A susceptible$S(t)$, infectious$I(t)$, and removed$R(t)$(SIR) family of deterministic, lumped-parameter models of directly transmitted infectious diseases is considered. A piecewise constant transmission rate is estimated via a Luenbergertype observer and used to adjust the recovery rate in an effort to maintain the basic reproduction number close to unity. The result is a mitigation strategy that avoids multiple infectious waves. A linear, discrete-time state-space model is used throughout with the transmission rate treated as an unknown but constant disturbance during a control design time window. The off-line simulations in discrete time may be used to produce heuristic policies implemented by public health and government organizations.

This paper presents a new method to design adaptive Proportional-Integral-Derivative (PID) controllers which optimize a performance criterion (integral absolute error or integral square error) subject to constraints such as controlled variable, manipulated variable and rate of change constraints. The design method is applicable to linear or nonlinear processes. Modeling of such processes is done using a linear ARX model. In addition, the design method is independent of the PID controller type and accounts for controllers with proportional or derivative action on the control error or the process variable. The proposed design method is not analytic in nature, but rather it is implemented using existing MATLAB optimization functions and demonstrated using simulation experiments for linear and nonlinear processes.

It is well known that the infinite horizon linear-quadratic tracking problem does not have a solution in the strict sense because in general the performance index is infinite. Additional computational difficulties arise for applications where real-time computations are needed. However, for applications where the reference signal is generated by an asymptotically stable system, then the problem has an optimal solution. In the present paper a methodology that can be used to design real-time infinite horizon linear-quadratic tracking controllers for vibration quenching in flexible beams is presented. A numerical example is included to illustrate the effectiveness of the method.

The goal of this article is to offer an automatic PID parameter adjustment strategy by using a grey predictor model. The grey predictor model together with a first-order low-pass alpha filter generates effective estimated values of the plant output. The output error is then embedded in a control algorithm that automatically tunes the PID parameters. The resulting PID/Grey controller is shown to outperform the PID controller that is tuned via the standard quarter-decay ratio method. The paper gives a detailed description of the system structure, the design algorithm, and its implementation. Regulation and tracking performance of the proposed PID/grey predictor controller are illustrated by means of computer simulation tests in the Matlab environment. Finally, a temperature regulation example is built by using LabVIEW programming and tested to validate the performance of the proposed controller scheme.

Consideration is given to the optimal relegation of system set-points as applied to the problem of self-motion control in redundant flexible robotic manipulators. A long planar flexible manipulator equipped with a four-degree-of-freedom rigid end effector is used as an example to illustrate the relegated controller design. The main drawbacks of the proposed scheme are the intensive computation required for computing the optimal set-points and the need for somewhat fast motor dynamics.>