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- W4313152817 abstract "We propose a novel strategy to construct optimal controllers for continuous-time nonlinear systems by means of linear-like techniques, provided that the optimal value function is differentiable and <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>quadratic-like</i> . This assumption covers a wide range of cases and holds locally around an equilibrium under mild assumptions. The proposed strategy does not require solving the Hamilton-Jacobi-Bellman equation, that is a nonlinear partial differential equation, which is known to be hard or impossible to solve. Instead, the Hamilton-Jacobi-Bellman equation is replaced with an easy-solvable state-dependent Lyapunov matrix equation. We exploit a linear-like factorization of the underlying nonlinear system and a policy-iteration algorithm to yield a linear-like policy-iteration for nonlinear systems. The proposed control strategy solves optimal nonlinear control problems in an asymptotically exact, yet still linear-like manner. We prove optimality of the resulting solution and illustrate the results via four examples." @default.
- W4313152817 created "2023-01-06" @default.
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- W4313152817 date "2023-10-01" @default.
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- W4313152817 title "Linear-like Policy Iteration based Optimal Control for Continuous-time Nonlinear Systems" @default.
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- W4313152817 doi "https://doi.org/10.1109/tac.2022.3226671" @default.
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