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We formulate an optimal control problem for hybrid systems with inputs and propose conditions for the design of state-feedback laws solving the optimal control problem. The optimal control problem has the flavor of an infinite horizon problem, but it also allows solutions to have a bounded domain of definition, which is possible in hybrid systems with deadlocks. Design conditions for optimal feedback laws are obtained by relating a quite general hybrid cost functional to a Lyapunov like function. These conditions guarantee closed-loop optimality and are given by constrained steady-state-like Hamilton-Jacobi-Bellman-type equations. Applications and examples of the proposed results are presented.

This paper deals with the problem of estimating the state of a nonlinear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error whenever a new measurement is available. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve exponential convergence with a given decay rate of the estimation error. Robustness with respect to external perturbations and L2-external stability from plant perturbations to a given performance output are considered. Computationally efficient algorithms based on the solution to linear matrix inequalities are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in an example.

Cost evaluation problems for hybrid inclusions are studied. Sufficient conditions, in the form of Lyapunov-like inequalities, are provided to derive an upper bound on the cost associated with the solution to a hybrid inclusion with respect to a hybrid cost functional. Under additional sufficient conditions, we determine the cost exactly without computing solutions. Constructive results are proposed to solve cost evaluation problems in some relevant applications. Numerical examples are presented.

Regional stability analysis of linear systems with multi-rate samplers and actuator saturation is studied. A hybrid controller is used to perform a fusion of measurements sampled at different times. In between sampling events, the controller behaves as a copy of the plant. When a new measurement is available, the controller state undergoes a jump. The resulting system is analyzed in a hybrid system framework. Sufficient conditions in the form of matrix inequalities are given to determine estimates of the basin of attraction of the closed-loop system. Finally, the effectiveness of the proposed methodology is shown in an example.

State-feedback optimal control and cost evaluation problems for constrained difference inclusions are considered. Sufficient conditions, in the form of Lyapunov-like inequalities, are provided to derive an upper bound on the cost associated with the solution to a constrained difference inclusion with respect to a given cost functional. Under additional sufficient conditions, we determine the cost exactly without computing solutions. The proposed approach is extended to study an optimal control problem for discrete-time systems with constraints. In this setting, sufficient conditions for closed-loop optimality are given in terms of a constrained steady-state-like Hamilton-Jacobi-Bellman equation. Applications and examples of the proposed results are presented.

Background and objectivesMultiple processes have been identified as potential contributors to chronic pain, with increasing evidence illustrating an association with aberrant levels of neuroimmune mediators. The primary objectives of the present study were to examine central nervous system cytokines, chemokines, and growth factors present in a chronic pain population and to explore patterns of the same mediator molecules over time. Secondary objectives explored the relationship of central and peripheral neuroimmune mediators while examining the levels of anxiety, depression, sleep quality, and perception of pain associated with the chronic pain patient experience.MethodsCerebrospinal fluid (CSF) from a population of majority postlaminectomy syndrome patients (N = 8) was compared with control CSF samples (N = 30) to assess for significant differences in 10 cytokines, chemokines, and growth factors. The patient population was then followed over time, analyzing CSF, plasma, and psychobehavioral measures.ResultsThe present observational study is the first to demonstrate increased mean CSF levels of interleukin-8 (IL-8; P

This paper deals with robust minimum-time control of a class of asymptotically null-controllable with bounded input planar systems. A hybrid controller is proposed to robustly achieve global finite time stability of a set of points wherein the plant state is zero. The resulting controller provides time optimal response from initial conditions in a certain subset of the state space, and finite time convergence elsewhere. Finally, the effectiveness of the proposed methods is demonstrated in a numerical example.

This paper deals with the state estimation of linear time-invariant systems for which measurements of the output are available sporadically. To solve the considered problem, we provide an observer with jumps triggered by incoming measurements, which is studied in a hybrid systems framework. Specifically, the resulting system is written in estimation error coordinates and augmented with a timer variable that triggers the event of new measurements arriving. Then, the observer design is performed to achieve global exponential stability (GES) of a closed set including the points for which the state of the plant and its estimate coincide. Furthermore, a computationally tractable design procedure for the proposed observer is presented. Finally, the effectiveness of the proposed methods is demonstrated in two numerical examples.

This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error at each sampling time. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve global exponential stability of a set wherein the estimation error is equal to zero. Moreover, three computationally efficient procedures are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in two examples.

