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Linear Quadratic Optimal Control Problems with Fixed Terminal States and Integral Quadratic Constraints

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Abstract

This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable and whose solution can be approximated by the solution for a suitable unconstrained LQ problem with penalized terminal state. Using results from duality theory, the optimal control is explicitly derived by solving the Riccati equation together with an optimal parameter selection problem. It turns out that the optimal control is a target-dependent feedback of the current state. Some examples are presented to illustrate the theory developed.

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  1. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Jingrui Sun

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  1. Jingrui Sun
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Correspondence to Jingrui Sun.

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Sun, J. Linear Quadratic Optimal Control Problems with Fixed Terminal States and Integral Quadratic Constraints. Appl Math Optim 83, 251–276 (2021). https://doi.org/10.1007/s00245-018-9532-7

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  • DOI: https://doi.org/10.1007/s00245-018-9532-7

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