Transcription of Linear Quadratic Optimal Control - Welcome to AUTOMATICA
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Linear Quadratic Optimal Control - Welcome to AUTOMATICA
Chapter 6 Linear Quadratic Optimal IntroductionIn previous lectures, we discussed the design of state feedback controllers using using eigenvalue(pole) placement algorithms. For single input systems, given a set of desired eigenvalues, thefeedback gain to achieve this is unique (as long as the systemis controllable). For multi-inputsystems, the feedback gain is not unique, so there is additional design freedom. How does oneutilize this freedom? A more fundamental issue is that the choice of eigenvalues is not obvious. Forexample, there are trade offs between robustness, performance, and Control Quadratic (LQ) Optimal Control can be used to resolvesome of these issues, by notspecifying exactly where the closed loop eigenvalues should be directly, but instead by specifyingsome kind of performance objective function to be optimized.
104 CHAPTER 6. LINEAR QUADRATIC OPTIMAL CONTROL Let us assume (and it can be proven) that X1(t) is invertible.We propose that the solution to the Hamilton-Jacobi equation (6.9)-(6.10) is …
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