Introduction to Control Theory, Including Optimal Control |
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a₁ adjoint variables assumed asymptotically stable augmented functional b₁ bang-bang control C₁ CHAPTER characteristic equation coefficients companion form consider constant constraint control theory corresponding cosh criterion determined diagram differential equation economic rent eigenvalues Euler equation example extremum values feedback follows G(iw given gives h₁ h₂ Hamiltonian Hence illustrated in Fig initial conditions input integral integrand K₁ K₂ Lagrange multiplier Laplace transform linear systems matrix maximise method minimise minimum non-singular obtain open-loop optimal control optimal path optimal trajectory output P₁ P₂ poles polynomial Pontryagin's Minimum Principle positive problem R₁ response s-plane shown in Fig sinh solution solving switching curve Sylvester's criterion system is controllable system is stable theorem transfer function G(s transversality condition uncontrollable unstable vector x₁ X₁(s zero ән