Unconstrained receding-horizon control of nonlinear systems

It is well known that unconstrained infinite-horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. We show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapunov function. Roughly speaking, the terminal control Lyapunov function (CLF) should provide an (incremental) upper bound on the cost. In this fashion, important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers. The absence of constraints allows a significant speedup in computation. Furthermore, it is shown that in order to guarantee stability, it suffices to satisfy an improvement property, thereby relaxing the requirement that truly optimal trajectories be found. We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon (restricted, of course, to the infinite horizon domain). Moreover, it is easily seen that both CLF and infinite-horizon optimal control approaches are limiting cases of our receding horizon strategy. The key results are illustrated using a familiar example, the inverted pendulum, where significant improvements in guaranteed region of operation and cost are noted

Parental Psychological Control and Autonomy Granting: Distinctions and Associations with Child and Family Functioning

Objective:This study utilized an observational coding scheme to identify parenting behavior reflecting psychological control and autonomy granting, and examined relations between these parenting dimensions and indices of child and family functioning. Design: A community sample of 90 preadolescents (aged 10.5 to 12 years) and both of their parents engaged in a triadic interaction that was coded for parental psychological control and autonomy granting. Participants also completed measures of child adjustment, interparental conflict, and triangulation. Results: Factor analyses indicated that a two-factor model better fit the data than a one-factor model, suggesting that psychological control and autonomy granting are best conceptualized as independent but related constructs. Parental psychological control and autonomy granting exhibited some shared and some unique correlates with indices of child and family functioning. Hierarchical regressions revealed significant interactions between these dimensions, suggesting that the strength of some associations between parents\u27 use of psychological control and youth adjustment problems depends on the level of autonomy granting exhibited by the parent. Conclusions: By examining psychological control and autonomy granting simultaneously as unique constructs, this study identifies patterns of psychological control and autonomy granting that undermine youth adjustment. Findings inform targeted intervention efforts for families of preadolescent youth

Marketing and Data Science: Together the Future is Ours

The synergistic use of computer science and marketing science techniques offers the best avenue for knowledge development and improved applications. A broad area of complementarity between the typical focus in statistics and computer science and that in marketing offers great potential. The former fields tend to focus on pattern recognition, control and prediction. Many marketing analyses embrace these directions, but also contribute by modeling structure and exploring causal relationships. Marketing has successfully combined foci from management science with foci from psychology and economics. These fields complement each other because they enable a broad spectrum of scientific approaches. Combined, they provide both understanding and practical solutions to important and relevant managerial marketing problems, and marketing science is already very successful at obtaining unique insights from big data

Metrics Thermostat

The explosion of information and information technology has led many firms to evolve a dispersed product development process with people and organizations spread throughout the world. To coordinate such dispersed processes managers attempt to establish a culture that implicitly rewards product development teams based on their ability to perform against a set of strategic metrics such as customer satisfaction, time to market, defect reduction, or platform reuse. Many papers have focused on selecting the right metrics and establishing the culture. In this paper we focus on a practical method to fine-tune a firm's relative emphasis on the metrics that they have chosen. In particular, we seek to advise a firm whether to increase or decrease their emphasis on each metric such that the change in emphasis improves profits. Using a thermostat analogy we apply an adaptive control feedback mechanism in which we estimate the incremental improvements in priorities that will increase profits. Iterations of adaptive control seek to maximize profits even if the environment is changing. We demonstrate the metric thermostat’s use in an application to a firm with over $20 billion in revenue. In developing the metric thermostat we recognize that there are hundreds of detailed actions, such as the use of the house of quality and the use of robust design, among which the product development team must choose. We also recognize that they will act in their own best interests to choose the actions that maximize their own implicit rewards as determined by the metrics. Management need not observe or dictate these detailed actions, but rather control the process by establishing the culture that sets the implicit weights on the metrics. The thermostat works by changing those implicit weights. We define the problem, introduce the adaptive control mechanism, modify “agency” theory to deal with incremental changes about an operating point, and derive methods that are practical and robust in light of the data that firms have available. Our methods include statistical estimation and internal surveys. The mathematics identify the critical few parameters that need be determined and highlight how to estimate them. Both the measures and the estimation are illustrated in our initial application to a large officeequipment firm. The metrics thermostat suggests that this firm has about the right emphasis on timeto- market, but has overshot on platform reuse and has lost its focus on customer satisfaction. We describe how the firm reacted to the recommendations and changed its organization. We describe additional ongoing applications with the US Air Force, the US Navy, and a major automobile and truck manufacturer.This research was funded by the Center for Innovation in Product Development (CIPD) and the International Center for Research on the Management of Technology (ICRMOT), M.I.T

