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Extended command governors (ECGs) are add-on schemes that modify set-point commands as necessary to ensure that imposed state and control constraints are not violated by closed-loop systems designed for set-point tracking. In this paper, we propose a reduced order ECG for systems with dynamics decomposable into slow and fast state variables. We demonstrate that ECG implementation can be based on slow states only, thus reducing the computational complexity. This is achieved by introducing additional constraints, and by slightly tightening the original constraints. We demonstrate that the proposed ECG maintains the response properties of the conventional ECG, including the convergence to the nearest feasible command in finite time in the case of constant reference commands. The results are also shown to apply to conventional command governors. For the case when the reduced order state is not directly measured, a formulation of the result in the presence of a state observer is developed.

The paper provides an overview of reference governors, command governors and extended command governors, which are add-on schemes for enforcing pointwise-in-time state and control constraints in set-point tracking problems. It emphasizes recent developments based on the authors work and a new strategy for implementing command governors as they apply to nonlinear systems. Comments on future directions in reference governor research are made. A list of references is included.

This paper considers a nonlinear feedback control policy that is an extension of those provided by command governors and reference governors. As in these control approaches it applies to discrete-time linear systems with hard constraints and set bounded disturbances. The control policy retains the main properties of traditional governors, such as straightforward direct implementation and finite-settling-time response to arbitrarily specified set points. Its principal advantage over traditional governors is a significantly larger domain of attraction, that may compete in size with those obtained by dynamic programming. Connections to model predictive control are made. Numerical examples illustrate advantageous features of the proposed approach.

This paper is concerned with outer approximations of the minimal disturbance invariant set (MDIS) of a discrete-time linear system with an additive set-bounded disturbance. The k-step disturbance reachable sets (Minkowski partial sums) are inner approximations of MDIS that converge to MDIS. Enlarged by a suitable scaling, they can lead to outer approximations of MDIS. Three families of approximations, each based on partial sums, are considered. Theoretical properties of the families are proved and interrelated. Algorithmic questions, including error bounds, are addressed. The results are illustrated by computational data from several examples.

In this paper, receding horizon model predictive control (RHMPC) of nonlinear systems subject to input and state constraints is considered. We propose to estimate the terminal region and the terminal cost off-line using support vector machine learning. The proposed approach exploits the freedom in the choices of the terminal region and terminal cost needed for asymptotic stability. The resulting terminal regions are large and, hence provide for large domains of attraction of the RHMPC. The promise of the method is demonstrated with two examples.

This paper develops a computational approach for characterizing the stability regions of constrained nonlinear systems. A decision function is constructed that allows arbitrary initial states to be queried for inclusion within the stability region. Data essential to the construction process are generated by simulating the nonlinear system with multiple initial states. Using special procedures based on known properties of the stability region, the state data are randomly selected so that they are concentrated in desirable locations near the boundary of the stability region. Selected states belong either to the stability region or do not, thus producing a two-class pattern recognition problem. Support vector machine learning, applied to this problem, determines the decision function. Special techniques are introduced that significantly improve the accuracy and efficiency of the learning process. Numerical examples illustrate the effectiveness of the overall approach.

This paper proposes a new approach to reference governor design. As in prior literature, the governor accepts input commands and modifies their evolution so that specified pointwise-in-time constraints on state and control variables are satisfied. The new approach applies to general discrete-time and continuous-time nonlinear systems with uncertainties. It relies on safety properties provided by sublevel sets of equilibria-parameterized functions. These functions need not be Lyapunov functions, and the corresponding sublevel sets need not be positively invariant. Technical conditions that capture the bare essentials of what is needed are identified and the usual desirable properties of reference governors are established. The new approach significantly broadens the class of methods available for constructing the nonlinear function that is required in the implementation of the reference governors. This advantage is illustrated in a nonlinear control problem where off-line, computer-based simulation is the basis for constructing the nonlinear function.

The interception of an ICBM at low altitude and in a short time requires hyperbolic speeds. At the acquisition time t0, if updated information about the trajectory of the target dictates a velocity correction for the interception, then it is of interest to assess the potential for interception. The reachable surface is defined as the boundary of the set of all attainable points at a given time t, for a fuel potential, conveniently expressed in terms of the Δv available. Properties of this surface are derived and its mathematical characterization is obtained. As an application of the concept, a necessary condition for a successful interception of a target given in terms of a capture function is explicitly derived.

