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EXISTENCE AND UNIQUENESS
CONTROLLABILITY 6 7
FEEDBACK CONTROL n 2
2 other sections not shown
0-stage adjoint equation adjoint solution apply the divergence Apply Theorem 2.3 blocks of B(x boundary conditions 4.2 BOUNDARY VALUE CONTROL bounded linear operator bounded operators Cg(x Chapter characteristic lines complete metric space consider constant construct a solution contraction mapping control F(t Control theory control which steers define denote Diagram 3.4 dimensional discontinuities divergence theorem domain of determinancy dxdt eigenvalues estimate exactly controllable existence and uniqueness expressed feedback control law feedback form finite following boundary condition given initial condition Hence HYPERBOLIC SYSTEMS independent solution integration K-B Sup k=i+l Lemma mapping matrix functions necessary conditions obtain off-diagonal blocks ordinary differential equation partial differential equations proof of Theorem remark satisfies the boundary semigroup steers the solution steers the system terminal value Theorem 2.2 thesis tion U_(x uncoupled system unique controllability result unique solution UQ(x UT(x x,t e A2uA2uA2 x,teD zn x,t