Continuity and Monotonicity of the MPC Value Function with respect to Sampling Time and Prediction Horizon

The digital implementation of model predictive control (MPC) is fundamentally governed by two design parameters; sampling time and prediction horizon. Knowledge of the properties of the value function with respect to the parameters can be used for developing optimisation tools to find optimal system designs. In particular, these properties are continuity and monotonicity. This paper presents analytical results to reveal the smoothness properties of the MPC value function in open- and closed-loop for constrained linear systems. Continuity of the value function and its differentiability for a given number of prediction steps are proven mathematically and confirmed with numerical results. Non-monotonicity is shown from the ensuing numerical investigation. It is shown that increasing sampling rate and/or prediction horizon does not always lead to an improved closedloop performance, particularly at faster sampling rates

Closeness of Solutions for Singularly Perturbed Systems via Averaging

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order O(\sqrt(\epsilon)), where \epsilon is the perturbation parameter

Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

AMENDING THE CORPORATE CRISIS RENEWAL MODEL: LESSONS FROM OIL AND PALM CRISES IN WEST AFRICA

This dissertation amends the Crisis Renewal Model of corporate rhetoric based on analyses of two multinational organizational crises in Nigeria and Cameroon. The Renewal model revises the dominant apologia model of corporate crisis rhetoric to focus on strengthening relationships with stakeholders following a crisis rather than solely on repairing or restoring reputation. Yet while the renewal model redresses the classic Aristotelian premises of apologia, the Nigerian and Cameroonian situations call for a significant reframing of rhetorical strategies in response to the colonialist legacies, cultural traditions, political volatilities, and socioeconomic particularities of these contexts. The research questions driving the dissertation are: What are the limitations of the Crisis Renewal model for multinationals operating in West African countries? How can this model be amended based on African communication principles? Data about the cases came from newspapers, company documents, and local and international NGO reports, and radio texts generated from LexisNexis. The data for Shell in Nigeria spans 1993-2016 while the data for Herakles Farms in Cameroon spans 2009-2016. The analyses found that both apologia and renewal were evident in corporate rhetoric produced by Shell and Herakles Farms; nonetheless, their respective crises damaged corporate reputation and stakeholder relationships. Drawing from lessons learned in these cases in West Africa, I turn to African communication concepts of communality and hybridity to rethink the Western premises of the Crisis Renewal model, particularly dimensions of ethical leadership, prospective vision, and organizational learning and build on Spivak’s arguments in “Can the Subaltern Speak?” and Kraidy’s notion of hybridity. I propose a concept I call responsive hybridity to modify the Crisis Renewal model. Responsive hybridity reframes renewal as a creative self-reflexive process producing hybrid forms, relationships, and practices

Applying the Rhetoric of Renewal Model in a Contemporary African Context: Lessons Learned from the Royal Dutch Shell Oil Crisis in Nigeria

This article applies the crisis renewal model to a multinational organizational crisis in Nigeria not only to analyze the crisis points of conflict in the multinational’s corporate rhetoric but also to examine how global relations; situated exigencies; and cultural, social, and economic tensions contextualize corporate communication strategies during crises. Rhetoric of renewal was evident as the multinational corporation responded to a prolonged crisis involving multiple state and local stakeholders. Although the renewal model itself redresses traditional Aristotelian crisis rhetoric models, the Nigerian situation calls for a significant reframing of rhetorical strategies accountable to the colonialist legacies, cultural traditions, political volatilities, and socioeconomic particularities of these contexts. Lessons learned and implications for organizational crisis rhetoric and practices in an age of increasing global interconnectedness are offered