Frontiers in Adaptive Control Part 9

Tham khảo tài liệu 'frontiers in adaptive control part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Advances in Parameter Estimation and Performance Improvement in Adaptive Control 191 where t R is the state and II G _R is the control input. The vector 0 G is the unknown parameter vector whose entries may represent physically meaningful unknown model parameters or could be associated with any finite set of universal basis functions. It is assumed that 0 is uniquely identifiable and lie within an initially known compact set - 1. The nx-dimensional vector f x u and the . . X III J-dimensional matrix . . II are bounded and continuous in their arguments. System 1 encompasses the special class of linear systems f x ti AqX Bou g x Ù Aia Biti A - x B2U . Anex Bneu where Ai and Bi for i 0 . . . Ill are known matrices possibly time varying. Assumption The following assumptions are made about system 1 . 1. The state of the system x f is assumed to be accessible for measurement. 2. There is a known bounded control law ÌI I . and a bounded parameter update law 9 that achieves a primary control objective. The control objective can be to robustly stabilize the plant and or to force the output to track a reference signal. Depending on the structure of the system 1 adaptive control design methods are available in the literature 12 16 . For any given bounded control and parameter update law the aim of this chapter is to provide the true estimates of the plant parameters in finite-time while preserving the properties of the controlled closed-loop system. 3. Finite-time Parameter Identification Let . denote the state predictor for 1 the dynamics of the state predictor is designed as I i . O I k .ij I wO. 2 where 0 is a parameter estimate generated via any update law kw 0 is a design matrix . if is the prediction error and w is the output of the filter .r. - . 3 Denoting the parameter estimation error as 9 9 9 it follows from 1 and 2 that i .r. u - k . - 11 0. 4 The use of the filter matrix w in the above development provides direct information about parameter .

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