Abstract
For a class of repetitive linear discrete-time-invariant systems with the unit relative degree, a learning-gain-adaptive iterative learning control (LGAILC) mechanism is exploited, for which the iteration-wise performance index is to maximize the declining quantity of tracking-error energies at two adjacent operations without considering control input and any parameters, and the argument is the iteration-time-variable learning-gain vector. By taking advantage of rows/columns exchanging transformations and matrix theory, an explicit learning-gain vector is solved, which exhibits that the learning-gain vector is not only dependent upon the system Markov parameters but also relevant to the iteration-time-wise tracking errors. Benefited from the orthogonality of the rows/columns exchanging transformation, it is derived that the LGAILC scheme is non-conditionally strictly monotonically convergent. For the sake of ensuring the LGAILC to be robust to the system parameters’ uncertainties, a pseudo-LGAILC strategy is developed whose system Markov parameter-based learning-gain vector involves the system parameters’ uncertainties. Rigorous induction delivers that the pseudo strategy is strictly monotonically convergent with a wider uncertainty degree, which implies that the pseudo strategy is robust to the system parameters’ uncertainties in a wider range. The numerical simulations demonstrate the validity and effectiveness.
Highlights
With rapid development of science and technology conforming to human beings continual pursuing of high-quality living convenience, it becomes quite popular for a machine such as a robot to have capability to learn from human beings
PSEUDO learning-gain-adaptive iterative learning control (LGAILC) RULE AND ROBUSTNESS TO SYSTEM PARAMETERS UNCERTAINTY Note that the result of Theorem 1 is expectedly perfect given that the system parameters are available in precise
Benefited from the feature of the linear discrete-timeinvariant systems with unity relative degree and based on algebraic approach regarding matrix theory, the learning-gain vector is determined in an explicit form which is adaptive to the iteration-wise tracking-error vector
Summary
With rapid development of science and technology conforming to human beings continual pursuing of high-quality living convenience, it becomes quite popular for a machine such as a robot to have capability to learn from human beings. For the sake of reducing the complexity, a substitutable approach is the parameter optimal ILC (POILC) scheme [34], where the argued parameter is the single-dimensional learning gain given that it is time-invariant but iteration-varying. Q1: For the full-dimensional iteration-time-variable learning-gain-argued ILC, what happens to the learninggain vector solution and convergence if no consideration of the learning effort intensity for composing the performance index?. Benefited from the scalar tuning factor choice w > 0, the additive learning effort intensity of the second term in the right hand of (9) makes the optimal learning-gain vector to be ordinarily solvable but it might confine the convergence rate. One alternative candidate is to set the tuning factor to be iteration-varying which has been involved in authors’ other work Another candidate is not to consider the learning effort intensity addressed in this paper. Throughout the paper, denote ρ(P) and λ(P) as the spectral radius and eigenvalue of the square matrix P, respectively
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