All forms of cognition, whether natural or artificial, are subject to constraints of their computing architecture. This assumption forms the tenet of virtually all general theories of cognition, including those deriving from bounded optimality and bounded rationality. In this letter, we highlight an unresolved puzzle related to this premise: what are these constraints, and why are cognitive architectures subject to cognitive constraints in the first place? First, we lay out some pieces along the puzzle edge, such as computational (...) tradeoffs inherent to neural architectures that give rise to rational bounds of cognition. We then outline critical next steps for characterizing cognitive bounds, proposing that some of these bounds can be subject to modification by cognition and, as such, are part of what is being optimized when cognitive agents decide how to allocate cognitive resources. We conclude that these emerging views may contribute to a more holistic perspective on the nature of cognitive bounds, as well as their alteration subject to cognition. (shrink)

This paper proposes a novel adaptive dynamic programming approach to address the optimal consensus control problem for discrete-time multiagent systems. Compared with the traditional optimal control algorithms for MASs, the proposed algorithm is designed on the basis of the event-triggered scheme which can save the communication and computation resources. First, the consensus tracking problem is transferred into the input-state stable problem. Based on this, the event-triggered condition for each agent is designed and the event-triggered ADP is (...) presented. Second, neural networks are introduced to simplify the application of the proposed algorithm. Third, the stability analysis of the MASs under the event-triggered conditions is provided and the estimate errors of the neural networks’ weights are also proved to be ultimately uniformly bounded. Finally, the simulation results demonstrate the effectiveness of the event-triggered ADP consensus control method. (shrink)

We explore the idea that eye-movement strategies in reading are precisely adapted to the joint constraints of task structure, task payoff, and processing architecture. We present a model of saccadic control that separates a parametric control policy space from a parametric machine architecture, the latter based on a small set of assumptions derived from research on eye movements in reading (Engbert, Nuthmann, Richter, & Kliegl, 2005; Reichle, Warren, & McConnell, 2009). The eye-control model is embedded in a (...) decision architecture (a machine and policy space) that is capable of performing a simple linguistic task integrating information across saccades. Model predictions are derived by jointly optimizing the control of eye movements and task decisions under payoffs that quantitatively express different desired speed-accuracy trade-offs. The model yields distinct eye-movement predictions for the same task under different payoffs, including single-fixation durations, frequency effects, accuracy effects, and list position effects, and their modulation by task payoff. The predictions are compared to—and found to accord with—eye-movement data obtained from human participants performing the same task under the same payoffs, but they are found not to accord as well when the assumptions concerning payoff optimization and processing architecture are varied. These results extend work on rational analysis of oculomotor control and adaptation of reading strategy (Bicknell & Levy, ; McConkie, Rayner, & Wilson, 1973; Norris, 2009; Wotschack, 2009) by providing evidence for adaptation at low levels of saccadic control that is shaped by quantitatively varying task demands and the dynamics of processing architecture. (shrink)

A nonlinear differential equation model is proposed to study the dynamics of HIV/AIDS and its effects on workforce productivity. The disease-free equilibrium point of the model is shown to be locally asymptotically stable when the associated basic reproduction number $$\mathcal{{R}}_{0}$$ is less than unity. The model is also shown to exhibit multiple endemic states for some parameter values when $$\mathcal{{R}}_{0} 1$$. Global asymptotic stability of the disease-free equilibrium is guaranteed only when the fractions of the Susceptible subclass populations are within (...) some bounds. Optimal control analysis of the model revealed that the most cost effective strategy that should be adopted in the fight against HIV/AIDS spread within the workforce is one that seeks to prevent infections and the treatment of infected individuals. (shrink)

Some evolutionary psychologists contend that the best way to discover the functions of our present psychological systems is by appealing to the notion of functional mesh, that is, the assumed tight fit between a trait's design and the adaptive problem it is supposed to solve. In this paper, I argue that there exist theoretical considerations and empirical evidence that undermine this assumption of optimal design. Instead, I suggest that cognitive systems are constrained by what I call bounded functionality. (...) This proposal makes use of Jacob's (1977) notion of evolution as a bricoleur and Simon's (1981) idea that problems can have ``satisficing'' solutions. Functional mesh will thus be shown to neglect constraints that are necessary to explain the evolution of psychological mechanisms. (shrink)

Despite several research on HIV/aids, it is still incumbent to investigate more effective control measures to mitigate its infection level. Therefore, we introduce an HIV/aids-resistant model with behavior change and study its basic properties. In order to determine the most sensitive parameters that are responsible for disease transmission with respect to the basic reproduction number and those responsible for disease prevalence with respect to the endemic equilibrium, the sensitivity analysis was established and it was confirmed that the influx rate (...) of people into the infected population and total abstinence from all risk practices and endemic areas are some of the most sensitive parameters for disease spread and disease eradication, respectively. Furthermore, by considering controls u1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_1$$\end{document} denoting the government’s intervention in promoting and encouraging behavior change, u2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_2$$\end{document} representing intake of balanced nutritional supplementation, and u3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_3$$\end{document} connoting antiretroviral therapy (ART), an optimal control problem was developed and analyzed. Before the establishment of the necessary conditions of the optimal control using Pontryagin’s Maximum Principle, we proved the existence of the optimal control triplet (u1(t),u2(t),u3(t)∈Φ,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(u_1(t),u_2(t),u_3(t)\in \Phi,$$\end{document} where Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi$$\end{document} is the control set at time t,) which has been neglected by many researchers in recent years. Using the Runge–Kutta scheme, the optimal control problem was solved to understand the best combination of control strategies. Using the demographic and epidemiological data for South Africa on HIV/aids, a numerical simulation was carried out and results are presented on 3D surface plots. The obtained results suggested that the combination of all the considered control measures is the best method to ensure disease eradication. (shrink)

Malaria is a Plasmodium parasitic disease transmitted by infected female Anopheles mosquitoes. Climatic factors, such as temperature, humidity, rainfall, and wind, have significant effects on the incidence of most vector-borne diseases, including malaria. The mosquito behavior, life cycle, and overall fitness are affected by these climatic factors. This paper presents the results obtained from investigating the optimal control strategies for malaria in the presence of temperature variation using a temperature-dependent malaria model. The study further identified the temperature ranges (...) in four different geographical regions of sub-Saharan Africa, suitable for mosquitoes. The optimal control strategies in the temperature suitable ranges suggest, on average, a high usage of both larvicides and adulticides followed by a moderate usage of personal protection such as bednet. The average optimal bednet usage mimics the solution profile of the mosquitoes as the mosquitoes respond to changes in temperature. Following the results from the optimal control, this study also investigates using a temperature-dependent model with insecticide-sensitive and insecticide-resistant mosquitoes the impact of insecticide-resistant mosquitoes on disease burden when temperature varies. The results obtained indicate that optimal bednet usage on average is higher when insecticide-resistant mosquitoes are present. Besides, the average bednet usage increases as temperature increases to the optimal temperature suitable for mosquitoes, and it decreases after that, a pattern similar to earlier results involving insecticide-sensitive mosquitoes. Thus, personal protection, particularly the use of bednets, should be encouraged not only at low temperatures but particularly at high temperatures when individuals avoid the use of bednets. Furthermore, control and reduction of malaria may be possible even when mosquitoes develop resistance to insecticides. (shrink)

In this work, a co-infection model for human papillomavirus and Chlamydia trachomatis with cost-effectiveness optimal control analysis is developed and analyzed. The disease-free equilibrium of the co-infection model is shown not to be globally asymptotically stable, when the associated reproduction number is less unity. It is proven that the model undergoes the phenomenon of backward bifurcation when the associated reproduction number is less than unity. It is also shown that HPV re-infection induced the phenomenon of backward bifurcation. Numerical (...) simulations of the optimal control model showed that: focusing on HPV intervention strategy alone, in the absence of C. trachomatis control, leads to a positive population level impact on the total number of individuals singly infected with C. trachomatis, Concentrating on C. trachomatis intervention controls alone, in the absence of HPV intervention strategies, a positive population level impact is observed on the total number of individuals singly infected with HPV. Moreover, the strategy that combines and implements HPV and C. trachomatis prevention controls is the most cost-effective of all the control strategies in combating the co-infections of HPV and C. trachomatis. (shrink)

