The author challenges the traditional approach to dealing with uncertainty in the management of such renewable resources as fish and wildlife. He argues that scientific understanding will come from the experience of management as an ongoing, adaptive, and experimental process, rather than through basic research or the development of ecological theory. 

The opening chapters review approaches to formulating management objectives as well as models for understanding how policy choices affect the attainment of these objectives. Subsequent chapters present various statistical methods for understanding the dynamics of uncertainty in managed fish and wildlife populations and for seeking optimum harvest policies in the face of uncertainty. The book concludes with a look at prospects for adaptive management of complex systems, emphasizing such human factors involved in decision making as risk aversion and conflicting objectives as well as biophysical factors. Throughout the text dynamic models and Bayesian statistical theory are used as tools for understanding the behavior of managed systems. These tools are illustrated with simple graphs and plots of data from representative cases. 

This text/reference will serve researchers, graduate students, and resource managers who formulate harvest policies and study the dynamics of harvest populations, as well as analysts (modelers, statisticians, and stock assessment experts) who are concerned with the practice of policy design.

http://www.swrcb.ca.gov/waterrights/water_issues/programs/bay_delta/docs/cmnt081712/dfg/cdfgwalters1986.pdf

Adaptive Management of Renewable Resources

First-order necessary conditions for quadratically optimal, steady-state,fixed-order dynamic compensation of a linear, time-invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form. In contrast to the pair of matrix Riccati equations for the full-order LQG case, the optimal steady-state fixed-order dynamic compensator is characterized by four matrix equations (two modified Riccati equations and two modified Lyapunov equations) coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains. The coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced-order controller case.

/pdf/the-optimal-projection-equations-for-fixed-order-dynamic-4k6rp57ler.pdf

The optimal projection equations for fixed-order dynamic compensation

A novel approach to tracking a maneuvering target is developed. This approach does not rely on a statistical description of the maneuver as a random process. Instead, the state model for the target is changed by introducing extra state components when a maneuver is detected. The maneuver, modeled as an acceleration, is estimated recursively. The performance of this estimator is shown to be superior to a recent algorithm presented by Chan et al. that handles the maneuver by estimating it as an unknown input. A significant departure from the current practice of comparison of algorithms is made: a recently introduced rigorous statistical methodology is used in the comparison of these estimators.

Variable Dimension Filter for Maneuvering Target Tracking

A sequential numerical algorithm is described which obtains gains minimizing a broad class of performance indexes, including the standard LQ case. The primary contribution is a proof that the algorithm converges to a local minimum under nonrestrictive assumptions. Numerical examples illustrate the theory. The second example demonstrates an important LQ design technique which permits the designer to prespecify the feedback structure, subject to the requirement of output feedback stabilizability.

Convergence of a numerical algorithm for calculating optimal output feedback gains

Iterative methods for finding the optimal constant feedback gains for parametric LQ problems, notably for optimal constant output feedback problems, are surveyed. The connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties. Especially, the descent Anderson-Moore method, Levine-Athans like methods, and the Newton method are considered. Convergence results are also included. The initialization problem and the output feedback stabilization problem are also discussed. Furthermore, it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric LQ problems as well, notably so-called robust parametric LQ problems.

Computational methods for parametric LQ problems--A survey

An algorithm is given for optimization of constant parameters in the controller for a time invariant linear system. The algorithm may be applied to linear controllers of arbitrary structure with any degree of decentralization in the distribution of information. Most important, it is not necessary to provide an initial controller of the specified structure which stabilizes the system. Rather, the structural constraints are initially relaxed to whatever degree necessary to obtain a stabilizing controller. The algorithm then gradually restores the constraints, converges to a local optimum solution, when one exists, and stabilizes any open loop system possessing a controllable unstable subspace. The necessary conditions while the optimum parameters must satisfy are developed for the arbitrarily constrained controller. The method of satisfying these necessary conditions involves use of a standard conjugate direction search together with a combined multiplier and penalty method for invoking the structural constraints. While attention is focused on the deterministic control problem, it is noted that systems with driving disturbances and measurement uncertainty may be handled with no significant modification of the algorithm. The result is a very practical tool for system design via parameter optimization.

Parameter optimization in linear systems with arbitrarily constrained controller structure

An adaptive dual control algorithm is presented for linear stochastic systems with constant but unknown parameters. The system parameters are assumed to belong to a finite set on which a prior probability distribution is available. The tool used to derive the algorithm is preposterior analysis: a probabilistic characterization of the future adaptation process allows the controller to take advantage of the dual effect. The resulting actively adaptive control called Model Adaptive Dual (MAD) control is compared to two passively adaptive control algorithms - the Heuristic Certainty Equivalence (HCE) and the Deshpande-Upadhyay-Lainiotis (DUL) model-weighted controllers. An analysis technique developed for the comparison of different controllers is used to show statistically significant improvement in the performance of the MAD algorithm over those of the HCE and DUL.

C. Wenk

Papers

Parameter optimization in linear systems with arbitrarily constrained controller structure

A multiple model adaptive dual control algorithm for stochastic systems with unknown parameters