A Resource-Constrained Optimal Control Model for Crackdown on Illicit Drug Markets

In this paper we present a budget-constrained optimal control model aimed at finding the optimal enforcement profile for a street-level, illicit drug crackdown operation. The objective is defined as minimizing the number of dealers dealing at the end of the crackdown operation, using this as a surrogate measure of residual criminal activity. Analytical results show that optimal enforcement policy will invariably use the budget resources completely. Numerical analysis using realistic estimates of parameters shows that crackdowns normally lead to significant results within a matter of a week, and if they do not, it is likely that they will be offering very limited success even if pursued for a much longer duration. We also show that a ramp-up enforcement policy will be most effective in collapsing a drug market if the drug dealers are risk-seeking, and the policy of using maximum enforcement as early as possible is usually optimal in the case when the dealers are risk averse or risk neutral. The work then goes on to argue that the underlying model has some general characteristics that are both reasonable and intuitive, allowing possible applications in focussed, local enforcement operations on other similar illegal activities.crackdown enforcement;illicit drug markets;optimal control

Risk Aversion in Finite Markov Decision Processes Using Total Cost Criteria and Average Value at Risk

In this paper we present an algorithm to compute risk averse policies in Markov Decision Processes (MDP) when the total cost criterion is used together with the average value at risk (AVaR) metric. Risk averse policies are needed when large deviations from the expected behavior may have detrimental effects, and conventional MDP algorithms usually ignore this aspect. We provide conditions for the structure of the underlying MDP ensuring that approximations for the exact problem can be derived and solved efficiently. Our findings are novel inasmuch as average value at risk has not previously been considered in association with the total cost criterion. Our method is demonstrated in a rapid deployment scenario, whereby a robot is tasked with the objective of reaching a target location within a temporal deadline where increased speed is associated with increased probability of failure. We demonstrate that the proposed algorithm not only produces a risk averse policy reducing the probability of exceeding the expected temporal deadline, but also provides the statistical distribution of costs, thus offering a valuable analysis tool

Risk-Averse Model Predictive Operation Control of Islanded Microgrids

In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors