This paper explores the iterative learning control (ILC) problem for two-dimensional (2d) multi-input multi-output nonlinear parametric systems by taking all nonrepetitive uncertainties of stochastic initial shifts, d...
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This paper explores the iterative learning control (ILC) problem for two-dimensional (2d) multi-input multi-output nonlinear parametric systems by taking all nonrepetitive uncertainties of stochastic initial shifts, different tracking tasks and nonuniform trial lengths into consideration. A 2d stochastic variable is defined with Bernoulli stochastic distribution for the first time to handle iteration-varying trial lengths. The desired output is incorporated into the learning control law as a feedback to compensate the iterative changes of the tracking tasks. An iterative 2d parameter updating law is established using a new defined virtue tracking error to well address the systems uncertainties and varying trial lengths. Consequently, a novel 2d adaptive ILC (2d-AILC) is presented by incorporating the control law and parameter updating law. The convergence is proved by introducing both the Lyapunov stability principle and the 2d key technique lemma into the repetitive 2dsystems even though the dynamic evolution along with two-dimensional directions makes it more difficult in the mathematic analysis. The simulation study tests the theoretical results: the presented2d-AILC scheme can still accomplish a tracking task exactly even though there exist random initial states, nonrepetitive reference trajectories, and iteration-varying trial lengths.
This study is concerned with the problem of stabilisation for a class of two-dimensional (2d) nonlinearsystems with intermittent measurements and sector nonlinearities. The intermittent measurement is modelled by a s...
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This study is concerned with the problem of stabilisation for a class of two-dimensional (2d) nonlinearsystems with intermittent measurements and sector nonlinearities. The intermittent measurement is modelled by a stochastic variable satisfying the Bernoulli random binary distribution. Our attention is focused on the design of a state feedback controller for such 2d stochastic system described by the Roesser model, such that the closed-loop system is mean-square asymptotically stable. A sufficient condition is established by means of linear matrix inequalities technique, and formulae can be given for the control law design. The result is also extended to more general cases where the system matrices contain uncertain parameters. Numerical examples are also given to illustrate the effectiveness of proposed approach.
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