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Optimal control of continuoustime switched affine systems
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2006
"... This paper deals with optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length, and that the decision variables are the switching instants and the s ..."
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Cited by 26 (5 self)
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This paper deals with optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length, and that the decision variables are the switching instants and the sequence of operating modes. We present two different approaches for solving such an optimal control problem. The first approach iterates between a procedure that finds an optimal switching sequence of modes, and a procedure that finds the optimal switching instants. The second approach is inspired by dynamic programming and identifies the regions of the state space where an optimal mode switch should occur, therefore providing a state feedback control law.
Synthesis of statefeedback optimal controllers for continuous time switched linear systems
 In Proc. 41th IEEE Conf. on Decision and Control, Las Vegas
, 2002
"... The paper deals with the optimal control of switched piecewise linear autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length: the unknown switching times and the switching sequence are the o ..."
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Cited by 10 (4 self)
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The paper deals with the optimal control of switched piecewise linear autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length: the unknown switching times and the switching sequence are the optimization parameters. We also assume that a cost may be associated to each switch. The optimal control for this class of systems takes the form of a state feedback, i.e., it is possible to identify a set of regions of the state space such that an optimal switch should occur if and only if the present state belongs to one of them. We show how the tables containing these regions can be computed offline through a numerical procedure. 1
Optimal control of switching surfaces
 in 43rd IEEE Conference on Decision and Control
, 2004
"... Abstract — This paper studies the problem of optimal switching surface design for hybrid systems. In particular, a formula is derived for computing the gradient of a given integral performance cost with respect to the switching surface parameters. The formula reflects the hybrid nature of the system ..."
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Cited by 8 (1 self)
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Abstract — This paper studies the problem of optimal switching surface design for hybrid systems. In particular, a formula is derived for computing the gradient of a given integral performance cost with respect to the switching surface parameters. The formula reflects the hybrid nature of the system in that it is based on a costate variable having a discrete element and a continuous element. A numerical example with a gradient descent algorithm suggests the potential viability of the formula in optimization.
A Provably Convergent Algorithm for TransitionTime Optimization in Switched Systems
"... Abstract — This paper concerns a modesequencing and switchingtime optimization problem defined on autonomous switchedmode hybrid dynamical systems. The design parameter consists of two elements: (i) the sequence of dynamicresponse functions associated with the modes, and (ii) the duration of each ..."
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Cited by 4 (1 self)
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Abstract — This paper concerns a modesequencing and switchingtime optimization problem defined on autonomous switchedmode hybrid dynamical systems. The design parameter consists of two elements: (i) the sequence of dynamicresponse functions associated with the modes, and (ii) the duration of each mode. The sequencing element is a discrete parameter which may render the problem of computing the optimal schedule exponentially complex. Therefore we are not seeking a global minimum, but rather a local solution in a suitable sense. To this end we endow the parameter space with a local continuous structure which allows us to apply gradientdescent techniques. With this structure, the problem is cast in the form of a nonlinearprogramming problem defined on a sequence of nested Euclidean spaces with increasing dimensions. We characterize suboptimality in an appropriate sense, define a corresponding convergence criterion, and devise a provablyconvergent optimization algorithm.
Petri Nets and Manufacturing Systems: An ExamplesDriven Tour
"... There exists ample literature on Petri nets and its potential in the modelling, analysis, synthesis and implementation of systems in the manufacturing applications domain (see for example [54, 15, 18]; besides, in [66] an important bibliography is presented). This paper provides an examplesdriven p ..."
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Cited by 4 (0 self)
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There exists ample literature on Petri nets and its potential in the modelling, analysis, synthesis and implementation of systems in the manufacturing applications domain (see for example [54, 15, 18]; besides, in [66] an important bibliography is presented). This paper provides an examplesdriven perspective. Nevertheless, not only complete examples from the application domain are considered. Manufacturing systems are frequently large systems, and conceptual complexity often appears because of some particular "local" constructions. The examples considered in this selected tour try to introduce in a progressive way some applied concepts and techniques. The starting point is an assembly cell, for which models concerning several phases of the design lifecycle are presented. Afterwards, some pull control and kanban management strategies are modelled. Then, two coloured models of production lines are presented. After that, a manufacturing system with two cells is modelled, and the diculty of the practical analysis is shown. For very populated manufacturing systems or systems with high cadence, relaxation of discrete event models leads to hybrid and continuous ap proximations, an example of which will be shortly introduced.
Sub optimal control of switched nonlinear systems under location and switching constraints,” IFAC World Congress
, 2005
"... Abstract: This paper considers an optimal control problem for switched nonlinear systems. The objective is to minimize an associated cost functional, by ¯nding an appropriate continuous control input and locations switching strategy. We propose an extension of an algorithm based on strong variations ..."
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Abstract: This paper considers an optimal control problem for switched nonlinear systems. The objective is to minimize an associated cost functional, by ¯nding an appropriate continuous control input and locations switching strategy. We propose an extension of an algorithm based on strong variations to handle constraints on both locations and switching instants. Numerical experiments testify the viability and the tractability of such a scheme.
Quantized optimal control of discretetime systems
"... In this paper we consider a quantized discretetime linear quadratic regulator (DLQR) problem, namely a DLQR problem where the input u may only take values in a given finite set U. Based on our previous results on the optimal control of hybrid systems we show that the optimal control law for the qua ..."
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In this paper we consider a quantized discretetime linear quadratic regulator (DLQR) problem, namely a DLQR problem where the input u may only take values in a given finite set U. Based on our previous results on the optimal control of hybrid systems we show that the optimal control law for the quantized DLQR problem takes the form of a feedback control law, that can be obtained from a partition of the state space C, computed offline. The numerical simulations carried out enabled us to observe a particular structure of C, related to the solution of the nonquantized DLQR problem. The lines of our future research in this topic are described in details in the last section, devoted to conclusions and future work. 1