An inverse optimal approach to design of feedback control: Exploring analytical solutions for the Hamilton-Jacobi-Bellman equation

Design of feedback control by an optimal control approach relies on the solutions of the Hamilton-Jacobi-Bellman (HJB) equation, while this equation rarely admits analytical solutions for arbitrary choices of the performance measure. An inverse optimal feedback design approach is proposed here in which analytical solutions are explored for the HJB equation that optimize some meaningful, but not necessarily ideal, performance measure. Such performance measure is exclusively selected from a family of cost functionals with an intended structural constraint which inherently yields analytical solutions to the HJB equation. This family includes a set of free parameters which are exploited to construct cost functionals adequately representing the design requirements. The structural constraint imposed on this cost functional family indeed narrows down the scope of the proposed method; yet, it is shown by several examples that this method can successfully address certain classes of feedback design problems.

Automated summary

The paper introduces an inverse optimal feedback design approach, exploring analytical solutions for the HJB equation by selecting cost functionals with a specific structural constraint. This method effectively addresses certain feedback design problems.