Abstract
The linear-quadratic and L1-cost control problems for hereditary dynamic systems are considered. The optimal control algorithm for the linear-quadratic problem is well known. However, a system of functional partial differential equations must be solved for its implementation. Approximate simpler control algorithms, which avoid the solving of this partial differential system, are constructed. Moreover, an estimate for the nonoptimality level of the approximate control algorithms is obtained. This estimate can be calculated without solving the initial complicated optimal linear-quadratic control problem. The L1-cost control problem is a difficult nonsmooth problem. Optimal algorithms for its solving are unknown. It is proposed to use the optimal control law (or the corresponding simplified control law) from an appropriate linear-quadratic problem for approximate solving the L1-cost problem. A simple estimate for the nonoptimality level of this suboptimal control law is constructed as well.
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