Invariants sets for a class of discrete-time lur'e Systems

16th IFAC World Congress. 03/07/2005. Praga (República Checa)We present a method to estimate the domain of attraction of a class of discrete-time Lur'e systems. A new notion of LNL-invariance, stronger than the traditional invariance concept, is introduced. An algorithm to determinate the largest LNL-invariant set for this class of systems is proposed. Moreover, it is proven that the LNL-invariant sets provided by this algorithm are polyhedral convex sets and constitute an estimation of the domain of attraction of the non-linear system

Algebraic methods for control system analysis and design Final report, Apr. 1967 - Apr. 1969

Algebraic methods for analysis and design of control system

STABILIZATION BY ADAPTIVE FEEDBACK CONTROL FOR POSITIVE DIFFERENCE EQUATIONS WITH APPLICATIONS IN PEST MANAGEMENT

An adaptive feedback control scheme is proposed for stabilizing a class of forced nonlinear positive difference equations. The adaptive scheme is based on so-called high-gain adaptive controllers and contains substantial robustness with respect to model uncertainty as well as with respect to persistent forcing signals, including measurement errors. Our results take advantage of the underlying positive systems structure and ideas from input-to-state stability from nonlinear control theory. Our motivating application is to pest or weed control, and in this context the present work substantially strengthens previous work by the authors. The theory is illustrated with examples

Stability analysis of a phase plane control system

Many aerospace attitude control systems utilize a phase plane control scheme which includes nonlinear elements such as dead zone and ideal relay. Nonlinear control techniques such as pulse width modulation (PWM), describing functions, and absolute stability are implemented to determine stability. To evaluate phase plane control robustness, stability margin prediction methods must be developed. While PWM has been used to predict stability margins, in this research, describing functions and absolute stability are extended to predict stability margins. Time domain simulations demonstrate all techniques yield conservative gain margin results. A constrained optimization approach is also used to design flex filters for roll control. The design goal is to optimize vehicle tracking performance while maintaining adequate stability margins. Two filters are designed in this thesis; one meets PWM stability margin specifications and the other holds for Popov stability

Optimized state feedback regulation of 3DOF helicopter system via extremum seeking

In this paper, an optimized state feedback regulation of a 3 degree of freedom (DOF) helicopter is designed via extremum seeking (ES) technique. Multi-parameter ES is applied to optimize the tracking performance via tuning State Vector Feedback with Integration of the Control Error (SVFBICE). Discrete multivariable version of ES is developed to minimize a cost function that measures the performance of the controller. The cost function is a function of the error between the actual and desired axis positions. The controller parameters are updated online as the optimization takes place. This method significantly decreases the time in obtaining optimal controller parameters. Simulations were conducted for the online optimization under both fixed and varying operating conditions. The results demonstrate the usefulness of using ES for preserving the maximum attainable performance

Modern control concepts in hydrology

Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise