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Register a new userToward a Scalable Upper Bound for a CVaR-LQ Problem
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We study a linear-quadratic, optimal control problem on a discrete, finite time horizon with distributional ambiguity, in which the cost is assessed via Conditional Value-at-Risk (CVaR). We take steps toward deriving a scalable dynamic programming approach to upper-bound the optimal value function for this problem. This dynamic program yields a novel, tunable risk-averse control policy, which we compare to existing state-of-the-art methods.
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We develop a risk-averse safety analysis method for stochastic systems on discrete infinite time horizons. Our method quantifies the notion of risk for a control system in terms of the severity of a harmful random outcome in a fraction of worst cases, whereas classical methods quantify risk in terms of probabilities. The theoretical arguments are based on the analysis of a value iteration algorithm on an augmented state space. We provide conditions to guarantee the existence of an optimal policy on this space. We illustrate the method numerically using an example from the domain of stormwater management.
The work aims to improve the existing fast load shedding algorithm for industrial power system to increase performance, reliability, and scalability for future expansions. The paper illustrates the development of a scalable algorithm to compute the shedding matrix, and the test performed on a model of the electric grid of an offshore platform. From this model it is possible to study the impact on the transients of various parameters, such as spinning reserve and delay time. Subsequently, the code is converted into Structured Text and implemented on an ABB PLC. The scalability of the load shedding algorithm is thus verified, confirming its performance with respect to the computation of the shedding matrix and the usefulness of the dynamic simulations during the design phase of the plant.
This paper presents a novel solution technique for scheduling multi-energy system (MES) in a commercial urban building to perform price-based demand response and reduce energy costs. The MES scheduling problem is formulated as a mixed integer nonlinear program (MINLP), a non-convex NPhard problem with uncertainties due to renewable generation and demand. A model predictive control approach is used to handle the uncertainties and price variations. This in-turn requires solving a time-coupled multi-time step MINLP during each time-epoch which is computationally intensive. This investigation proposes an approach called the Scenario-Based Branch-and-Bound (SB3), a light-weight solver to reduce the computational complexity. It combines the simplicity of convex programs with the ability of meta-heuristic techniques to handle complex nonlinear problems. The performance of the SB3 solver is validated in the Cleantech building, Singapore and the results demonstrate that the proposed algorithm reduces energy cost by about 17.26% and 22.46% as against solving a multi-time step heuristic optimization model.
This paper considers the vehicle routing problem of a fleet operator to serve a set of transportation requests with flexible time windows. That is, the operator presents discounted transportation costs to customers to exchange the time flexibility of pickup or delivery. A win-win routing schedule can be achieved via such a process. Different from previous research, we propose a novel bi-level optimization framework, to fully characterize the interaction and negotiation between the fleet operator and customers. In addition, by utilizing the property of strong duality, and the KKT optimality condition of customer optimization problem, the bi-level vehicle routing problem can be equivalently reformulated as a mixed integer nonlinear programming (MINLP) problem. Besides, an efficient algorithm combining the merits of Lagrangian dual decomposition method and Benders decomposition method, is devised to solve the resultant MINLP problem. Finally, extensive numerical experiments are conducted, which validates the effectiveness of proposed bi-level model on the operation cost saving, and the efficacy of proposed solution algorithm on computation speed.
Algorithms having uniform convergence with respect to their initial condition (i.e., with fixed-time stability) are receiving increasing attention for solving control and observer design problems under time constraints. However, we still lack a general methodology to design these algorithms for high-order perturbed systems when we additionally need to impose a user-defined upper-bound on their settling time, especially for systems with perturbations. Here, we fill this gap by introducing a methodology to redesign a class of asymptotically, finite- and fixed-time stable systems into non-autonomous fixed-time stable systems with a user-defined upper-bound on their settling time. Our methodology redesigns a system by adding time-varying gains. However, contrary to existing methods where the time-varying gains tend to infinity as the origin is reached, we provide sufficient conditions to maintain bounded gains. We illustrate our methodology by building fixed-time online differentiators with user-defined upper-bound on their settling time and bounded gains.
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