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Willems, J. C.

Publications and source records attributed to Willems, J. C..

17 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Stochastic control and the second law of thermodynamics

The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.

Brockett, R. W.↗
NASA NTRS1975

Algebraic methods in system theory

Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.

Brockett, R. W.↗
NASA NTRS1974

Parameter identifiability of linear dynamical systems

It is assumed that the system matrices of a stationary linear dynamical system were parametrized by a set of unknown parameters. The question considered here is, when can such a set of unknown parameters be identified from the observed data? Conditions for the local identifiability of a parametrization are derived in three situations: (1) when input/output observations are made, (2) when there exists an unknown feedback matrix in the system and (3) when the system is assumed to be driven by white noise and only output observations are made. Also a sufficient condition for global identifiability is derived.

Glover, K.↗
NASA NTRS1973

On the stability of numerical integration routines for ordinary differential equations.

Numerical integration methods for the solution of initial value problems for ordinary vector differential equations may be modelled as discrete time feedback systems. The stability criteria discovered in modern control theory are applied to these systems and criteria involving the routine, the step size and the differential equation are derived. Linear multistep, Runge-Kutta, and predictor-corrector methods are all investigated.

Glover, K.↗
NASA NTRS1973

On the identifiability of linear dynamical systems

Consider the situation in which the unknown parameters of a stationary linear system may be parametrized by a set of unknown parameters. The question thus arises of when such a set of parameters can be uniquely identified on the basis of observed data. This problem is considered here both in the case of input and output observations and in the case of output observations in the presence of a white noise input. Conditions for local identifiability are derived for both situations and a sufficient condition for global identifiability is given for the former situation, i.e., when simultaneous input and output observations are available.

Glover, K.↗
NASA NTRS1972

An approach to the linear multivariable servomechanism problem.

This paper presents a state-space approach to the multivariable 'type one' servomechanism problem. Necessary and sufficient conditions for the controllability of such systems are derived and applied to the observability of the (dual) state reconstructor problem for a system with an unknown constant input. The paper also presents a simple systematic design algorithm which provides type one servomechanism performance to command inputs, together with pre-specified closed-loop pole locations. Examples are given to illustrate the utility of the design procedure.

Young, P. C.↗
NASA NTRS1972

On the stability of numerical integration routines.

Numerical integration methods for the solution of initial value problems for ordinary vector differential equations may be modelled as discrete time feedback systems. The stability criteria discovered in modern control theory are applied to these systems and criteria involving the routine, the step size and the differential equation are derived. Linear multistep, Runge-Kutta, and predictor-corrector methods are all investigated.

Glover, K.↗