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NASA NTRS1977

The uncertainty threshold principle - Some fundamental limitations of optimal decision making under dynamic uncertainty

This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications of this result are discussed.

Athans, M.↗

NASA NTRS1977

The Uncertainty Threshold Principle: Some Fundamental Limitations of Optimal Decision Making Under Dynamic Uncertainity

This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications of this result are discussed.

Athans, M.↗

NASA NTRS1976

The uncertainty threshold principle - Fundamental limitations of optimal decision making under dynamic uncertainty

The fundamental limitations of the optimal control of dynamic systems with random parameters are analyzed by studying a scalar linear-quadratic optimal control example. It is demonstrated that optimum long-range decision making is possible only if the dynamic uncertainty (quantified by the means and covariances of the random parameters) is below a certain threshold. If this threshold is exceeded, there do not exist optimum decision rules. This phenomenon is called the 'uncertainty threshold principle'. The implications of this phenomenon to the field of modelling, identification, and adaptive control are discussed.

Athans, M.↗

NASA NTRS1973

On the adaptive control of linear systems using the open-loop-feedback-optimal approach.

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with uncertain or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (OLFO) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.

Ku, R.↗

NASA NTRS1973

Open-loop-feedback-optimal adaptive stochastic control of linear systems

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.

Ku, R.↗

NASA NTRS1972

On the adaptive control of linear systems using the open-loop-feedback-optimal approach.

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (O.L.F.O.) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first order systems are presented.

Ku, R.↗