Quadratic Gaussian Optimal Control Research Articles

Dynamic Personalized Monitoring and Treatment Control of Glaucoma

To e↵ectively manage chronic disease patients, clinicians must know (1) how to monitor each patient (i.e., when to schedule the next visit and which tests to take), and (2) how to control the disease (i.e., what levels of controllable risk factors will su ciently slow progression). Our research addresses these questions simultaneously and optimally by employing linear quadratic Gaussian state space systems modeling and optimal control of measurement adaptive systems. For the new quadratic objective of minimizing disease progression over time, we show that the classical two-way separation of estimation and control holds, thereby making a previously intractable problem solvable by decomposition into two separate, tractable problems while maintaining optimality. The resulting optimization is applied to the management of glaucoma. Based on data from two large randomized clinical trials, we found that fast-progressing patients, who are most at risk for disease progression, show an average of 38% to 58% less loss of peripheral vision per year, leading to 21% to 32% better quality of vision after 10 years when compared to existing treatment controls attained in the clinical trials. This methodology can be applied to a broad range of chronic diseases to optimally devise patient-specific monitoring and treatment plans.

Active vibration control of an arbitrary thick piezolaminated beam with imperfectly integrated sensor and actuator layers

A spatial state-space formulation based on the linear twodimensional piezoelasticity theory and involving local/global transfer matrices is applied to investigate the active vibration suppression of a simply supported, arbitrarily thick, orthotropic elastic beam, imperfectly integrated with spatially distributed piezoelectric actuator and sensor layers on its top and bottom surfaces, respectively. A linear spring-layer model is adopted to simulate the bonding imperfections between the host structure and the piezoelectric layers. To assist control system design, system identification is conducted by applying a frequency domain subspace approximation method with N4SID algorithm based on the first five structural modes of the system. The state space model is constructed from system identification and used for state estimation and development of control algorithm. A linear quadratic Gaussian (LQG) optimal controller is subsequently designed and simulated based on the identified model in order to actively control the response of the smart structure in both frequency and time domains.

Optimal Controller for Stochastic Polynomial Systems with State-Dependent Polynomial Input

This paper presents an optimal quadratic-Gaussian controller for stochastic polynomial systems with a state-dependent polynomial control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As an intermediate result, the paper gives a closed-form solution of the optimal regulator (control) problem for polynomial systems with a state-dependent polynomial control input and a quadratic criterion. Performance of the obtained optimal controller is verified in an illustrative example against a conventional linear-quadratic-Gaussian (LQG) controller that is optimal for linearized systems. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.

Experimental Study of Adaptive-$Q$ Control for Disk Drive Track-Following Servo Problem

This paper presents the design of an adaptive-Q control algorithm for minimizing the position error signal (PES) in a hard-disk-drive track-following servo. Also, we discuss the results obtained from experiments done on a commercial disk drive using the said scheme. The adaptive- Q control algorithm approach uses the well-known result that all stabilizing controllers for a plant can be synthesized by conveniently parametrized augmentation to a nominal controller. The augmentation to a linear quadratic Gaussian (LQG) optimal control is parametrized by a stable filter Q. The Q filter is restricted to a finite-impulse response filter, which minimizes the rms value of the track following error. Experiments done with a fifth-order adaptive filter that uses PES signal as feedback show a 15% improvement in the achievable track misregistration over a model-based LQG controller. The adaptive-Q algorithm implemented via a recursive least squares numerically stable adaptive algorithm shows fast convergence rate and a consistent performance improvement over a fixed controller for various track locations. Also, the tracking performance improves with increase in the adaptive filter order.

Optimal controller for uncertain stochastic polynomial systems with deterministic disturbances

This article presents the optimal quadratic-Gaussian controller for uncertain stochastic polynomial systems with unknown coefficients and matched deterministic disturbances over linear observations and a quadratic criterion. The optimal closed-form controller equations are obtained through the separation principle, whose applicability to the considered problem is substantiated. As intermediate results, this article gives closed-form solutions of the optimal regulator, controller and identifier problems for stochastic polynomial systems with linear control input and a quadratic criterion. The original problem for uncertain stochastic polynomial systems with matched deterministic disturbances is solved using the integral sliding mode algorithm. Performance of the obtained optimal controller is verified in the illustrative example against the conventional quadratic-Gaussian controller that is optimal for stochastic polynomial systems with known parameters and without deterministic disturbances. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.

Optimal controller for uncertain stochastic polynomial systems

This paper presents the optimal quadratic-Gaussian controller for uncertain stochastic polynomial systems with linear control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As intermediate results, the paper gives closed-form solutions of the optimal regulator and controller problems for stochastic polynomial systems with linear control input and a quadratic criterion. Performance of the obtained optimal controller is verified in the illustrative example against the conventional quadratic-Gaussian controller that is optimal for stochastic polynomial systems with known parameters. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.

Control of transient flow in irrigation canals using Lyapunov fuzzy filter-based Gaussian regulator

An optimal fuzzy filter was applied to solve the state estimation problem of the controlled irrigation canals. Using linearized finite-difference model of the open-channel flow, a canal operation problem was formulated as an optimal control problem and an algorithm for gate openings in the presence of unknown external disturbances was derived. A fuzzy filter was designed to estimate the state variables at the intermediate nodes based upon measured values of depth at the points in the canal. A Lyapunov function was utilized as a performance index to formulate the fuzzy interference rules of the optimal fuzzy filter. A linear quadratic Gaussian (LQG) optimal controller for a multi-pool irrigation canal was considered as an example. The state estimation problem in the controller was simulated using two techniques: Kalman estimator and the proposed fuzzy filter. The performance of the fuzzy state estimator designed using the Lyapunov fuzzy technique was compared with the results obtained using the Kalman estimator technique. The obvious advantages of the fuzzy filter were the lower computational costs and ease of implementation. The results of this study demonstrated that proposed Lyapunov-type fuzzy filter provides both good stability and simplicity in the control of irrigation canals more than a Kalman filter. Copyright © 2005 John Wiley & Sons, Ltd.

Application of the l/sup 1/-optimal regulation strategy to a hard disk servo system

This paper examines the use of the l/sup 1/-optimal regulation strategy on a hard disk servo system. The l/sup 1/-optimal regulation algorithm seeks to minimize the maximum position error signal (PES), which is the deviation of the read/write head from the center of the track. Comparison studies were made against the linear quadratic Gaussian (LQG) optimal control strategy. Experimental results show that the LQG control algorithm helps to reduce the energy of the PES, but does not help to reduce the maximum error signal. On the other hand, the l/sup 1/-optimal control scheme reduces the maximum error signal. The energy of the error signal, however, is larger.