This paper suggests an online solution for the optimal tracking control of robotic systems based on a single critic neural network -based reinforcement learning method. To this end, we rewrite the robotic system model as a state-space form, which will facilitate the realization of optimal tracking control synthesis. To maintain the tracking response, a steady-state control is designed, and then an adaptive optimal tracking control is used to ensure that the tracking error can (...) achieve convergence in an optimal sense. To solve the obtained optimal control via the framework of adaptive dynamic programming, the command trajectory to be tracked and the modified tracking Hamilton-Jacobi-Bellman are all formulated. An online RL algorithm is the developed to address the HJB equation using a critic NN with online learning algorithm. Simulation results are given to verify the effectiveness of the proposed method. (shrink)

This article deals with optimal control applied to vaccination and treatment strategies for an SIRS epidemic model with logistic growth and delay. The delay is incorporated into the model in order to modeled the latent period or incubation period. The existence for the optimal control pair is also proved. Pontryagin’s maximum principle with delay is used to characterize these optimal controls. The optimality system is derived and then solved numerically using an algorithm based on the (...) forward and backward difference approximation. (shrink)

In order to avoid the motor damage caused by excessive temperature rise of armature winding of the walking motor during braking of high-voltage inspection robot in complexity microgrid networks, an unpowered downhill speed and energy recovery optimization control strategy is proposed based on temperature rise characteristics of the walking motor. Firstly, the thermal equivalent circuit model of the walking motor is established, and the mapping relationship between the armature winding temperature of the walking motor and ambient temperature is solved; (...) secondly, the influence of armature winding temperature on unpowered downhill speed and energy recovery control strategy of robot is analyzed; thirdly, according to the temperature of front and rear wheel walking motors and the temperature difference between them, the optimal control strategy of unpowered downhill speed and energy recovery of robot is put forward; fourthly, by adjusting the duty ratio u of the energy consumption speed control system and the front wheel feedback brake distribution factor λ, the temperature difference between the front and rear wheel walking motors is reduced. Through the experimental analysis on the simulated line, it is verified that the unpowered downhill speed and energy recovery optimization control method based on the temperature rise characteristics of the walking motor can effectively reduce the temperature difference between the front and rear wheels. (shrink)

This paper is concerned with the optimal output feedback control problem for networked control systems with Markovian packet losses. In this paper, the packet losses occur both between the sensor and controller and between the controller and actuator. Moreover, the packet loss channels are described with two-state Markov chains. Since the precise state information cannot be obtained, thus an optimal recursive estimator is designed. Furthermore, by adopting the dynamic programming approach, we derive the optimal output (...) feedback control, which is based on the solution to a given modified Riccati equation. The obtained results can be seen as an important implementation of the control theory for NCSs with unreliable communication channels. (shrink)

Humans regularly pursue activities characterized by dramatic success or failure outcomes where, critically, the chances of success depend on the time invested working toward it. How should people allocate time between suchmake‐or‐breakchallenges and safe alternatives, where rewards are more predictable (e.g., linear) functions of performance? We present a formal framework for studying time allocation between these two types of activities, and we explore optimal behavior in both one‐shot and dynamic versions of the problem. In the one‐shot version, we illustrate (...) striking discontinuities in the optimal time allocation policy as we gradually change the parameters of the decision‐making problem. In the dynamic version, we formulate the optimal strategy—defined by agiving‐upthreshold—which adaptively dictates when people should stop pursuing the make‐or‐break goal. We then show that this strategy is computationally inaccessible for humans, and we explore boundedly rational alternatives. We compare the performance of the optimal model against (a) a myopic giving‐up threshold that is easier to compute, and even simpler heuristic strategies that either (b) only decide whether or not to start pursuing the goal and never give up or (c) consider giving up at a fixed number of control points. Comparing strategies across environments, we investigate the cost and behavioral implications of sidestepping the computational burden of full rationality. (shrink)

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin’s maximum principle, and it is observed that full treatment effort should be given (...) while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point. (shrink)

It is known that, on average, people adapt their choice of memory strategy to the subjective utility of interaction. What is not known is whether an individual's choices are boundedly optimal. Two experiments are reported that test the hypothesis that an individual's decisions about the distribution of remembering between internal and external resources are boundedly optimal where optimality is defined relative to experience, cognitive constraints, and reward. The theory makes predictions that are tested against data, not fitted to (...) it. The experiments use a no-choice/choice utility learning paradigm where the no-choice phase is used to elicit a profile of each participant's performance across the strategy space and the choice phase is used to test predicted choices within this space. They show that the majority of individuals select strategies that are boundedly optimal. Further, individual differences in what people choose to do are successfully predicted by the analysis. Two issues are discussed: the performance of the minority of participants who did not find boundedly optimal adaptations, and the possibility that individuals anticipate what, with practice, will become a bounded optimal strategy, rather than what is boundedly optimal during training. (shrink)

