Suboptimal Control of Linear Systems with Bounded Disturbances using Krotov sufficient Conditions

This article considers the problem of sub optimal regulator design for linear systems subject to additive but bounded disturbances. The information regarding the bounds is used to formulate another optimal control problem. The system used in the latter problem is the original system subject to worst case of disturbance. Then the latter optimal control problem is solved using Krotov sufficient conditions via selection of the so-called Krotov function. The selection of Krotov function is made such that the iterative computation of solutions (which is required while employing these conditions) is avoided. The resulting controller, which is sub-optimal for the original problem, is comprised of a state-feedback term and a time-varying term which compensates for the effect of disturbances. The numerical examples demonstrate the application of developed methodology.

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