Abstract
In this article, the repetitive finite-length linear discrete-time singular system is formulated as an input-output equation by virtue of the lifted-vector method and a gain-optimized P-type iterative learning control profile is architected by sequentially arguing the learning-gain vector in minimizing the addition of the quadratic norm of the tracking-error vector and the weighed quadratic norm of the compensation vector. By virtue of the elementary permutation matrix and the property of the quadratic function, the optimized-gain vector is solved and explicitly expressed by the system Markov matrix and the iteration-wise tracking error. Then the linearly monotonic convergence of the tracking error is derived under the assumption that the initial state of the dynamic subsystem is resettable. Furthermore, for the circumstance that the system parameters uncertainties exist, the quasi scheme is established by replacing the exact system Markov matrix with the approximated one in the optimized gain. Rigorous analysis conveys that the proposed gain-optimized scheme is robust to the system internal disturbance within a suitable range. The validity and effectiveness are demonstrated numerically.
Highlights
In mathematical, the hybrid differential/difference-algebraic equations constitute of a singular system, where the differential/difference equation describes the faster dynamic subsystem whilst the algebraic equation models the slower static subsystem, respectively [1]
By reformulating the discrete-time difference-algebraic singular systems as an algebraic input-output transmission, a gain-adaptive iterative learning control (ILC) (GAILC) has been explored where the minimization problem is consisting of the quadratic norm of the tracking-error vector and the argument is the P-type iteration-time-wise learning-gain vector [38]
This paper explores a P-type gain-optimized iterative learning control (GOILC) strategy for a linear discrete-time singular system
Summary
The hybrid differential/difference-algebraic equations constitute of a singular system, where the differential/difference equation describes the faster dynamic subsystem whilst the algebraic equation models the slower static subsystem, respectively [1]. By reformulating the discrete-time difference-algebraic singular systems as an algebraic input-output transmission, a gain-adaptive ILC (GAILC) has been explored where the minimization problem is consisting of the quadratic norm of the tracking-error vector and the argument is the P-type iteration-time-wise learning-gain vector [38]. This paper explores a P-type gain-optimized iterative learning control (GOILC) strategy for a linear discrete-time singular system. The scheme argues the sequential learning-gain vector while minimizing the sequential performance index composed by the additive quadratic tracking-error vector and the weighed quadratic compensation term by an iteration-wise tuning factor. SYSTEM REFORMULATION AND P-TYPE GAIN-OPTIMIZED ITERATIVE LEARNING CONTROL STRATEGY Consider a class of repetitive linear discrete-time singleinput-single-output singular systems taking the form of.
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