.pd

Parameter-Dependent Lyapunov Functions and the Popov Criterion in Robust Analysis and Synthesis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57842/1/ParDepPopovTAC1995.pd

The Optimal Projection Equations with Petersen-Hollot Bounds: Robust Stability and Performance Via Fixed-Order Dynamic Compensation for Systems with Structured Real-valued Parameter Uncertainty

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57883/1/BernsteinPHBounds.pd

OPTIMAL REDUCED-ORDER SUBSPACE-OBSERVER DESIGN WITH A FREQUENCY -DOMAIN ERROR BOUND

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57840/1/OptimalReduced_OrderSubspace_ObserverDesignwithaFrequency_DomainErrorBound.pd