Elements of a Theory of Design Limits to Optimal Policy

This paper presents a framework for understanding the limits that exist in optimal policy design in dynamic contexts. We consider the design of policies in the context of dynamic linear models. Fundamental design limits exist for policy rules in such environments in the sense that any policy rule embodies tradeoffs between the magnitudes of different frequency-specific components of the variance. Hence policies that are effective in eliminating low frequency variance components of a state variable can only do so at the cost of exacerbating high frequency variance components, and vice versa. Examples of the implications of such tradeoffs are considered.

Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information

In this paper, we study fundamental limitations of disturbance attenuation of feedback systems, under the assumption that the controller has a finite horizon preview of the disturbance. In contrast with prior work, we extend Bode's integral equation for the case where the preview is made available to the controller via a general, finite capacity, communication system. Under asymptotic stationarity assumptions, our results show that the new fundamental limitation differs from Bode's only by a constant, which quantifies the information rate through the communication system. In the absence of asymptotic stationarity, we derive a universal lower bound which uses Shannon's entropy rate as a measure of performance. By means of a case-study, we show that our main bounds may be achieved

Hybrid operator models for digitally implemented control systems

A method of analysis for digitally implemented (hybrid) control systems based on conic sector concepts from functional analysis was established. Data sampling is addressed

A Bode Sensitivity Integral for Linear Time-Periodic Systems

Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result

Bode Integral Limitation For Irrational Systems

Bode integrals of sensitivity and sensitivity-like functions along with complementary sensitivity and complementary sensitivity-like functions are conventionally used for describing performance limitations of a feedback control system. In this paper, we investigate the Bode integral and evaluate what happens when a fractional order Proportional-Integral-Derivative (PID) controller is used in a feedback control system. We extend our analysis to when fractal PID controllers are applied to irrational systems. We split this into two cases: when the sequence of infinitely many right half plane open-loop poles doesn't have any limit points and when it does have a limit point. In both cases, we prove that the structure of the Bode Integral is similar to the classical version under certain conditions of convergence. We also provide a sufficient condition for the controller to lower the Bode sensitivity integral.Comment: 13 pages, 7 figure

Optimal greenhouse cultivation control: survey and perspectives

Abstract: A survey is presented of the literature on greenhouse climate control, positioning the various solutions and paradigms in the framework of optimal control. A separation of timescales allows the separation of the economic optimal control problem of greenhouse cultivation into an off-line problem at the tactical level, and an on-line problem at the operational level. This paradigm is used to classify the literature into three categories: focus on operational control, focus on the tactical level, and truly integrated control. Integrated optimal control warrants the best economical result, and provides a systematic way to design control systems for the innovative greenhouses of the future. Research issues and perspectives are listed as well