Metrics Thermostat

The explosion of information and information technology has led many firms to evolve a dispersed product development process with people and organizations spread throughout the world. To coordinate such dispersed processes managers attempt to establish a culture that implicitly rewards product development teams based on their ability to perform against a set of strategic metrics such as customer satisfaction, time to market, defect reduction, or platform reuse. Many papers have focused on selecting the right metrics and establishing the culture. In this paper we focus on a practical method to fine-tune a firm's relative emphasis on the metrics that they have chosen. In particular, we seek to advise a firm whether to increase or decrease their emphasis on each metric such that the change in emphasis improves profits. Using a thermostat analogy we apply an adaptive control feedback mechanism in which we estimate the incremental improvements in priorities that will increase profits. Iterations of adaptive control seek to maximize profits even if the environment is changing. We demonstrate the metric thermostat’s use in an application to a firm with over $20 billion in revenue. In developing the metric thermostat we recognize that there are hundreds of detailed actions, such as the use of the house of quality and the use of robust design, among which the product development team must choose. We also recognize that they will act in their own best interests to choose the actions that maximize their own implicit rewards as determined by the metrics. Management need not observe or dictate these detailed actions, but rather control the process by establishing the culture that sets the implicit weights on the metrics. The thermostat works by changing those implicit weights. We define the problem, introduce the adaptive control mechanism, modify “agency” theory to deal with incremental changes about an operating point, and derive methods that are practical and robust in light of the data that firms have available. Our methods include statistical estimation and internal surveys. The mathematics identify the critical few parameters that need be determined and highlight how to estimate them. Both the measures and the estimation are illustrated in our initial application to a large officeequipment firm. The metrics thermostat suggests that this firm has about the right emphasis on timeto- market, but has overshot on platform reuse and has lost its focus on customer satisfaction. We describe how the firm reacted to the recommendations and changed its organization. We describe additional ongoing applications with the US Air Force, the US Navy, and a major automobile and truck manufacturer.This research was funded by the Center for Innovation in Product Development (CIPD) and the International Center for Research on the Management of Technology (ICRMOT), M.I.T

A marketing science perspective on recognition-based heuristics (and the fast-and-frugal paradigm)

Marketing science seeks to prescribe better marketing strategies (advertising, product development, pricing, etc.). To do so we rely on models of consumer decisions grounded in empirical observations. Field experience suggests that recognition-based heuristics help consumers to choose which brands to consider and purchase in frequently-purchased categories, but other heuristics are more relevant in durable-goods categories. Screening with recognition is a rational screening rule when advertising is a signal of product quality, when observing other consumers makes it easy to learn decision rules, and when firms react to engineering-design constraints by offering brands such that a high-level on one product feature implies a low level on another product feature. Experience with applications and field experiments suggests four fruitful research topics: deciding how to decide (endogeneity), learning decision rules by self-reflection, risk reduction, and the difference between utility functions and decision rules. These challenges also pose methodological cautions.Sloan School of Managemen

The Virtual Customer

Communication and information technologies are adding new capabilities for rapid and inexpensive customer input to all stages of the product development (PD) process. In this article we review six web-based methods of customer input as examples of the improved Internet capabilities of communication, conceptualization, and computation. For each method we give examples of user-interfaces, initial applications, and validity tests. We critique the applicability of the methods for use in the various stages of PD and discuss how they complement existing methods. For example, during the fuzzy front end of PD the information pump enables customers to interact with each other in a web-based game that provides incentives for truth-telling and thinking hard, thus providing new ways for customers to verbalize the product features that are important to them. Fast polyhedral adaptive conjoint estimation enables PD teams to screen larger numbers of product features inexpensively to identify and measure the importance of the most promising features for further development. Meanwhile, interactive web-based conjoint analysis interfaces are moving this proven set of methods to the web while exploiting new capabilities to present products, features, product use, and marketing elements in streaming multimedia representations. User design exploits the interactivity of the web to enable users to design their own virtual products thus enabling the PD team to understand complex feature interactions and enabling customers to learn their own preferences for new products. These methods can be valuable for identifying opportunities, improving the design and engineering of products, and testing ideas and concepts much earlier in the process when less time and money is at risk. As products move toward pretesting and testing, virtual concept testing on the web enables PD teams to test concepts without actually building the product. Further, by combining virtual concepts and the ability of customers to interact with one another in a stock-market-like game, securities trading of concepts provides a novel way to identify winning concepts. Prototypes of all six methods are available and have been tested with real products and real customers. These tests demonstrate reliability for web-based conjoint analysis, polyhedral methods, virtual concept testing, and stock-market-like trading; external validity for web-based conjoint analysis and polyhedral methods; and consistency for web-based conjoint analysis vs. user design. We report on these tests, commercial applications, and other evaluations.Center for Innovation in Product Development and the MIT Center for eBusines

On the stability of unconstrained receding horizon control with a general terminal cost

This paper deals with unconstrained receding horizon control of nonlinear systems with a general, non-negative terminal cost. Earlier results have indicated that when the terminal cost is a suitable local control Lyapunov function, the receding horizon scheme is stabilizing for any horizon length. In a recent paper, the authors show that there always exist a uniform horizon length which guarantees stability of the receding horizon scheme over any sub-level set of the finite horizon cost when the terminal cost is identically zero. In this paper, we extend this result to the case where the terminal cost is a general non-negative function