Dimensional properties of optimal and sub-optimal nonlinear control systems

BackgroundThe real-world application of STRIDE-II treatment targets to identify whether disease control is optimal in Crohn’s disease (CD) and ulcerative colitis (UC) is not well known.AimsThis study aimed to estimate proportions of patients with suboptimally controlled CD and UC in real-world Canadian healthcare settings and the impact on quality of life (QoL).MethodsThe noninterventional, multicenter, observational IBD-PODCAST Canada study comprised a single study visit involving routine assessments, patient- and clinician-completed questionnaires, and a retrospective chart review. Primary outcomes were proportions of patients with STRIDE-II-based red flags indicative of suboptimal disease control and mean ± standard deviation Short Inflammatory Bowel Disease Questionnaire (SIBDQ) scores. Secondary outcomes included proportions of patients and clinicians subjectively reporting suboptimal control.ResultsAmong 163 enrolled patients from 10 sites, 45/87 patients with CD (51.7%; 95% CI: 40.8%, 62.6%) and 33/76 patients with UC (43.3%; 95% CI: 32.1%, 55.3%) had suboptimal disease control based on STRIDE-II criteria. Suboptimal control was subjectively reported at lower proportions (patients: CD, 15.0%; UC, 18.6%; clinicians: CD, 19.5%; UC, 25.0%). Numerically lower SIBDQ scores were observed with suboptimal control (CD, 43.0 ± 10.8; UC, 42.5 ± 12.0) than with optimal control (CD, 58.2 ± 7.2; UC, 57.8 ± 6.6).ConclusionsApproximately 50% (CD) and 40% (UC) of patients from real-world Canadian practices had suboptimal disease control based on STRIDE-II criteria. Suboptimal control was underestimated by patients and clinicians and accompanied by reduced QoL, suggesting further efforts to implement STRIDE-II treat-to-target strategies are needed.

A new method for suboptimal feedback control of certain classes of distributed systems based on successive instantaneous minimization of the performance functional kernel is presented. This method is applicable to both linear and nonlinear systems.The Lyapunov functional approach is extended to distributed systems, yielding two new suboptimal feedback control techniques. Also, an application of multilevel bang‐bang control to the first‐order hyperbolic system is presented and generalized.Advantages and disadvantage ofthe suboptimal control techniques vis á vis open loop optimal control methods are listed, as well as comparative features of the suboptimal control methods.

Introduction:Optimal asthma control is a major aim of childhood asthma management. This study aimed to determine factors associated with suboptimal asthma control at the pediatric chest clinic of a resource-poor center.Methods:Over a 12-month study period, children aged 2–14 years with physician-diagnosed asthma attending the pediatric chest clinic of the Wesley Guild Hospital (WGH), Ilesa, Nigeria were consecutively recruited. Asthma control was assessed using childhood asthma control questionnaire. Partly and uncontrolled asthma was recorded as a suboptimal control. Relevant history and examinations findings were compared between children with good and suboptimal asthma control. Binary logistic regression analysis was used to determine the predictors of suboptimal asthma control.Results:A total of 106 children participated in the study with male:female ratio of 1.5:1, and majority (83.0%) had mild intermittent asthma. Suboptimal asthma control was observed in 19 (17.9%) of the children. Household smoke exposure, low socioeconomic class, unknown triggers, concomitant allergic rhinoconjunctivitis, and poor parental asthma knowledge, were significantly associated with suboptimal control (P < 0.05). Low socioeconomic class (odds ratio [OR] =6.231; 95% confidence interval [CI] =1.022–8.496; P = 0.005) and poor parental asthma knowledge (OR = 7.607; 95% CI = 1.011–10.481; P = 0.007) independently predict suboptimal control.Conclusion:Approximately, one in five asthmatic children attending the WGH pediatric chest clinic who participated in the study had suboptimal asthma control during the study. More comprehensive parental/child asthma education and provision of affordable asthma care services may help improve asthma control among the children.

