Cheap Control Problem of Linear Systems With Delays: A Singular Perturbation Approach
A quadratic cheap control of linear systems with multiple state delays is considered. This optimal control problem is transformed to an optimal control problem of singularly perturbed systems. A composite suboptimal control of the latter is designed based on its asymptotic decomposition into two much simpler parameter-free subproblems, the slow and fast ones. Using this composite control, a suboptimal control of the original cheap control problem is constructed and justified for two classes of the initial function for the state variable. An illustrative example is presented.
keywordstime-delayed system cheap control singular perturbation composite control
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