Due to the nonconvex binary constraints of unit commitment (UC), no uniform linear pricing scheme supports the optimal dispatch. Convex hull pricing (CHP) and copositive duality pricing (CDP) both address this problem. CHP derives the price from the subgradient of the value function of the convex hull relaxation of UC. CDP refers to several different pricing mechanisms that can be constructed from the dual multipliers of the completely positive programming reformulation. In this work, we define a centralized convex hull price over the joint feasible set of UC and prove that, under non-degeneracy, it coincides with the marginal copositive duality price. Numerical experiments on the Scarf example validate this equivalence and quantify the pricing gap introduced by the semidefinite restriction.
We introduce an open-source library for machine-checked control theory in the interactive proof assistant Lean to lay foundations for the verification of cyber-physical systems. To this end, as representative theorems, we present formalizations of Lyapunov stability theory and th…
Digital twins are often used to predict how a system would respond to an intervention. In systems with feedback, a twin must reproduce an equilibrium counterfactual, and a twin developed in one domain may fail after mechanisms change. We study when these predictions can be valida…
In this paper, we study the control co-design (CCD) synthesis problem for a class of systems with parabolic partial differential equation (PDE) dynamics. We first derive a sufficient stability condition for the PDE. By spatially discretizing the PDE and using the sufficient stabi…
This paper presents a method for computing inner polytopic approximations of admissible sets for continuous-time linear control systems subject to affine state constraints. Building upon barrier theory and the explicit solution of linear systems, a structured sampling procedure i…
Promoting cooperative behaviour amongst decision makers has key implications for the long term sustainability of social systems. Incentives can promote cooperation in situations where defection is more favourable. Previous research has identified optimal decentralised incentives…
Motivated by stochastic model predictive control applications, we present a semi-algebraic approach to constraint tightening for chance-constrained systems with unbounded additive disturbances and saturated inputs. The saturated error dynamics are handled via their exact piecewis…