An expected utility model of individual choice is formulated which allows the decision maker to specify his available actions in the form of controls (partial contingency plans) and to simultaneously choose goals and controls in end-mean pairs. It is shown that the Savage expected utility model, the Marschak- Radner team model, the Bayesian statistical decision model, and the standard optimal control model can be viewed as special cases of this goal-control expected utility model.

To improve the accuracy and timeliness of the trajectory tracking control of the driverless racing car during the race, this paper proposes a track tracking control method that integrates the rear wheel differential drive and the front wheel active steering based on optimal control theory and fuzzy logic method. The model of the lateral track tracking error of the racing car is established. The model is linearized and discretized, and the quadratic optimal steering control (...) problem is constructed. Taking advantage of the differential drive of dual-motor-driven racing car, the dual motors differential drive fuzzy controller is designed and integrated driving with active steering control. Simulation analysis and actual car verification show that this integrated control method can ensure that the car tracks different race tracks well and improve the track tracking control accuracy by nearly 30%. (shrink)

The aim of this study is to introduce a novel method to solve a class of two-dimensional fractional optimal control problems. Since there are some difficulties solving these problems using analytical methods, thus finding numerical methods to approximate their solution is a challenging topic. In this study, we use transcendental Bernstein series. In fact, for solving the problem, we generalize the Bernstein polynomials to a larger class of functions which can provide more accurate approximate solutions. The convergence theorem (...) is proved. Some examples are solved to demonstrate the validity and applicability of this technique. Comparing the results with other methods, we can find the efficiency and applicability of the scheme. (shrink)

Adaptive dynamic programming, which belongs to the field of computational intelligence, is a powerful tool to address optimal control problems. To overcome the bottleneck of solving Hamilton–Jacobi–Bellman equations, several state-of-the-art ADP approaches are reviewed in this paper. First, two model-based offline iterative ADP methods including policy iteration and value iteration are given, and their respective advantages and shortcomings are discussed in detail. Second, the multistep heuristic dynamic programming method is introduced, which avoids the requirement of initial admissible (...) class='Hi'>control and achieves fast convergence. This method successfully utilizes the advantages of PI and VI and overcomes their drawbacks at the same time. Finally, the discrete-time optimal control strategy is tested on a power system. (shrink)

The two-wheeled self-balancing robot is based on the axletree and inverted pendulum. Its balancing problem requires a control action. To speed up the response of the robot and minimize the steady state error, in this article, a grey wolf optimizer method is proposed for TWSBR control based on state space feedback control technique. The controller stabilizes the balancing robot and minimizes the overshoot value of the system. The dynamic model of the system is derived based on Euler (...) formula and linearized to state space representation to enhance the control technique. Then, the GWO optimizes the state feedback controller parameters. Simulation results show that the system reaches the zero steady-state error with less than 2 ms, which proves the effectiveness of the proposed controller over the classical state feedback controller in terms of fast response, very small overall error, and minimum overshoot. (shrink)

Visual illusions provide a means of investigating the rules and principles through which approximate number representations are formed. Here, we investigated the developmental trajectory of an important numerical illusion – the connectedness illusion, wherein connecting pairs of items with thin lines reduces perceived number without altering continuous attributes of the collections. We found that children as young as 5 years of age showed susceptibility to the illusion and that the magnitude of the effect increased into adulthood. Moreover, individuals with greater (...) numerical acuity exhibited stronger connectedness illusions after controlling for age. Overall, these results suggest the approximate number system expects to enumerate over bounded wholes and doing so is a signature of its optimal functioning. (shrink)

