Session: Optimization in Control - Algorithms and Applications
Chair: Arvind Raghunathan
Cluster: Interplay Between Continuous and Discrete Optimization
Talk 1: Optimization based control of networked systems
Speaker: Sridharakumar Narasimhan
Abstract: Process industries often use multiple units in series parallel combination, e.g., heat exchangers, pumps, compressors, fuel cells/solar cells etc. Optimal operation of such a network involves determining the appropriate loads of each equipment optimally by minimizing a cost function (e.g., power consumed, current drawn, heat loss) while satisfying safety constraints and meeting overall constraints on flow, power, etc. This results in a constrained optimization problem. Real time optimization or optimal control requires such a problem to solved in real time using measurements with uncertain plant models. In this work, we present a methodology for optimal control of a network of equipment using the structure of the optimal solution, e.g., . In many networked systems, optimality requires that the gradients of the cost function with respect to manipulated variables are equal. Hence, the optimal loads in the different branches of the network are manipulated such that the optimality conditions are satisfied. This is demonstrated using numerical simulations of a fuel cell stack.
Talk 2: Strong Disjunctive Cuts for MIP formulations of Optimal Control of Piecewise Affine Systems
Speaker: Prachi Shah
Abstract: Hybrid systems governed by piecewise affine dynamics are widely used in modern control applications, yet their optimal control remains a computational challenge due to weak relaxations of traditional mixed-integer programming (MIP) formulations. In this work, we present a novel methodology that introduces strong disjunctive cuts derived from the convex hull of a subproblem restricted to consecutive time intervals. Our approach tightens the linear relaxation of any choice of MIP formulation while keeping the cut-generation complexity independent of the overall time horizon. Comprehensive computational experiments on benchmark problems demonstrate that this strategy not only yields tighter bounds at the root node but also reduces the solution time of the MIP.
Talk 3: On global convergence of MPEC methods for Optimal Control of Hybrid Dynamical Systems
Speaker: Saif Kazi
Abstract: Optimal control of a Hybrid Dynamical System is a difficult problem because of unknown non differentiable points or switches in the solution of discontinuous ODEs. The optimal control problem for such hybrid dynamical system can be reformulated into a dynamic complementarity system (DCS) problem. Subsequently, the differential equation system is further reformulated using numerical discretization schemes such as Implicit Runge Kutta (IRK) or Orthogonal Collocation method for higher order accurate numerical solutions. Since the solutions are non-differentiable, a moving finite element with switch detection method is implemented to ensure higher order accuracy along with different reformulations for the non-smooth complementarity constraints such as relaxation based formulations or the l1-penalty term formulation. In this paper, we analyze the global convergence properties of such reformulations and introduce a mixed active-set based strategy to converge to real optimal solutions and escape spurious stationary points.
