A hierarchical time-splitting approach for solving finite-time optimal control problems

We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the prediction horizon. Each subproblem is solved in parallel and further split into three by separating the objective from the equality and inequality constraints respectively, such that an analytic solution can be achieved for each subproblem. The proposed solution approach leads to a nested decomposition scheme, which is highly parallelizable. We present a numerical comparison with standard state-of-the-art solvers, and provide analytic solutions to several elements of the algorithm, which enhances its applicability in fast large-scale applications

Distributed LQR Design for Dynamically Decoupled Systems

We consider a set of identical decoupled dynamical systems and a control problem where the performance index couples the behavior of the systems. The coupling is described through a communication graph where each system is a node and the control action at each node is only function of its state and the states of its neighbors. A distributed control design method is presented which requires the solution of a single LQR problem. The size of the LQR problem is equal to the maximum vertex degree of the communication graph plus one. The design procedure proposed in this paper illustrates how stability of the large-scale system is related to the robustness of local controllers and the spectrum of a matrix representing the sparsity pattern of the distributed controller design problem

A distributed accelerated gradient algorithm for distributed model predictive control of a hydro power valley

A distributed model predictive control (DMPC) approach based on distributed optimization is applied to the power reference tracking problem of a hydro power valley (HPV) system. The applied optimization algorithm is based on accelerated gradient methods and achieves a convergence rate of O(1/k^2), where k is the iteration number. Major challenges in the control of the HPV include a nonlinear and large-scale model, nonsmoothness in the power-production functions, and a globally coupled cost function that prevents distributed schemes to be applied directly. We propose a linearization and approximation approach that accommodates the proposed the DMPC framework and provides very similar performance compared to a centralized solution in simulations. The provided numerical studies also suggest that for the sparsely interconnected system at hand, the distributed algorithm we propose is faster than a centralized state-of-the-art solver such as CPLEX

Flight test of a receding horizon controller for autonomous UAV guidance.

This paper describes the receding horizon controller (RHC) design process and demonstration scenarios which were designed to exercise and evaluate the primary functionalities of the control system. Simulation results of the key capabilities are shown and compared with recorded flight data for evaluation purposes

Robust model predictive control for an uncertain smart thermal grid

The focus of this paper is on modeling and control of Smart Thermal Grids (STGs) in which the uncertainties in the demand and/or supply are included. We solve the corresponding robust model predictive control (MPC) optimization problem using mixed-integer-linear programming techniques to provide a day-ahead prediction for the heat production in the grid. In an example, we compare the robust MPC approach with the robust optimal control approach, in which the day-ahead production plan is obtained by optimizing the objective function for entire day at once. There, we show that the robust MPC approach successfully keeps the supply-demand balance in the STG while satisfying the constraints of the production units in the presence of uncertainties in the heat demand. Moreover, we see that despite the longer computation time, the performance of the robust MPC controller is considerably better than the one of the robust optimal controller

Robust model predictive control for an uncertain smart thermal grid

The focus of this paper is on modeling and control of Smart Thermal Grids (STGs) in which the uncertainties in the demand and/or supply are included. We solve the corresponding robust model predictive control (MPC) optimization problem using mixed-integer-linear programming techniques to provide a day-ahead prediction for the heat production in the grid. In an example, we compare the robust MPC approach with the robust optimal control approach, in which the day-ahead production plan is obtained by optimizing the objective function for entire day at once. There, we show that the robust MPC approach successfully keeps the supply-demand balance in the STG while satisfying the constraints of the production units in the presence of uncertainties in the heat demand. Moreover, we see that despite the longer computation time, the performance of the robust MPC controller is considerably better than the one of the robust optimal controller

Az elméletileg elérhető legjobb irányítás algoritmusainak kutatása = Investigation of the theoretically reachable best control algorithms

Módszert dolgoztunk ki lineáris, állandó paraméterű folyamatok szabályozási köreiben a beavatkozó szervek és magának a folyamatnak a tulajdonságaiból adódó korlátozásoktól függő határ-optimális szabályozók tervezésére. Algoritmust fejlesztettünk ki a beavatkozó szerv amplitudó korlátozásától függő elérhető legjobb tervezési cél (referencia modell) meghatározására. Megadtuk a nominális és az előző módszerrel kapott optimális referencia modellektől függő optimális szabályozók algoritmusait, amelyek a realizálhatósági veszteséget minimalizálják. Az optimális szabályozókat stabilis folyamatok Youla parametrizált szabályozási köreire határoztuk meg. Az optimalitás kritériumaként a H2, Hinf és L2, Linf normákat alkalmaztuk. A realizálhatósági veszteség H2, L2 normák szerinti optimalitását a szabályozók - speciális Diofantoszi egyenletek alapján számolt - belső szűrőinek felhasználásával biztosítottuk. A realizálhatósági veszteség Hinf, Linf normák szerinti optimalitását a szabályozók - speciális Nevanlinna-Pick approximációs egyenletek alapján számolt - belső szűrőinek alkalmazásával biztosítottuk. A H2, Hinf normák alkalmazásával csak nem integráló optimális szabályozó nyerhető. Optimális integráló szabályozóhoz az eredeti normákat speciális ""energia"" illetve ""supremum"" normákká kellett kiegészíteni az L2, Linf normák egyidejű alkalmazásával és nem Dirac-delta alakú gerjesztés feltételezésével. Új iteratív módszert vezettünk be a modellezési veszteség optimalizálására is. | A new method was developed for design of the (reachable) best controllers for LPI processes when the activator has an amplitude constraint and the process has invariant properties. A procedure was suggested to compute the best (reachable) reference model for tracking and disturbance rejection. A new approach was introduced to minimize the realizability degradation part of the sensitivity function using nominal process models. This optimization uses Youla parametrized regulators for open-loop stable plants. H2, Hinf and L2, Linf norms are used in this procedure. The H2, L2 norm based optimization uses special Diophantine equation to calculate the optimal embedded filter in the regulators. The Hinf, Linf norm based optimization uses special Nevanlinna-Pick approximation to calculate the optimal imbedded filter in the regulators. The original norm formulation was used in a combined way forming general ''energy'' and ''supremum'' norms assuming higher order excitations than the Dirac-delta to ensure integrating optimal regulators, too. New iterative algorithm was developed to minimize the modeling degradation part of the sensitivity function

An iterative scheme for distributed model predictive control using Fenchel’s duality,

Abstract We present an iterative distributed version of Han's parallel method for convex optimization that can be used for distributed model predictive control (DMPC) of industrial processes described by dynamically coupled linear systems. The underlying decomposition technique relies on Fenchel's duality and allows subproblems to be solved using local communications only. We investigate two techniques aimed at improving the convergence rate of the iterative approach and illustrate the results using a numerical example. We conclude by discussing open issues of the proposed method and by providing an outlook on research in the field