Power provision is coming to be the most important constraint to data center development. The efficient management of power consumption according to the loads of the data center is urgent. As the load for every application hosted in every server node of the data center and corresponding Service Level Agreement requirements can be quite different, it is hard to deploy a power strategy at application. The asynchronies and abruptness characteristics of workload fluctuation make power management policymaking using periodic resource scheduling (...) method invalid. In this article, the design and implementation of the request–response distributed power management scheme is elaborated. Bound by linear time complexity, the method proposed integrates dynamic voltage/frequency scaling, power-on–power-off, and virtual machine migration mechanisms and dynamically optimizes the power consumption of a cloud data center. The significant advantage of the scheme is that it does not need synchronous scheduling between all SNs. Simulation results showed that the scheme could effectively decrease the power consumption of the data center, with a tiny reduction in performance as centralized control methods. (shrink)

In complex systems, agents often interact with others in two distinct types of interactions, pairwise interaction and group interaction. The Deffuant–Weisbuch model adopting pairwise interaction and the Hegselmann–Krause model adopting group interaction are the two most widely studied opinion dynamics. In this study, we propose a novel opinion dynamics by combining pairwise and group interactions for agents and study the effects of the combination on consensus in the population. In the model, we introduce a parameter α to control the (...) weights of the two interactions in the dynamics. Through numerical simulations, we find that there exists an optimal α, which can lead to a highest probability of complete consensus and minimum critical bounded confidence for the formation of consensus. Furthermore, we show the effects of α on opinion formation by presenting the observations for opinion clusters. Moreover, we check the robustness of the results on different network structures and find the promotion of opinion consensus by α not limited to a complete graph. (shrink)

This work is an initial step toward developing a cognitive theory of cyber deception. While widely studied, the psychology of deception has largely focused on physical cues of deception. Given that present‐day communication among humans is largely electronic, we focus on the cyber domain where physical cues are unavailable and for which there is less psychological research. To improve cyber defense, researchers have used signaling theory to extended algorithms developed for the optimal allocation of limited defense resources by using (...) deceptive signals to trick the human mind. However, the algorithms are designed to protect against adversaries that make perfectly rational decisions. In behavioral experiments using an abstract cybersecurity game (i.e., Insider Attack Game), we examined human decision‐making when paired against the defense algorithm. We developed an instance‐based learning (IBL) model of an attacker using the Adaptive Control of Thought‐Rational (ACT‐R) cognitive architecture to investigate how humans make decisions under deception in cyber‐attack scenarios. Our results show that the defense algorithm is more effective at reducing the probability of attack and protecting assets when using deceptive signaling, compared to no signaling, but is less effective than predicted against a perfectly rational adversary. Also, the IBL model replicates human attack decisions accurately. The IBL model shows how human decisions arise from experience, and how memory retrieval dynamics can give rise to cognitive biases, such as confirmation bias. The implications of these findings are discussed in the perspective of informing theories of deception and designing more effective signaling schemes that consider human bounded rationality. (shrink)

A long-standing problem in biology, economics, and social sciences is to understand the conditions required for the emergence and maintenance of cooperation in evolving populations. This paper investigates how to promote the evolution of cooperation in the Prisoner’s Dilemma game. Differing from previous approaches, we not only propose a tag-based control mechanism but also look at how the evolution of cooperation by TBC can be successfully promoted. The effect of TBC on the evolutionary process of cooperation shows that it (...) can both reduce the payoff of defectors and inhibit defection; although when the cooperation rate is high, TBC will also reduce the payoff of cooperators unless the identified rate of the TBC is large enough. An optimal timing control of switched replicator dynamics is designed to consider the control costs, the cooperation rate at terminal time, and the cooperator’s payoff. The results show that the switching control between an optimal identified rate control of the TBC and no TBC can properly not only maintain a high cooperation rate but also greatly enhance the payoff of the cooperators. Our results provide valuable insights for some clusters, for example, logistics parks and government, to regard the decision to promote cooperation. (shrink)