BackgroundMany studies have assessed the efficacy of radiofrequency ablation to denervate the facet joint as an interventional means of treating axial low-back pain. In these studies, varying procedural techniques were utilized to ablate the nerves that innervate the facet joints. To date, no comparison studies have been performed to suggest superiority of one technique or even compare the prevalence of side effects and complications.Materials and methodsA retrospective chart review was performed on patients who underwent a lumbar facet denervation procedure. Each patient's chart was analyzed for treatment technique (early versus advanced Australian), preprocedural visual numeric scale (VNS) score, postprocedural VNS score, duration of pain relief, and complications.ResultsPre- and postprocedural VNS scores and change in VNS score between the two groups showed no significant differences. Patient-reported benefit and duration of relief was greater in the advanced Australian technique group (P=0.012 and 0.022, respectively). The advanced Australian technique group demonstrated a significantly greater median duration of relief (4 months versus 1.5 months, P=0.022). Male sex and no pain-medication use at baseline were associated with decreased postablation VNS scores, while increasing age and higher preablation VNS scores were associated with increased postablation VNS scores. Despite increasing age being associated with increased postablation VNS scores, age and the advanced Australian technique were found to confer greater patient self-reported treatment benefit.ConclusionThe advanced Australian technique provides a significant benefit over the early Australian technique for the treatment of lumbar facet pain, both in magnitude and duration of pain relief.

We consider the problem of stabilizing a linear time-invariant system in the presence of sporadic output measurements and intermittent access to the plant input. The plant is equipped with a zero-order hold device which stores the value of the input between transmissions. We propose an observer-based controller composed consisting of a measurement-triggered observer which experiences jumps in its state whenever a new measure is available, a state-feedback control law computed from the estimated state, and a copy of the zero-order hold device feeding the plant, which jumps whenever the control input is transmitted to the plant. The closed-loop system is modeled as a hybrid system that includes two timers triggering the two different events. The resulting hybrid system is analyzed as the cascade of hybrid systems and its asymptotic stability properties are established through a separation principle. In addition, an efficient design procedure is presented and illustrated in an example.

BackgroundMyofascial pain syndrome is a regional condition of muscle pain and stiffness and is classically characterized by the presence of trigger points in affected musculature. Botulinum toxin type A (BoNT-A) has been shown to have antinociceptive properties and elicit sustained muscle relaxation, thereby possibly affording even greater relief than traditional strategies. Our goal was to determine whether direct injection of BoNT-A into painful muscle groups is effective for cervical and shoulder girdle myofascial pain.MethodsAn enriched protocol design was used, wherein 114 patients with cervical and shoulder girdle myofascial pain underwent injection of BoNT-A to determine their response to the drug. Fifty-four responders were then enrolled in a 12-week, randomized, double-blind, placebo-controlled trial. Pain scales and quality of life measures were assessed at baseline and at routine follow-up visits until completion of the study after 26 weeks.ResultsInjection of BoNT-A into painful muscle groups improved average visual numerical pain scores in subjects who received a second dose of BoNT-A compared to placebo (P = 0.019 [0.26, 2.78]). Subjects who received a second dose of BoNT-A had a reduced number of headaches per week (P = 0.04 [0.07, 4.55]). Brief Pain Inventory interference scores for general activity and sleep were improved (P = 0.046 [0.038, 3.700] and 0.02 [0.37, 4.33], respectively) in those who received a second dose of BoNT-A.ConclusionBoNT-A injected directly into painful muscle groups improves average pain scores and certain aspects of quality of life in patients experiencing severe cervical and shoulder girdle myofascial pain.

This paper deals with the estimation of the state of linear time invariant systems for which measurements of the output are available sporadically. An observer with jumps triggered by the arrival of such measurements is proposed and studied in a hybrid systems framework. The resulting system is written in estimation error coordinates and augmented with a timer variable that triggers the event of new measurements arriving. The design of the observer is performed to achieve uniform global asymptotic stability (UGAS) of a closed set including the points for which the state of the plant and its estimate coincide. Furthermore, a computationally tractable design procedure for the proposed observer is presented and illustrated in an example.

Background and objectives: This study attempts to assess the intensity and quality of pain and health-related quality of life in patients with sacroiliac syndrome and to compare those constructs to patients with lumbar radiculopathy. Methods: A retrospective review of patient records with the diagnosis of sacroiliac syndrome or lumbar radiculopathy was performed. Patients with sacroiliac syndrome were age and gender matched to patients with lumbar radiculopathy. Data from the McGill Pain Questionnaire, visual numerical pain scores, and SF-36 health-related quality of life measure (version 2) were compared between groups. Results: The age of patients with a traumatic etiology for sacroiliac syndrome was lower than those with previous back surgery and "idiopathic" etiologies (P < .02). Duration of pain in patients with "idiopathic" etiology was longer in comparison to those with previous back surgery (P < .005). No statistical difference occurred between patients with sacroiliac syndrome and lumbar radiculopathy with respect to McGill pain scores, visual numerical pain scores, and SF-36 health-related quality of life measure. Conclusions: The results of this study suggest the following: (1) no true difference exists in the health-related quality of life or pain scores/descriptors between patients with SI syndrome or lumbar radiculopathy, or (2) the presence of comorbid spinal conditions confounds the ability of the SF-36 to detect disparities in health-related quality of life among differing etiologies of low-back pain, despite the use of rigorous diagnostic criteria, and/or (3) other factors besides the diagnostic categories of low-back pain (e.g., functional capability, psychological stress) may be primary determinants of health-related quality of life. To our knowledge, no other study has attempted to use the SF-36 to detect differences in health-related quality of life among patients with different spinal diagnoses.