We develop a multi-input, multi-output direct adaptive controller for discrete-time, possibly nonminimumphase, systems with unknown nonminimum-phase zeros. The adaptive controller requires limited modeling information about the system, specifically, Markov parameters from the control input to the performance variables. Often, only a single Markov parameter is required, even in the nonminimum-phase case. We analysis the stability of the algorithm using a time-andfrequency-domain approach. We demonstrate the algorithm on disturbance-rejection problems, where the disturbance spectra are unknown. This controller is based on a retrospective performance objective, where the controller is updated using either batch or recursive least squares.
In this paper we investigate the robustness of an extended version of retrospective cost adaptive control (RCAC), in which less modeling information is required than in prior versions of this method. RCAC is applicable to MIMO possibly nonminimum-phase (NMP) plants without the need to know the locations of the NMP zeros. The only required modeling information is an FIR approximation of the plant, which may be based on a limited number of Markov parameters. In this paper we investigate the effect of phase mismatch between the true plant and the FIR approximation. Numerical examples demonstrate the relationship between phase mismatch at the command and disturbance frequencies as well as the required level of regularization in the controller update.
We develop a multi-input, multi-output direct adaptive controller for discrete-time, possibly nonminimum-phase, systems with unknown nonminimum-phase zeros. The adaptive controller requires limited modeling information about the system, specifically, Markov parameters from the control input to the performance variables. Often, only a single Markov parameter is required, even in the nonminimum-phase case. We demonstrate the algorithm on command-following and disturbance-rejection problems, where the command and disturbance spectra are unknown. This controller is based on a retrospective performance objective, where the controller is updated using either batch or recursive least squares.
Legal certainty decreases over time. Rules and principles of law become more and more uncertain in content and in application because legal systems are biased in favor of unravelling those rules and principles. In this article I attempt to show what these biases are, and why commentators who have argued that the law tends toward certainty are wrong, then describe various attempts which have been made at restoring certainty, and why these attempts have generally not worked. My conclusion is that these proposals are at best holding actions, and that the tendency toward increasing uncertainty in the law is inexorable.
Mathematical models of physical phenomena are of critical importance in virtually all applications of science and technology. This paper addresses the problem of how to use data to improve the fidelity of a given model. We approach this problem using retrospective cost optimization, which uses data to recursively update an unknown subsystem interconnected to a known system. Applications of this technique are relevant to applications that depend on large-scale models based on firstprinciples physics, such as the global ionosphere-thermosphere model (GITM). Using GITM as the truth model, we demonstrate that measurements can be used to identify unknown physics. Specifically, we estimate static thermal conductivity parameters, as well as a dynamic cooling process.
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