Current models of speech motor control rely on either trajectory-based control (DIVA, GEPPETO, ACT) or a dynamical systems approach based on feedback control (Task Dynamics, FACTS). While both approaches have provided insights into the speech motor system, it is difficult to connect these findings across models given the distinct theoretical and computational bases of the two approaches. We propose a new extension of the most widely used dynamical systems approach, Task Dynamics, that incorporates many of the strengths (...) of trajectory-based approaches, providing a way to bridge the theoretical divide between what have been two separate approaches to understanding speech motor control. The Task Dynamics (TD) model posits that speech gestures are governed by point attractor dynamics consistent with a critically damped harmonic oscillator. Kinematic trajectories associated with such gestures should therefore be consistent with a second-order dynamical system, possibly modified by blending with temporally overlapping gestures or altering oscillator parameters. This account of observed kinematics is powerful and theoretically appealing, but may be insufficient to account for deviations from predicted kinematics—i.e., changes produced in response to some external perturbations to the jaw, changes in control during acquisition and development, or effects of word/syllable frequency. Optimization, such as would be needed to minimize articulatory effort, is also incompatible with the current TD model, though the idea that the speech production systems economizes effort has a long history and, importantly, also plays a critical role in current theories of domain-general human motor control. To address these issues, we use Dynamic Movement Primitives (DMPs) to expand a dynamical systems framework for speech motor control to allow modification of kinematic trajectories by incorporating a simple, learnable forcing term into existing point attractor dynamics. We show that integration of DMPs with task-based point-attractor dynamics enhances the potential explanatory power of TD in a number of critical ways, including the ability to account for external forces in planning and optimizing both kinematic and dynamic movement costs. At the same time, this approach preserves the successes of Task Dynamics in handling multi-gesture planning and coordination. (shrink)

Security issue against different attacks is the core topic of cyberphysical systems. In this paper, optimal control theory, reinforcement learning, and neural networks are integrated to provide a brief overview of optimal robust control strategies for a benchmark power system. First, the benchmark power system models with actuator and sensor attacks are considered. Second, we investigate the optimal control issue for the nominal system and review the state-of-the-art RL methods along with the NN implementation. (...) Third, we propose several robust control strategies for different types of cyberphysical attacks via the optimal control design, and stability proofs are derived through Lyapunov theory. Furthermore, the stability analysis with the NN approximation error, which is rarely discussed in the previous works, is studied in this paper. Finally, two different simulation examples demonstrate the effectiveness of our proposed methods. (shrink)

Cancer chemotherapy has been the most common cancer treatment. However, it has side effects that kill both tumor cells and immune cells, which can ravage the patient’s immune system. Chemotherapy should be administered depending on the patient’s immunity as well as the level of cancer cells. Thus, we need to design an efficient treatment protocol. In this work, we study a feedback control problem of tumor-immune system to design an optimal chemotherapy strategy. For this, we first propose a (...) mathematical model of tumor-immune interactions and conduct stability analysis of two equilibria. Next, the feedback control is found by solving the Hamilton–Jacobi–Bellman equation. Here, we use an upwind finite-difference method for a numerical approximate solution of the HJB equation. Numerical simulations show that the feedback control can help determine the treatment protocol of chemotherapy for tumor and immune cells depending on the side effects. (shrink)

In the debate between simple inference heuristics and complex decision mechanisms, we take a position squarely in the middle. A decision making process that extends to both naturalistic and novel settings should extend beyond the confines of this debate; both simple heuristics and complex mechanisms are cognitive skills adapted to and appropriate for some circumstances but not for others. Rather than ask `Which skill is better?'' it is often more important to ask `When is a skill justified?'' The selection and (...) application of an appropriate cognitive skill for a particular problem has both costs and benefits, and therefore requires the resolution of a tradeoff. In revisiting satisficing, we observe that the essence of satisficing is tradeoff. Unlike heuristics, which derive their justification from empirical phenomena, and unlike optimal solutions, which derive their justification by an evaluation of alternatives, satisficing decision-making derives its justification by an evaluation of consequences. We formulate and present a satisficing decision paradigm that has its motivation in Herbert Simon''s work on bounded rationality. We characterize satisficing using a cost–benefit tradeoff, and generate a decision rule applicable to both designing intelligent machines as well as describing human behavior. (shrink)

The notion of optimality is often invoked informally in the literature on metacognitive control. We provide a precise formulation of the optimization problem and show that optimal time allocation strategies depend critically on certain characteristics of the learning environment, such as the extent of time pressure, and the nature of the uptake function. When the learning curve is concave, optimality requires that items at lower levels of initial competence be allocated greater time. On the other hand, with logistic (...) learning curves, optimal allocations vary with time availability in complex and surprising ways. Hence there are conditions under which optimal strategies will be relatively easy to uncover, and others in which suboptimal time allocation might be expected. The model can therefore be used to address the question of whether and when learners should be able to exercise good metacognitive control in practice. (shrink)