The purpose of this study is to assess whether a stage-based program of brief physician-delivered smoking-cessation advice changes smoking stages of readiness to quit smoking. First-year residents were trained to assess the stage of their continuity care patients who smoke, using Prochaska and DiClemente's methods, and to deliver brief messages and handouts based on the stages of precontemplation, contemplation, and action. Concurrent with the training, we administered a survey to 252 smokers, before their physician encounter. Eighty-nine smokers saw trained residents (intervention group), and 163 saw untrained residents (usual care group). A follow-up survey was administered six months later. Seventy-four percent of the subjects completed the follow-up survey. After we controlled for baseline stage, the percentage of precontemplators was lower in the intervention group (25%) than in the usual care group (36%) (P < .05, log-linear model). In the intervention group, 50% of the subjects had positive stage shifts versus 40% in the usual care group (P = .2). Subjects in the intervention group moved ahead a mean of 0.63 stage per subject, whereas subjects in the usual care group moved ahead 0.34 stage per subject (P < .05). The self-reported cessation rate was 15.5% and did not differ between the two groups. We conclude that our stage-specific brief advice program enhances short-term movement through the stages-of-change of smoking cessation. Measurement of this movement may be an important intermediary in evaluating small clinical trials of brief advice. Our findings indicate potential benefits of a staged approach for both clinicians and their patients.

The paper reviews, in a simplified form, recent research [8] concerning the role of first order necessary conditions in a general optimal periodic control problem (OPC). Three notions of optimality are considered: solutions of OPC; solutions of OPC which are steady-state (constant); solutions of OSS, a steady-state optimization problem subsumed in OPC. The three types of optima and the corresponding necessary conditions are studied by introducing a theory of solution sets. This puts earlier research into a comprehensive framework and establishes certain limits to what can be proved. A principal topic is tests for proper (time-dependent control is better than steady-state control). Some sufficient conditions for global optima of OPC are given and related to the necessary conditions. These results are new and generate an interesting class of OPC problems which are not proper.

It is shown that time-dependent periodic control can improve the fuel economy of vehicles in cruise. The time-dependent controls considered are relaxed steady-state (RSS) control, quasi-steady-state (QSS) control and quasi-relaxed steady-state (QRSS) control. Examples are given which show that QRSS control may give better performance than either RSS or QSS control. Properties of optimal cost functions, dependent on the minimum required average speed, are derived. The possibility or impossibility of improved performance through the use of QRSS, QSS and RSS control is investigated in terms of assumptions on the vehicle drag and fuel-consumption functions.

This paper describes experiments to test the action of ionizing radiation on the development of Australorbis glabratus eggs. It was demonstrated that radiation effects on the development of the eggs range from delay in embryonic development to death of embryos. The sensitivity to acute radiation is dependent upon the stage of development of eggs at exposure. The period of maximum sensitivity coincides with the morula, blastula, and gastrula stages. The slow development of eggs exposed to sublethal radiation doses suggests that recovery from radiation damage may occur during the delayed period of embryonic differentiation.

The toxicity of dimethyl sulfoxide (DMSO) to mice was measured by giving ip doses in concentrations of 25, 50, 75, or 100%. It was found that the LD50 increased somewhat as the concentration decreased, but the increase was significant only at the interval between 50 and 25%. The LD50 values found for the above four concentrations were 15.4, 13.3, 11.9, and 10.9 g/kg, respectively.

We describe the management of a patient with a Staphylococcus epidermidis infection of an Ommaya reservoir that was being used for the treatment of carcinomatous meningitis. Intravenous vancomycin failed to eradicate the organism. We treated our patient successfully with parenteral antibiotics and local instillation of vancomycin (25 μg/ml) without removing the reservoir. The patient tolerated the intraventricular vancomycin well. We recommend this approach in the treatment of infected Ommaya reservoirs in patients who have diseases with extremely poor prognoses and who wish to be discharged from the hospital early.