The time-optimal control of a system of rigid bodies connected in series by single-degree-of-freedom joints is studied. The dynamical equations of the system are highly nonlinear, and a closed-form representation of the minimum-time feedback control is not possible. However, a suboptimal feedback control, which provides a close approximation to the optimal control, is developed. The suboptimal control is expressed in terms of switching curves for each of the system controls. These curves are obtained from the linearized equations of motion for the system. Approximations are made for the effects of gravity loads and angular velocity terms in the nonlinear equations of motion. Digital simulation is used to obtain a comparison of response times of the optimal and suboptimal controls. The speed of response of the suboptimal control is found to compare quite favorably with the response speed of the optimal control.

This paper is devoted to exposition of some results that are related to numerical synthesis of stochastic optimal control systems and also to numerical analysis of different approximate analytical synthesis methods. This trend of investigations was desoribed in detail in the paper

A class of adaptive control systems which are not only asymptotically stable but also optimal or sub-optimal to some meaningful cost functionals, are derived. By relating Lyapunov functions with solutions of Hamilton-Jacobi (-Isaacs) equations, three types of adaptive optimal control problems are solved (Type 1/spl sim/3), and the adaptive /spl Hscr//sup 2/ (Type 2) and /spl Hscr//sup /spl infin// (Type 1 and 3) optimal (sub-optimal) control systems are constructed for generalized adaptive control problems.

Synthesis of optimal stochastic control systems by the method of successive approximations: PMM vol. 43, no. 1. 1979, pp. 7–16

An iterative method for suboptimal control of linear time-delayed systems

Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept

This paper presents a now method of optimal digital PID feedback control for a linear multivariate system by using a, parameter optimization technique. The most difficult points for the design of optimal digital PID feedback control system by the modern control theory are : (1) the control structure of it is specified in advance, (2) unless all the state variables are fed back, the optimal control cannot be obtained by dynamic programming or the maximum principle. However, the optimal digital PID feedback gains are determined by using the parameter optimization technique in this paper. When there are some states which are not fed back in the control system, the optimal feedback gains depend on the initial states. First, the optimal solution is presented in the case where all the initial Btates are known. Next, it is extended to the case where the initial states are random variables and their statistical properties are known,

9 - Optimal and robust control system design

The development of on-ramp metering control strategies for a freeway can be aided by the well-developed theory of linear optimal control. However, an adequate model of an appropriate form must be available. Recently developed "aggregate variable" models appear to be best suited to this purpose. In these models the freeway is sectioned into lengths of about <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\frac{1}{2}</tex> mi and traffic is described in terms of the aggregate variables section speed, section density, and volume. The model is used to formulate a linear regulator problem with quadratic cost for the purpose of determining a feedback control rule which returns the freeway to nominal conditions after a disturbance. The solution of the regulator problem involves considerable computation difficulty when the order of the system is large. In a large class of applications the optimal control law has a local structure which can be exploited in a computationally efficient manner to yield a suboptimal control with little loss of system performance. A new technique, the augmentation method, is presented for constructing a suboptimal control from a set of optimal controls for low-order sub-systems. New results are presented which provide a rational and elegant measure for the additional cost associated with an arbitrary stabilizing suboptimal control. Additional results pertain especially to the augmentation procedure. The models and suboptimal control scheme are applied to a specific detailed design for an 8-mi segment of the San Diego Freeway in Los Angeles. Simulations are shown illustrating the effectiveness of such traffic-responsive controls in clearing up congestion due to traffic incidents.

Suboptimal feedback control of flow over a sphere

In this paper, the periodic event-triggered suboptimal control (PETSOC) method is developed for continuous-time linear systems. Different from event-triggered control, where the triggering condition is monitored continuously, the developed PETSOC method only verifies the triggering condition periodically at sampling instants, which further reduces computational resources. First, the control gain of the PETSOC is designed based on the algebraic Riccati equation. Subsequently, the periodic event-triggering condition is proposed for the suboptimal control method, which is only verified at sampling instants periodically. The sampling period is determined and analyzed based on the continuous form of the triggering condition. Moreover, the stability and the performance upper bound of the closed-loop system with the PETSOC are proved. Finally, the effectiveness of the developed PETSOC is validated through simulation on an unstable batch reactor.

A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal control systems allows us to formulate geometrically the necessary conditions given by a weak form of Pontryagin's maximum principle, provided that the differentiability with respect to controls is assumed and the space of controls is open. Furthermore, our method is also valid for implicit optimal control systems and, in particular, for the so-called descriptor systems (optimal control problems including both differential and algebraic equations).