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MultiParametric Toolbox 3.0
"... of algorithms for modeling, control, analysis, and deployment of constrained optimal controllers developed under Matlab. It features a powerful geometric library that extends the application of the toolbox beyond optimal control to various problems arising in computational geometry. The new version ..."
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of algorithms for modeling, control, analysis, and deployment of constrained optimal controllers developed under Matlab. It features a powerful geometric library that extends the application of the toolbox beyond optimal control to various problems arising in computational geometry. The new version 3.0 is a complete rewrite of the original toolbox with a more flexible structure that offers faster integration of new algorithms. The numerical side of the toolbox has been improved by adding interfaces to state of the art solvers and by incorporation of a new parametric solver that relies on solving linearcomplementarity problems. The toolbox provides algorithms for design and implementation of realtime model predictive controllers that have been extensively tested. I.
Fault Tolerant Control Allocation for a ThrusterControlled Floating Platform using Parametric Programming
"... Abstract — The task in control allocation is to determine how to generate a specified generalized force from a redundant set of control effectors where the associated actuator control inputs are constrained, and other physical and operational constraints and objective should be met. In this paper we ..."
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Abstract — The task in control allocation is to determine how to generate a specified generalized force from a redundant set of control effectors where the associated actuator control inputs are constrained, and other physical and operational constraints and objective should be met. In this paper we consider a convex approximation to a control allocation problem for a thrustercontrolled floating platform. The platform has eight rotatable azimuth thrusters and the high level controller is assumed to specify three generalized forces; surge, sway and yaw. The control allocation problem is formulated as a convex quadraticor linear program, where the constraints are dependent on the specified generalized force. The problem is solved explicitly by viewing the generalized forces as a vector of parameters and utilizing parametric programming techniques. For convex parametric quadratic programs (pQP) or parametric linear programs (pLP) with a linear parametrization of the constraints, there always exists a continuous piecewise affine (PWA) minimizer function. Consequently, the conventional online optimization can be replaced by a simple evaluation of a PWA function. Experimental results for a scale model of a platform are presented. It is shown how thruster failure scenarios can be handled by automatic reconfiguration of the control allocation, exploiting symmetry of the thruster configuration.
An OutputSensitive Algorithm for MultiParametric LCPs with Sufficient Matrices
"... Abstract. This paper considers the multiparametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise affine function that maps each feasible parameter to a ..."
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Abstract. This paper considers the multiparametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise affine function that maps each feasible parameter to a solution of the associated LCP in such a way that the function is affine over each cell of the decomposition. The algorithm is outputsensive in the sense that its time complexity is polynomial in the size of the input and linear in the size of the output, when the problem is nondegenerate. We give a lexicographic perturbation technique to resolve degeneracy as well. Unlike for the nonparametric case, the resolution turns out to be nontrivial, and in particular, it involves linear programming (LP) duality and multiobjective LP. 1.
Process Operations with Uncertainty and Integration Considerations
, 2010
"... There has been a lot of attention in recent years towards the application of mathematical modeling and optimization approaches for the solution of production planning and scheduling problems. This is mainly due to the changing economic environment which pushes for more efficient process operations. ..."
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There has been a lot of attention in recent years towards the application of mathematical modeling and optimization approaches for the solution of production planning and scheduling problems. This is mainly due to the changing economic environment which pushes for more efficient process operations. However, there are still a number of challenges that restrict the effective application of optimization for planning and scheduling problem especially in the process industry. First, decision making in process operations is frequently based on parameters of which the values are uncertain. A systematic treatment of those uncertainties (e.g., processing time variations, rush orders, failed batches, machine breakdowns, etc) is necessary to satisfy the customer demands, increase the efficiency of operations and improve the plant profitability. Moreover, the interactions between the different decisionmaking levels were often ignored in existing solution approaches, which leads to suboptimal and even infeasible solutions. Thus the integration of different decision making levels has been recognized by the research community as an imperative problem. In this work, systematic methods have been developed to address the above challenges. First, different methodologies are proposed to address the uncertainties in process scheduling problem: robust optimization based preventive scheduling strategy which aims at generating a robust preventive schedule to handle the