DocumentCode :
646204
Title :
Stationary trajectories, singular Hamiltonian systems and ill-posed interconnection
Author :
Jugade, Shriram C. ; Pal, Debdas ; Kalaimani, R.K. ; Belur, Madhu N.
Author_Institution :
Dept. of Electr. Eng., Indian Inst. of Technol., Mumbai, Mumbai, India
fYear :
2013
fDate :
17-19 July 2013
Firstpage :
1740
Lastpage :
1745
Abstract :
We study Hamiltonian systems, namely, systems comprising of trajectories which are `stationary´ with respect to a quadratic performance index: they play a central role in many optimal control problems. A typical assumption in the literature is that of `regularity´: the resulting first-order dynamical system is a regular state space system and not a singular descriptor system. In this paper we show that the first order representation of a Hamiltonian is a singular descriptor system if and only if the interconnection of a related MIMO system G(s) with its dual (i.e. its adjoint) is ill-posed. We address the possibility of existence of inadmissible initial conditions, i.e. initial conditions that give rise to impulsive solutions. We characterize conditions on G(s) under which the corresponding singular Hamiltonian system has inadmissible initial conditions. Under suitable simplifying assumptions, which amount to studying an extreme case of ill-posedness, our main result states that there exist no inadmissible initial conditions if and only if the skew-symmetric part of the first moment about s = ∞ of the transfer matrix G(s) is nonsingular; a condition we show that is opposite to that for G(s) to be an all-pass filter. As a corollary, ill-posed interconnection of a square MIMO system with odd number of inputs (in particular, SISO systems) with its adjoint always contains in inadmissible initial conditions.
Keywords :
MIMO systems; matrix algebra; optimal control; state-space methods; trajectory control; first order Hamiltonian representation; first-order dynamical system; ill-posed interconnection; inadmissible initial conditions; multiple-input multiple-output system; optimal control problems; quadratic performance index; regular state space system; singular Hamiltonian systems; singular descriptor system; square MIMO system; stationary trajectories; transfer matrix; Context; Interconnected systems; Kernel; Polynomials; Trajectory; Vectors; Hamiltonian matrix; adjoint system; all-pass filter; dissipativity; dual system; inadmissible initial conditions; well-posedness; zeros at infinity;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Control Conference (ECC), 2013 European
Conference_Location :
Zurich
Type :
conf
Filename :
6669612
Link To Document :
بازگشت