Adaptive guaranteed cost control of systems with uncertain parameters

Abstract

Guaranteed cost control is a method of synthesizing a closed-loop system in which the controlled plant has large parameter uncertainty. This paper gives the basic theoretical development of guaranteed cost control, and shows how it can be incorporated into an adaptive system. The uncertainty in system parameters is reduced first by either: 1) on-line measurement and evaluation, or 2) prior knowledge on the parametric dependence of a certain easily measured situation parameter. Guaranteed cost control is then used to take up the residual uncertainty.It is shown that the uncertainty in system parameters can be taken care of by an additional term in the Riccati equation. A Fortran program for computing the guaranteed cost matrix and control law is developed and applied to an airframe control problem with large parameter variations.

Robust guaranteed cost control of linear systems with norm bounded uncertainties and external disturbance

“…The parameter d is the distance between the centers of the two wheels. The parameter 1 d is the length of the front or rear arm. The inclination angle of the power transmission line is represented by a, which can be measured by the inclination sensor mounted on the surface of the body.…”

“…Y>0 and LMI (22) It should be noted that this problem is not a convex one due to 1 Y . To obtain a convex problem, the term can be obtained to optimize the quadratic and H performance levels, where 2 .…”

“…As a result, it is desirable to design a controller to make the closed loop system stable and guarantee an adequate performance level. One method to solve this problem is the so-called Guaranteed Cost Control (GCC) approach [1,2].…”

Robust Stability and Control of Linear Interval Parameter Systems Using Quantitative (State Space) and Qualitative (Ecological) Perspectives

“…Reference [17] compares several techniques for designing linear controllers for robust stability for a class of uncertain linear systems. Among the methods considered are the standard linear quadratic regulator (LQR) design, Guaranteed Cost Control (GCC) method of [18], Multistep Guaranteed Cost Control (MGCC) of [17]. In these methods, the weighting on state in a quadratic cost function and the Riccati equation are modified in the search for an appropriate controller.…”

Membership-Function-Dependent Stability Analysis and Control Synthesis of Guaranteed Cost Fuzzy-Model-Based Control Systems

“…The guaranteed performance control aims at not only stabilizing the system, but also guaranteeing the specific cost of the system through pre-defined cost function [25,26]. Also there is a guaranteed cost approach introduced by works in [27], which is able to provide an upper bound on a given performance index and the performance of the system is guaranteed to be less than the boundary. Guan and Chen applied this method on T-S fuzzy systems with time delay in [28], Chen and Liu adopted the method in nonlinear systems with time-varying delay in [29], the problem of interval time-varying delay in T-S fuzzy systems is considered in [30], both state and input delays in the guaranteed cost T-S fuzzy systems are considered in work [31] and further related works can be found in [32][33][34][35], also some industrial applications of guaranteed cost T-S fuzzy systems can be found in [36][37][38][39].…”