Panaceas, uncertainty, and the robust control framework in sustainability science

Abstract

A critical challenge faced by sustainability science is to develop strategies to cope with highly uncertain social and ecological dynamics. This article explores the use of the robust control framework toward this end. After briefly outlining the robust control framework, we apply it to the traditional Gordon-Schaefer fishery model to explore fundamental performance-robustness and robustness-vulnerability trade-offs in natural resource management. We find that the classic optimal control policy can be very sensitive to parametric uncertainty. By exploring a large class of alternative strategies, we show that there are no panaceas: even mild robustness properties are difficult to achieve, and increasing robustness to some parameters (e.g., biological parameters) results in decreased robustness with respect to others (e.g., economic parameters). On the basis of this example, we extract some broader themes for better management of resources under uncertainty and for sustainability science in general. Specifically, we focus attention on the importance of a continual learning process and the use of robust control to inform this process.

Fig. 1.

Examples of feedback system block diagrams. (A) The single loop depiction frequently used in resource management problems. (B) A hierarchical control system with an “outer loop” that sets a goal and an “inner loop” that achieves the goal.

Fig. 2.

Control and state trajectories for the renewable resource problem. (Upper) General optimal control and state trajectories for initial biomass x_o lower and higher than the long-run optimal x*_e (solid and dashed lines, respectively). (Lower) Examples of alternative control laws examined. The alternative control laws differ in that they switch earlier (A and B) or later (C–G) than the optimal and approach the long-run equilibrium smoothly rather than abruptly (compare C in lower right with the solid black curve in the upper right graphs).

Fig. 3.

Explanation of Pareto plots.

Fig. 4.

Sensitivity–performance trade-offs for four bioeconomic cases. IC, initial condition. See Fig. 3 for the interpretation of the graphs.

Fig. 5.

Social welfare vs. k_c for different controllers. (A) J vs. k_c for the optimal and two examples of region A and region E controllers. (B and C) J vs. k_c for region A and region E controllers with x_d = (1 + α)x*_e for α = 0, 0.2, 0.4, 0.6, 0.8, and 1.0, respectively.